Der Beitrag 10 out of 200: From classical ballet to modern mathematics – Dragana Radojičić makes sense of stock markets erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Dragana Radojičić, and I was born and raised in Serbia.**Where did you study and where are you currently based?**

I finished my B. Sc. in mathematics at the faculty of mathematics, University of Belgrade. I received my M. Sc. in mathematics at the TU Berlin, as a scholarship holder of the Berlin Mathematical School (BMS). Moreover, as a member of the BMS graduate program, I took many courses on three big Universities in Berlin (TU, HU, and FU).**What is your current position?**

I am currently a Ph.D. candidate at the Vienna University of Technology, where I also work as a teaching assistant at the Department for Financial and Actuarial Mathematics.

**What is the focus of your research? What is your research project?**

I work on mathematical modeling of the High-frequency trading, an important and challenging part of modern electronic markets. My project is to tackle this problem with two different approaches. The first one is a more theoretical point of view and is based on using adequate stochastic models to describe dynamics of the Limit Order Book (LOB). Moreover, I also employ machine learning techniques to get more insights from the market data and behavior of the market. My research is based on real market data from the past, more precisely on the high-frequency data set of the Nasdaq Stock Market (second-largest stock exchange in the world).**Why did you become a mathematician?**

Although I always have had so many different interests and hobbies, math was something that I have had continuously been very good at and what I like to do the most. I can’t say that the decision I made was easy, but my BSc studies at the Faculty of Mathematics, University of Belgrade made me realize I was right to choose mathematics as a carrier path. Moreover, I enjoy doing math while listening to music, I think music genuinely helps me to keep focus.**What are some of the fundamental challenges you have faced in your academic career?**

The main challenge that I have as a researcher is the uncertainty of success when dealing with challenging mathematical problems. But we have to keep working despite that.**What do you feel are the greatest pressures facing scientists today?**

An adequate understanding of the environment and the lack of funding in developing countries. **What are you doing besides research?**

When I was 4 I started dancing ballet, since then I have loved it and have danced it, but not professionally as I did before, now I train ballet as a hobby. Moreover, I try to spend my free time with my family and friends as much as possible. Apart from that, I enjoy reading, skiing, swimming, rollerblading and traveling**How did you hear about the HLF and why did you apply?**

A few years ago I heard a very nice experience from some friends of mine. Then, my sister Nina attended the Forum last year, and she came back thrilled and with extremely amazing impressions. Moreover, I received an email with the call for application, and without a second thought, I started my application procedure**What do you expect from this meeting?**

I expect to meet laureates and gain both knowledge and insights from their talks. Moreover, I am looking forward to meeting other young researchers from all over the world and exchange experiences with them. I expect to feel even more motivated to do my research after this meeting.**Which laureates present at the forum would you really like to talk to and what do you want to ask them?**

It is hard to make a choice among so many great scientists. First and foremost, I am extremely excited to meet Martin Hairer who is an expert in stochastic analysis, a field that I am very interested in. Moreover, I would like to discuss the future of the digital age with Vinton Gray Cerf, known as one of “the fathers of the internet”. Furthermore, I hope to talk to Yoshua Bengio regarding some newly introduced machine learning techniques that have recently attracted my attention.**Who were your most important mentors and what lessons did they pass on to you?**

Many people have influenced me during my education process and it is not possible for me to mention all the important mentors, so I will mention just two. My Ph.D. supervisor Thorsten Rheinländer has made a big influence on my research process and encouraged me to work on very interesting topics. Moreover, an important influence on my career path made my professor Antonis Papapanteleon whose course on financial mathematics I took during my master studies in Berlin and his perspective on this field has influenced my decision to pursue a Ph.D. in financial mathematics.**You used to have your own TV show in Serbia. How do you benefit as a young researcher from what you have learned during that time?**

I believe it helped me improve my social skills, which is very important in the scientific world. I think developing a good relationship between co-workers is crucial for doing qualitative work and exchanging ideas and knowledge. Moreover, I hope that I will even more benefit from this experience since, in the future, I would like to work on promoting math for a wider audience and tend to change the incorrect stereotypes about mathematicians.

Der Beitrag 10 out of 200: From classical ballet to modern mathematics – Dragana Radojičić makes sense of stock markets erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: From diagrams to formulas via computers – Ricardo Buring loves teaching math erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Ricardo Buring and I’m Dutch.**Where did you study and where are you currently based?**

I started studying mathematics at the University of Groningen in the Netherlands and got my bachelor’s and master’s degrees there. Now I’m living and working in Mainz, Germany. **What is your current position?**

I’m a math Ph.D. student at Johannes Gutenberg-Universität Mainz.**What is the focus of your research? What is your research project?**

I study the action of graph complexes on Poisson structures. On the one hand graphs (diagrams consisting of dots and lines) are discrete combinatorial objects (fig. 1).

On the other hand, a Poisson structure is a geometric object. It is defined on a manifold, whose points we interpret as states (e.g. of a physical system). Namely, a Poisson structure sends any number-valued function on the manifold to a vector field on that manifold. (A vector field is an assignment of a tangent vector/direction to every state.) The Poisson structure interprets the input function as the energy, and (by the vector field pointing in a direction) it gives the corresponding laws of motion on the manifold. (Consequently, it also dictates the time-evolution of the value of any number-valued function on the manifold.) For example, the motion of a spinning top can be described as a Poisson system, by considering the angular momentum (pseudo)vector \(L\) as a state in a natural coordinate system fixed to the body (fig. 2).

Here the green ellipsoid is a surface consisting of states with a given constant energy, and the blue sphere is a surface of constant (squared) magnitude. One can verify that the energy and (squared) magnitude are always constant in time (i.e. \(\frac{dH}{dt} = \{H,H\} = 0\) and \(\frac{dL^2}{dt} = \{L^2, H\} = 0\)), so the motion of any state must take place in the intersection of such level-surfaces. The exact motion of the endpoint of a vector \(L\) (drawn in red) is given by the time-evolution of its coordinates, in terms of the Poisson bracket with \(H\).

More generally, a Poisson structure is given in local coordinates on the manifold by an antisymmetric matrix of functions governed by the Jacobi partial differential equations. As above, it provides a mapping from energy to dynamics.

At first glance, Poisson structures and graphs live in totally different worlds, and they seem to have nothing to do with each other. The link between them (due to Kontsevich, who was inspired by Feynman diagrams from physics) is that one can build formulas – depending on a Poisson structure – out of graphs: vertices (containing functions) represent factors in a product, outgoing edges represent upper indices, incoming edges represent derivatives, and we sum over repeated indices (fig. 3).

This turns out to be a powerful idea. By force of our will, we can introduce relations on the space of sums of graphs which would hold on the level of formulas for every Poisson structure. Consequently, proving an identity on the level of graphs will prove it for all Poisson structures at the same time.

The main reason this graph formalism was invented – by Maxim Kontsevich, who received the Fields Medal in 1998 for this work among other things – is that these graphs can be used to solve the problem of formal deformation quantization on affine Poisson manifolds. This entails deforming the ordinary pointwise product of number-valued functions into a “quantum product” which is still associative but generally noncommutative: the commutator is a deformation of the Poisson bracket. Secondly, non-oriented graph cocycles yield “universal” deformations of Poisson structures (or symmetries of the Jacobi identity); their nature is still a mystery at the time of this answer. The underlying reason for these two theorems is the existence of certain \(L_\infty\)-morphisms, also due to Kontsevich. While much has been written about all this, parts of these theorems were not written very explicitly in the literature. My supervisor Arthemy Kiselev and I have been remedying this, presenting the results (with proofs) in an explicit and accessible way, and giving very concrete examples which were not available before. During my master’s thesis, I also started to implement the graph calculus in software, and I am still improving and extending that package. This enabled us to do some big calculations involving millions of graphs, has allowed for easy checking of results in the literature (which also revealed some errors), and yielded new results like an expression for the star-product up to order 4.

**Why did you become a mathematician?**

My interest in math came as a result of trying to solve the Project Euler programming problems in high school. These are problems that can be solved by writing an appropriate computer program. The catch was that the “naive” solution was always a suboptimal one; making use of mathematical insights would yield much more efficient solutions. This fascinated me and led me into the rabbit hole of mathematics. I still particularly enjoy constructive proofs and explicit algorithms. In my view, it is very beneficial and fun to be able to play with mathematical objects on a computer. In some sense, these objects really exist, in their own world inside the computer, which becomes a playground for the mathematician.

**What are some of the fundamental challenges you have faced in your academic career?**

I had a slightly rocky start. In high school, I had barely passing grades in math, and I had to retake the final math exam. In retrospect, my approach to studying was wrong. I was tricking myself into believing that I understood, by just reading and not doing, by following solution manuals instead of thinking for myself. Now I strongly believe that after reading or listening to a lecture, you must do the math yourself (and fail, identify your mistakes and gaps in your knowledge, and get help to fix them) and there is no way around that. By contrast, learning programming was almost all learning by doing, so I could have realized this earlier. After high school, I studied computer science at the Hanzehogeschool Groningen for one year, during which I also took an extra math course. At the end of the first year, I applied to the University of Groningen to study math. I had to take an entrance exam, which I failed the first time. Finally, I passed – with many thanks to the course I took at the Hanze – and I was accepted. My grades in the first semester were not great, largely due to leftovers of my high school mentality, which had evolved into “calculations are beneath me, I want to do proofs” (I now find this to be a special kind of stupid). Proofs are fantastic of course, but also algorithms are everywhere (even inside proofs), and the value of doing computations (to get a feeling of what you are working with, and to illustrate general results) cannot be overstated. Eventually, I adjusted and my grades improved. For my Ph.D. I moved to Germany and it was a challenge to pick up the German language, but I’m doing alright (supertoll) now.**What do you feel are the greatest pressures facing scientists today?**

The greatest tragedy of our lifetime is the extinction of blackboards. More seriously, I feel that there is much pressure to publish when the alternative is to perish. Also, in my limited experience, the amount of funding available for pure math research seems to be small. I understand that it will likely stay small in a relative sense (say, compared to funding for medical research) but I hope that it will increase in an absolute sense, as the number of math Ph.D. students is also increasing.

More tangentially, I have found many math papers (both old and new) containing very few examples or even no examples whatsoever. In my opinion, this puts pressure on the reader to provide his own examples, who may not even be able to do so. Examples clarify general theorems a great deal, and I feel they should not be withheld.**What are you doing besides research?**

The past few semesters I’ve taught exercise classes in discrete math and computer algebra, which I enjoyed a lot. My approach is to make a list of all possible mistakes which are revealed by correcting the homework and to discuss all of them in the tutorial, because you can learn a lot from your mistakes and the mistakes of others. I also tutor students in these subjects and a few more. Besides this, I enjoy answering questions online, on the Math StackExchange, MathOverflow, and on Ask SageMath (where I’ve answered 139 questions about the computer algebra system SageMath). This also helps to keep me sharp. It is said that teaching a subject is the best way to learn it, and this is a mini version of that. My two main hobbies are video game design and development and skateboarding. My side gig is software development, mainly web applications (the latest was a mobile web app for employees to record the hours that they worked). For leisure, I enjoy reading books (currently East of Eden by John Steinbeck), listening to music (mainly indie rock, e.g. Modest Mouse), going to the movies and watching many television series (The Sopranos is the best of all time).**How did you hear about the HLF and why did you apply?**

It came highly recommended by my friend Tamás Görbe, who attended the 6^{th} HLF. I applied because I didn’t want to miss the opportunity to attend this event, even if it seemed like a long shot to me. I was delighted to hear that I had been selected.**What do you expect from this meeting?**

I expect to meet interesting people. All the young researchers having applied for the HLF means we’ll have some ambition in common. I look forward to hearing about everyone’s work and their hobbies. As for the talks, it is always a pleasure to hear experts talk about their specialties.**Which laureates present at the forum would you really like to talk to and what do you want to ask them?**

I would like to talk with Leslie Lamport, who has interesting ideas about how proofs should be written. I’d also like to ask Gregory Margulis about his work on affine manifolds and Efim Zelmanov about his work on Lie algebras. Maybe most of all (talking-wise) I look forward to listening to everyone’s stories and anecdotes. It will also be great to meet some of the people whose work I encountered during my undergraduate studies (which shows how fundamental their work is), such as the pair behind the Diffie-Hellman key exchange, Dana Scott who (jointly with Michael O. Rabin) introduced the nondeterministic finite automaton, and Stephen Smale who introduced the horseshoe map (I co-wrote a report about it in the first year of my bachelor’s).**Who were your most important mentors and what lessons did they pass on to you?**

My most important mentors were my thesis advisors, who also taught some of my favorite courses. Arthemy Kiselev – my master’s thesis advisor and currently my Ph.D. thesis advisor – has taught me a lot about how to do research, how to approach mathematical problems, and about writing. The teaching style of Jaap Top – my bachelor’s thesis advisor – also had a big influence on me.**What are your preferred formats to communicate your research to others and why?**

I like to write articles with extensive examples, including sample code which the reader can run, preferably in some free software. I think this can help the reader a lot with understanding (it certainly helps me) and it makes the whole a lot livelier. I also like giving talks, preferably on a blackboard but possibly with some supporting slides showing pictures which would take a long time to draw live.

Der Beitrag 10 out of 200: From diagrams to formulas via computers – Ricardo Buring loves teaching math erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: The who’s who of the internet – Janelle Mason improves our cybersecurity erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Janelle Mason. I am from the United States of America.**Where did you study and where are you currently based?**

I studied and am currently studying at North Carolina Agricultural and Technical State University, in Greensboro, North Carolina, in the United States of America. Currently, I live in Greensboro, North Carolina.**What is your current position?**

My current position entails being a student, where I am a Ph.D. Candidate in Computer Science. I serve in the position of the lab manager for the Raven Computer Science Lab, a leader in the Computer Aided Forensic Reasoning and Evidence in Criminal Investigation (CAFRECI) research group, and a Delegate for North Carolina Agricultural and Technical State University. **What is the focus of your research? What is your research project?**

A fundamental social need that has grown in importance and difficulty as societies have grown in size is the need to identify people, and this need has become the central issue in Web security. Our research addresses the principled use of information as evidence for the identity of a human agent. The person might be of interest for several reasons including investigation of crime, including cybercrime, or, more generally, identification (where we determine who it is so we may treat them appropriately) or authentication (that someone is who they say they are, generally so we may grant them the privileges they are due). In developing a computational framework for identity, we collaborate with our criminal-justice colleagues as that is the discipline that has addressed identity for centuries. Semantic-Web standards are used to define concepts used in encoding identity cases. The information thus captured allows identity hypotheses to be ranked. For biometric-based identification, metadata on such things as the current setting and the machine-learning technique used allow us to discount and combine scores from the matching programs. The linguistic nature of identity, both the descriptive and the referential aspect, is taken seriously. Referentially, the Semantic Web’s IRIs provide global names for individuals perhaps known only by their role in a situation; investigation may reveal that two such IRIs actually denote the same individual. The resources used in our framework also allow common reasoning patterns regarding the identity to be automated. The principal benefit of this research is understanding the concepts involved in our framework. A specific benefit will be a Web-based tool we are developing for criminal-justice students. More generally, our framework could be helpful for anyone, such as law enforcement, seeking an answer to “who done it” or needing to identify or authenticate agents.**Why did you become a computer scientist?**

As a child, I enjoyed math, science, both playing and listening to music, completing puzzles, and playing sports. As I matriculated through school, my passion in these areas grew and flourished. In high school, I had a teacher who strongly encouraged me to pursue computer science because he could see my potential from a computer programming perspective. When I entered college, I wanted to choose a degree that would entail my passions and allow me to be creative.

**What are some of the fundamental challenges you have faced in your academic career?**

I always strive for perfection, meaning a 4.0 grade point average. I had to learn that sometimes you will not get an A in every course. My lessons learned have been as long as you worked hard, learned something from the course, and you are able to apply the information, that is what truly matters.

When I did not understand the information in a course, I would ask questions during and after class to my classmates, the professor, teacher assistants, etc. to gain clarity and to ensure I understood the content.**What do you feel are the greatest pressures facing scientists today?**

One pressure some scientists face from a research perspective is having good research ideas, but they lack the funding to fully support the research effort. This causes some scientists to become creative to produce prototypes and/or proof of concepts to bring attention to their research ideas.**What are you doing besides research?**

I enjoy mentoring and working with students. I also enjoy participating in physical activities such as doing CrossFit and swimming. I enjoy playing board and card games, ping pong, billiards, and bowling. Traveling, eating the local cuisine, and learning about the history of the destination I am visiting is something I am passionate about. I thoroughly enjoy going to a place of worship.**How did you hear about the HLF and why did you apply?**

I heard about the HLF through the Computer Science Department at North Carolina Agricultural and Technical State University via email. I decided to apply because I believe this is going to be an extraordinary opportunity to learn and grow from a research perspective as well as gain insights from all participants.**What do you expect from this meeting?**

I am interested in meeting other young researchers, learn about their research, and exchange academia experiences. I am hoping to further my knowledge with respect to computer science and to enhance my research interests.**Which laureates present at the forum would you really like to talk to and what do you want to ask them?**

It would be a phenomenal honor and privilege to meet Whitfield Diffie, Martin Hellman, Ivan Sutherland, and Raj Reddy. As Whitfield Diffie and Martin Hellman are the *inventors of asymmetric public-key cryptography. *I would ask them about their perspectives on encryption from the aspect of future technology and cybersecurity.* Ivan Sutherland, the pioneer of computer graphics and the inventor of Sketchpad. *I would ask him about his perspective regarding augmented reality and virtual reality. *Raj Reddy, the pioneer of design and construction of large scale artificial intelligence systems and technology. *I would inquire about his successful implementation of the “Million Book Project” and his perspective about how humans are embracing robots from a near and long term point of view.**Who were your most important mentors and what lessons did they pass on to you?**

All of my academic advisors and professors, including my Undergraduate, Masters, and Ph.D., as well as my professional development advisors – both during internships and my career have all served as mentors. Each in their unique way has inspired me to continue to think critically and analyze problems.

My family has served as important mentors in my life, my grandmothers and grandfathers, where they passed on the importance of being respectful, acquire your education, and to travel the world; my brother and sister (André and Rhonda, Olivia) stress how important it is to be an example because someone is always watching. Lastly, my parents, William and Jewel Mason, passed on the importance of acquiring my education and taught me to always trust in the Lord.**Besides your research, you are a passionate swimmer. Is there anything swimming and cybersecurity have in common?**

Swimming compares to cybersecurity from the perspective that both consist of a team event (i.e., a relay) and an individual event, such as an individual medley (IM) in swimming. In cybersecurity, there is an importance of being able to identify vulnerabilities and knowing how to use tools to detect and discover vulnerabilities. These are some examples of an individual event. From the team perspective, it can be seen as continuous monitoring, detecting, and educating employees within a company about cybersecurity. Swimming and cybersecurity entail both a physical and mental challenge. Through years of training and conditioning, along with exposure to assessing networks and computing devices, I have been able to increase and strengthen my skill set to handle and operate efficiently during intense situations, which is applicable and necessary in both swimming and cybersecurity.

Der Beitrag 10 out of 200: The who’s who of the internet – Janelle Mason improves our cybersecurity erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: Serving the people – Khac-Hoang Ngo improves our telecommunication erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Khac-Hoang Ngo. I am a Vietnamese citizen.**Where did you study and where are you currently based?**

I completed my B.E. program in Electronics and Telecommunications at Vietnam National University, Hanoi in 2014 with a short internship at the National University of Singapore in 2012. I then moved to France for a M.Sc. degree in Advanced Wireless Communication Systems at CentraleSupélec, which I received in 2016. After that, I stayed in France to do a Ph.D. in Wireless Communications. I am currently living in the southern suburbs of Paris.**What is your current position?**

I am a third-year Ph.D. student. I work at both CentraleSupélec, University of Paris-Saclay and Mathematical and Algorithmic Sciences Laboratory, Paris Research Center, Huawei Technologies France.**What is the focus of your research? What is your research project?**

My research has been focusing on information and communication theory. In particular, I am interested in fundamental limits of and physical layer algorithms for wireless communication networks.

To quote Claude E. Shannon, ‘*The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.*‘ In a common wireless communication model, the message-carrying signal is multiplied with a channel matrix and added with noise before reaching the receiver. The channel matrix contains the electromagnetic gains between the transmission antennas and the receiving antennas. In practice, these gains are random and vary due to the relative velocity of the transmitter, the receiver, and the possible reflectors. Thus the propagation channels fade over time and frequencies. Coping with this fading effect has been one of the main challenges in designing communication systems.

Conventionally, the receiver estimates the channel gains with the help of reference symbols and then uses the channel estimate to reconstruct the transmitted signal. This is called *coherent* communications. On the other hand, in my Ph.D. thesis entitled *Non-coherent Wireless Communications for Multi-User Multi-Antenna Systems*, we consider an alternative approach consisting in designing the data transmission and reception without resorting to the hypothesis that the instantaneous state of the channel is known or estimated. This can have an advantage over coherent communications when, for example, the channel gains change very rapidly and channel estimation becomes formidable or overconsumes the communication resources. This situation is present in high mobility networks.**Why did you become a computer scientist?**

I started growing curious about telecommunications since childhood when telephones emerged in my hometown. At that time, a family equipped with a fixed telephone served as a communication center for the neighborhood. It became even more interesting when mobile phones appeared. Harboring the question of how a telecommunication system works, I got engaged in mathematics and physics in school, which I thought would provide me the answer. Then I enrolled in a bachelor program in electronics and telecommunications in 2010. Back then, I just wished to become an engineer and work for a local telecommunication provider. Fortunately, my bachelor program encouraged students to learn the ropes of research and offered us a good condition to do so. I tried and became fascinated. I enjoyed stretching my mind through pondering a question and the excitement of learning or finding something new. Furthermore, I realized that I could contribute to the evolution of global communication systems through my research. This has been motivating me to pursue a Ph.D. degree and a long-term research career in this domain.**What are some of the fundamental challenges you have faced in your academic career?**

I would say that is mathematics. I work with wireless communication models in which the transmitted signal, the propagation channel, and the noise are all modeled as random processes and they are linked together by algebraic operations. Thus, studying a communication system requires a solid mathematical background including probability and statistics, algebra, and analysis. It most of the time boils down to mathematical problem-solving. I got stuck in a problem many times when it reached the boundary of my mathematical knowledge, but by working out the solution (with the help of my advisors), I extended that boundary.**What do you feel are the greatest pressures facing scientists today?**

I think that is the publish-or-perish pressure. Scientists are often obliged to publish quickly and continually to sustain and advance their career. This shortens the time they spend on research work, which may put incremental research over more long-term and impactful research, and put quantity over quality. Furthermore, scientists also face the pressure to have funding for their work. To get funded, scientists tend to go for hot topics and spend (a disproportionate amount of) time writing grants which nicely fit the selection criteria. This can prevent scientists from freely shaping their research and drive them away from their initial career plan.

In fact, it is not easy to decide on an appropriate motive for doing research in this money-driven world. I believe that the ultimate goal of technology research is not for the benefit of the industrial market, but to serve people and improve people’s lives. I adopted this view from Soichiro Honda, the founder of Honda Motor Company and the Honda Foundation. My favorite saying of his is *‘Whether it be learning or technology, everything in this world is nothing more than a mean to serve people. Maybe the most important thing of all is to have love for people.’***What are you doing besides research?**

In my leisure time, I practice sports. I run, swim, and play soccer. I am a big fan of Manchester United Football Club. Besides, I like listening to classical music and reading. I usually read on the train to/from work. My favorite author is Haruki Murakami because I find a bit of myself in each of his main characters. I also take French evening classes. **How did you hear about the HLF and why did you apply?**

My advisor, Dr. Maxime Guillaud, told me about the HLF and encouraged me to apply. I took a look at the program and got impressed by the opportunity that it offers the participants.

In 2015, I joined hands to organize a similar networking event for young engineers and scientists in Asia – the Honda Y-E-S Forum. It was a venue to discuss the issues in the region and the role that science and technology should fulfill in resolving them. During the preparation and organization of this forum, I met other young people from Japan, Vietnam, and other developing countries in Asia. We had fruitful discussions and exchanged ideas. I also had the opportunity to attend the Honda Prize Ceremonies and met the laureates. I admired them for the impact of their works on improving human life through technology. It was indeed a great honor and very inspiring to meet and talk to them. I found the HLF a similar source of inspiration, so I applied.**What do you expect from this meeting?**

I expect to meet, learn from and get inspired by great minds who made a high impact in the world through their research. I have looked into their profiles and was impressed by their contributions.

Furthermore, I desire to meet other young researchers to discuss, exchange ideas, and get inspired by them as well. I have seen the interviews of the past participants and got impressed by their enthusiasm and diverse backgrounds and perspectives. Some of them are also from developing countries who have a strong willingness to make a change in their country. There were also people with disabilities who keep pursuing their passion and want to encourage others of the same circumstance to do so. I wish to see people with great passion like them at the HLF this year.

Last but not least, I want to broaden my knowledge through the lectures at the HLF.

In general, I want to ask the laureates a question that I have been harboring: How to identify the important problems and come up with the “big idea” without being stuck in incremental research that has only limited impact?

In particular, I am looking forward to attending a lecture of Prof. Joseph Sifakis on system design in order to gain insights into the problem of communication network design.**Who were your most important mentors and what lessons did they pass on to you?**

All my advisors since my bachelor have been my important mentors in research and self-development. I treasure every lesson I got from them. In particular, my bachelor advisor, Prof. Linh-Trung Nguyen, passed on to me the lesson: never avoid the difficulty in research, keep going straight and raze it. When I started working with him, I usually switched to alternative ways when I got stuck solving a problem, which admittedly often carried me away from the initial direction. His advice helped me to be more consistent. My academic Ph.D. advisor, Prof. Sheng Yang, taught me to try to see the essence of a problem, often through a simple but comprehensive enough example, without getting lost in the maze of details. My industrial Ph.D. advisor, Dr. Maxime Guillaud, showed me the benefit of scientific discussion and building collaboration among individuals with diverse but complementary expertise and perspectives.**What are flexible wireless networks and how could developing countries especially benefit from them?**

In my vision, flexible wireless networks are ones which can be self-organized under less stringent constraints. Such a network should allow heterogeneous network entities to cooperate in order to assist each other in retrieving the needed information. In addition, the network algorithms should be implemented distributively such that there is no need for an expensive central processing unit and new devices can be easily admitted into the system. Furthermore, the network functions can be flexibly defined in software such that any network establishment or modification would not require a substantial infrastructure change.

My desire for a flexible network grows from observing the situation in developing countries. These countries do not have a communication infrastructure as good as in developed countries and face some typical challenges. For example, my home country Vietnam is high ranked globally for the strong effects of shocks and natural disasters related to climate change. We are hit by more than ten typhoons each year (16 in 2017), which flood many towns for weeks. On top of that, quick urbanization results in the fact that more than 35% of the population is living in urban areas. In the case of disaster, especially if the electricity is idle, a flexible self-organized communication network, for example between unmanned aerial vehicles, would greatly facilitate the salvage.

Der Beitrag 10 out of 200: Serving the people – Khac-Hoang Ngo improves our telecommunication erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: Of cats and donuts – Adele Jackson uses topology to tackle classification problems erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Adele Jackson and I am from Australia.**Where did you study and where are you currently based?**

I completed my undergraduate degree at the Australian National University, Canberra, Australia. I am in the process of moving to Oxford.**What is your current position?**

I am about to start a Ph.D. in mathematics at the University of Oxford, in the topology research group.**What is the focus of your research? What is your research project?**

I work on low-dimensional topology. Topological is the study of spaces and shapes where we consider two spaces to be the same if we can turn one into the other by bending or stretching them. For example, I think of a sphere and a cube as the same, but a sphere and a doughnut as different. I think about three-manifolds, which are spaces that locally look like three-dimensional space. One subfield of topology that I am particularly interested in is finding algorithms to solve topological problems. I am also working on a paper on a presentation of the mapping class group.

I am also very interested in topological data analysis. I just finished working at CSIRO, Australia’s national research agency, using my topological skills to understand some of the latest techniques in machine learning. Looking at the shape of data can give us useful insights into it. **Why do you want to become a mathematician?**

Understanding how mathematical systems and objects work is endlessly interesting and rewarding. I was a student in the Australian informatics olympiad training program in high school. I quickly realised that I enjoyed it for the mathematical ideas behind the algorithms rather than for the programming itself. I love how thinking about these abstract logical systems can give surprising insights and applications.**What are some of the fundamental challenges you have faced in your academic career?**

Balancing mathematics and my life outside it is always a challenge, but I am improving at it.**What do you feel are the greatest pressures facing scientists today?**

It seems to me that job and funding uncertainty is a substantial impediment to researchers. Going into this field, if you aim to work in a postdoctoral position after your Ph.D., you will likely move continents every couple of years and have little to no control over where you live for a substantial period. This is both an exciting opportunity to see what living in other countries is like, and quite challenging. **What are you doing besides research?**

I play ultimate frisbee and love getting outdoors. I am very excited to do lots of hiking in Europe. Right before the HLF, I will be doing a walk in northern Sweden: fingers crossed I see reindeer!**How did you hear about the HLF and why did you apply?**

I read about it on the Math With Bad Drawings blog in 2016, when I was a couple of years into my undergraduate degree. It sounded like a fantastic opportunity.**What do you expect from this meeting?**

I look forward to meeting like-minded people: it will be wonderful to spend a week meeting both the laureates and the young researchers. I expect to meet people from many different fields, who all love to learn and understand the world around them.

I would like to meet Robert Tarjan. I was substantially influenced towards pure mathematics by my time in the Australian informatics olympiad training program, which I now tutor for. One of the first papers I remember reading was his analysis of the computational complexity of union-find.**Who were your most important mentors and what lessons did they pass on to you?**

The mathematics faculty at ANU has been incredibly supportive. Attending seminars over my degree has exposed me to many areas of mathematics. In particular, Joan Licata, who supervised my honours thesis, gave me the opportunity to do proper research for the first time, with all its rewards and frustrations.**What is topological data analysis and what can we use it for in everyday life?**

Topological data analysis is what it says on the tin: applications of topological to analysing data. I am particularly interested in applications to machine learning.

For example, if we are trying to classify a dataset into two classes, we could look at topological properties of the decision boundary that splits the classes in the dataset. If the decision boundary is very complicated, it is likely we are picking up artefacts in our particular dataset rather than trends that we can generalise to other contexts. We can use this to optimise the classification to reduce this overfitting. Classification problems are ubiquitous in everyday life. We might want to decide whether an image has a cat in it, or whether a scan of a rock is of limestone or sandstone. Topological data analysis can help us develop more robust techniques for solving these problems.

Der Beitrag 10 out of 200: Of cats and donuts – Adele Jackson uses topology to tackle classification problems erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: Of math, memory, and marathon – Bastian Wiederhold is on the fast track erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality?**

My name is Bastian Wiederhold and I am from Stuttgart, Germany.**Where did you study and where are you currently based?**

Recently, I completed a B.Sc. Mathematics at the University of Stuttgart. In October, I will start as a graduate student at the University of Oxford.**What is the focus of your research? What is your research project?**

I am passionate about statistics and probability. The general question of how to formularize a not determined process into a theoretical structure intrigues me. In my bachelor’s thesis, I focused on reproducing kernel Hilbert spaces and hope to do research in this and related fields in the coming years.**Why do you want to become a mathematician?**

I have always been interested in many subjects such as physics, chemistry, cosmology, economics or architecture. Sooner or later, I came across mathematics in nearly all of these areas. Thus, when I was still in school, I decided to become a junior student in mathematics at Stuttgart University. Right from the start I was fascinated by the creativity and elegance of mathematical proofs and enjoyed mathematics ever since. I want to become a mathematician for those two reasons: to describe and solve problems elegantly and generically and to learn the language humans use to explore the world from a rational perspective.**What are some of the fundamental challenges you have faced in your academic career?**

Completing my B.Sc. in two years instead of three was hard sometimes. When I finished school, I already had some knowledge of university mathematics from my studies as a junior student. In the beginning, I was still recommended to graduate in standard three years. After one year I realized that I was too fast for three years: either I would have to finish in two years and apply for a master’s degree immediately or slow down my pace. I chose the first option and was happy to get an offer from the University of Oxford. However, this resulted in the next challenge: the semesters in England are time-shifted and I had to finish a thesis which needed a month to be examined. So, I even had to finish another two months earlier! In the end, I managed to master this challenge and finished a three-year degree in under two years.**What do you feel are the greatest pressures facing scientists today?**

There are some topics like climate change or immigration where the public debates are not decided by arguments but rather by feelings. The side with the more vociferous and mightier supporters gets more public attention and independent research is less considered. If decisions are no longer based on rational arguments and what is best for most people, this is a dangerous development for scientists and the whole society.**What are you doing besides research?**

I always loved to acquire knowledge and started to deal with memory techniques. Over the years I become a memory athlete placed in the top 50 worldwide, e.g. I memorized a 380-digit-number in 5 minutes. Other interests of mine include marathon running and juggling.**How did you hear about the HLF and why did you apply?**

I remember reading a newspaper article about the HLF when I was in school. From then on, I knew that I would apply one day. The HLF is a great opportunity to learn more about mathematics, to get new ideas in which areas to specialize and to learn from experienced scientists what steps to take in life to be able to research in a facilitating environment. Furthermore, I love meeting outstanding people from all over the world.**What do you expect from this meeting?**

I hope to get new ideas in which fields of mathematics I would like to do research. Of course, I am looking forward to meeting people I can collaborate with. In any case, I expect the HLF to be an enjoyable week full of inspiring conversations with leading and future leading scientists.

I am very much looking forward to talking with laureates who deal with probability, stochastics, machine learning… However, I expect great conversations with all the laureates and will use the opportunities that arise.**Who were your most important mentors and what lessons did they pass on to you?**

My parents always supported me and taught me to believe that almost anything is possible if you are willing to train.

Felix Dörre and Jan Rapp introduced me to programming and higher mathematics when I was in school. In a way, meeting them was the beginning of my path to mathematics.**In 2016, you were a key-contact of the Philippine delegation at the World Schools Debating Championships. You have also participated in national events in Germany as a debater. How do you benefit from your communication skills as a mathematician?**

In general, mathematics has a lot more to do with communication than people might think at first: every proof is about conveying ideas in neat ways and many mathematical works are the results of collaborations. Every mathematician knows the feeling of being stuck on a problem and solving it by talking to a friend or supervisor, simply because they can give a different perspective.

Expressing ideas in a structured and eloquent way makes it easier for other mathematicians to follow your ideas and is precisely what you train in debating. No matter if you collaborate for exercises or research, it helps to be good at making new friends and work as a team.

Der Beitrag 10 out of 200: Of math, memory, and marathon – Bastian Wiederhold is on the fast track erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag Michael Atiyah – ein Vorbild für junge Wissenschaftler erschien zuerst auf Heidelberg Laureate Forum.

]]>Doch wer war dieser Michael Atiyah, der vergangenes Jahr mit seiner Ankündigung, die *Riemannsche Vermutung* und damit das wohl anspruchsvollste offene Problem der Mathematik gelöst zu haben, für manch einen Medienrummel — sogar außerhalb mathematischer Kreise — sorgte? Er war natürlich weit mehr als das. Nach einer Generation renommierter Mathematiker, die nach der Wende ins 20. Jahrhundert vor allem daran arbeiteten, die Grundlagen der Mathematik auf sicheres Terrain zu bewegen, gehörte Atiyah zu denen, die sich anschließend die Ärmel hochkrempelten und sich an praktische Probleme herantasteten. Und wie er das tat! Nun könnte man eben all diese mathematischen Erfolge Atiyahs und die Würdigungen, die ihm deswegen zuteil wurden, hier anführen. Jedoch ließe sich all diese Information auch bei einer kurzen Recherche selbst herausfinden. Es sind all diese Aspekte, die Atiyah zu großer Berühmtheit führten und ihn zu dem Mathematiker machten, der er war. Und dennoch: Der Person Michael Atiyah wird man mit einer solchen Auflistung nicht gerecht.

Doch kann man so etwas, also die Bedeutung seiner Person in vollem Umfang darzustellen, überhaupt erreichen? Vermutlich nicht gänzlich. Und wahrscheinlich bin ich selbst auch nicht die geeignetste Person für ein solches Unterfangen. Ich werde hier aber versuchen, einen Beitrag dazu zu leisten und dabei eher auf sein Auftreten eingehen, da vor allem das dazu führte, dass er beim HLF eine so bedeutende Rolle spielte. Ich möchte hier Facetten seiner Person, seines Wesens und seiner Natur schriftlich festhalten, und somit all denen etwas von Atiyah weitergeben, die nicht das Vergnügen hatten, sich mit ihm zu unterhalten oder ihn live zu erleben.

Ein Bild spricht ja bekanntlich mehr als tausend Worte und ein kurzer Austausch mit Atiyah sprach wohl mehr als tausend Bilder. Als Young Researcher beim HLF versucht man bei der Interaktion mit den Laureaten meistens, von deren Lebenserfahrung zu lernen und stellt entsprechend ein Meer an Fragen. Die erfahrenen Mathematiker und Computerwissenschaftler antworten sehr gerne darauf und so entstehen bemerkenswerte und vielschichtige Gespräche. Atiyah war in dieser Hinsicht schon ein bisschen anders, da er direkt den Spieß umdrehte, kaum Fragen zuließ und selbst die jungen Wissenschaftler bis ins kleinste Detail befragte. Sei es über Persönliches oder über den akademischen Werdegang. Alles weckte sein Interesse und über alles schien er zu grübeln und zu sinnieren. Anschließend kamen seine Kommentare dazu und so konnte es passieren, dass seine Tipps und Bemerkungen hinsichtlich der Forschungsarbeit eines jungen Wissenschaftlers so tiefgründig und weitreichend waren, dass daraus ruhig eine ganze Doktorarbeit hätte entstehen können. Als junger Forscher war diese zuvorkommende Art Atiyahs von unschätzbarem Wert, da seine Fähigkeit, Potenzial in jedem zu finden und jeden einzelnen als ungeschliffenen Diamanten zu sehen, in einer akademischen Welt, in der man sich nicht selten mit Selbstzweifeln plagt, besonders ermutigend ist.

Atiyah sprach ständig davon, wie wichtig die nächste Generation Mathematiker und Computerwissenschaftler sei und welche Verantwortung sie übernehmen müsse. Es mag übertrieben klingen, doch fühlte es sich wirklich so an, als würde er eine Woche lang die Figur eines Großvaters der Young Researcher übernehmen. Denn es war nicht so, als wolle er die Nachwuchswissenschaftler mahnen oder warnen, sondern ihnen vielmehr ihre Bedeutung für die Zukunft klarmachen, indem er sie beim HLF in den Vordergrund stellte. Es gab sehr viele kleine Gesten, mit denen Atiyah dies erreichte. Als Beispiel möchte ich hier eine persönliche Erfahrung anführen, die ich mit ihm während des Bayerischen Abends beim HLF erlebte. Wir wurden von den Organisatoren eingeladen, zu dieser Gelegenheit traditionelle Kleidung unseres Heimatlandes zu tragen und da ich selbst einer deutschen Volkstanzgruppe in Argentinien angehöre, ließ ich es mir nicht nehmen, meine Tracht samt Lederhose und traditionellem Hut anzuziehen und anschließend zusammen mit der Gruppe, die dort eine Tanzvorführung präsentierte, selbst zu tanzen. Nach der *Amboss-Polka* kam Atiyah zu mir, um mir für meinen Auftritt zu gratulieren. Er tat dies aber, indem er angetanzt kam und dabei versuchte, die Bewegungen des Schuhplattlers nachzumachen. Seine Begleitung sagte mir später, dass es für sie witzig sei, dass man immer wieder behaupte, Michael Atiyah würde andere Menschen inspirieren, wenn es doch in diesem Fall ich war, der ihn inspiriert hatte. Seit langem war er nicht so lebensfroh und energisch gehüpft und seit langem hatte er nicht mehr so getanzt, wie dort auf dem Bayerischen Abend. Zu guter Letzt ist diese kleine Geschichte nicht nur ein Beispiel dafür, wie er mit kleinen, subtilen Gesten andere würdigte, sondern auch dafür, dass das HLF für ihn wie eine Verjüngungskur war, in der er sich mit Lebenslust und Jugend umgab und sich ein bisschen davon mitnahm. Mich nannte er seit diesem Abend *the Bavarian dancer from Argentina*.

Es war aber nicht notwendig, mit ihm zu interagieren, um zu merken, was für ein Mensch er war. Es reichte schon aus, ihn einfach nur zu beobachten und ihm zuzuhören, wenn er was zu sagen hatte, was überdies recht häufig passierte. Kein Thema in der Mathematik oder in den Computerwissenschaften schien ihm uninteressant zu sein und zu allem gab es etwas, was er beitragen konnte. Bis zum letzten Tag zeigte er sich fasziniert von der schöpferischen Kraft der Mathematik, fast schon wie ein stolzer Vater, der der Geburt seines Kindes beiwohnt. Dieser Enthusiasmus und diese Energie hatten etwas Jugendliches, was bestimmt auch erklärt, warum er sich so wohl unter jungen Wissenschaftlern beim HLF fühlte und warum diese ihn so sehr schätzten. Ein weiterer Grund dafür ist sicherlich auch die Art und Weise, wie er über Mathematik sprach. Weit entfernt vom gängigeren mathematischen Diskurs, der sich in Fachwörtern verliert und an dem der gewöhnliche Nicht-Akademiker kaum teilhaben kann, schien Michael Atiyah dank seiner Liebe zu dieser Wissenschaft beinahe schon eine poetische Redensweise angenommen zu haben. Sein Gedicht *Dreams* etwa spiegelt dies perfekt wider. Auch sprach er zum Beispiel vom *Schlüssel zum geheimen Garten der Mathematik*, den er besäße und dass er ab und zu jüngere Mathematiker einlade, kurz in den Garten hineinzuschnuppern. Auf jeden Fall war es immer erfrischend, ihm zuzuhören.

Vieles vom dem, was hier geschildert wird, trifft natürlich nicht nur auf Michael Atiyah zu, sondern auf eine Vielzahl der Teilnehmer am HLF, nicht ausschließlich Laureaten. Jedoch kann mit Gewissheit gesagt werden, dass Atiyah wohl diese Eigenschaften in ihrer Gesamtheit verkörperte. Es ist, was ihn für jüngere Wissenschaftler so besonders machte, aber in keine Beschreibung seines Werks passt. So ist dies auch eine Danksagung für den positiven Einfluss, den er auf so viele Menschen hatte. Ich bin froh, dass ich das große Glück habe, einer von diesen Menschen zu sein. Und ich weiß schon jetzt, dass er beim HLF sehr vermisst wird.

Der Beitrag Michael Atiyah – ein Vorbild für junge Wissenschaftler erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: For a better tomorrow – Anmol Kabra applies machine learning to sustainability problems erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and nationality? **

My name is Anmol Kabra and I’m from India.**Where did you study and where are you currently based?**

I completed high school in Patna, Bihar, India. I’m currently based in Ithaca, New York, United States.**What is your current position?**

I’m a senior (4^{th} year) undergraduate student in Computer Science at Cornell University.**What is the focus of your research? What is your research project?**

I’m interested in understanding Machine Learning models and why they work. Furthermore, I’m interested in interdisciplinary research in CS, specifically in Machine Learning, targeted towards solving sustainability problems.

Throughout my undergraduate career, I have worked on several research projects. The most prominent project was to develop a fast and scalable Machine Learning framework for incentivizing citizens to complete scientific tasks in crowdsourcing programs. By strategically distributing incentives, scientists could reduce sampling bias and improve the data’s quality for scientific modeling. In a project in Natural Language Processing last summer, I worked on understanding dialog similarity and devising good embeddings for dialogs. Before that, I also worked on predicting chemical crystals from diffraction spectrograms and creating embeddings for elements. My work has been quite interdisciplinary so far, and loosely driven by sustainability problems.**Why do you want to become a computer scientist?**

I was interested in Environmental Engineering and Waste Management in high school, but I soon realized that Computer Science had an overarching influence on many fields and adapted a more general approach to problem-solving. I like how complex problems can be broken into simpler ones and be solved at scale. My interest in Computer Science originated from this idea, supplemented by my professors’ and peers’ support. With the field becoming increasingly interdisciplinary, I think it’s a great time to be in Computer Science.**What are some of the fundamental challenges you have faced in your academic career?**

I have struggled with communicating my findings and keeping up with the pace of Machine Learning research. In the recent deluge of amazing research, it has been challenging for me to distinguish promising research from mainstream, insignificant contributions. I also find it hard to identify when a research idea is worth pursuing and when it’s not, but I hope to learn this skill from experience and with time.**What do you feel are the greatest pressures facing scientists today?**

Communicating science to policy makers and the public remains a challenge, and increasingly so, in these times of targeted misinformation and corporate greed. Great scientific advances are being made every day, but they get swept under the rug due to various factors. We as scientists have a responsibility to make our work known and influential in shaping humanity’s future, and I feel that this pressures many scientists.**What are you doing besides research?**

I like to play table-tennis, hike, bike, and follow Formula 1. I also enjoy reading non-fiction books and watching documentaries.**How did you hear about the HLF and why did you apply?**

I heard about it on the internet and from a professor who I took a class with. Since this was my last year as an undergraduate and I didn’t want to miss this opportunity, I thought that applying was worth a shot. **What do you expect from this meeting?**

I hope to consult senior researchers on how they conduct research and what types of questions they ask. I am also excited to meet fellow young researchers, who I could collaborate with and learn from. Interacting with people from around the world will be insightful.

I would be honored to interact with Yoshua Bengio, who is increasingly interested in using AI to solve sustainability problems and ameliorate climate change. I would also like to ask him how application areas can help advance AI, in ways other than serving as test-beds for algorithms. Moreover, I’m currently reading Leslie Valiant’s 1994 book Circuits of the Mind, and I’m interested in asking Valiant’s views on how his proposed theories fit into or conflict with the developments in AI we have seen recently.**Who were your most important mentors and what lessons did they pass on to you?**

My family has always supported me, left space to explore and grow, and encouraged me to persevere when I failed. In college, my first research mentors, Yexiang Xue, and Carla Gomes, showed faith in me when I worked on research projects and challenged my skills. I also owe gratitude to some of my high school friends, teachers, and college professors, who have helped make learning fun.**What did teaching others teach you about yourself?**

Teaching has not only helped me empathize with the different paces and ways others learn but has also made me introspective and self-aware of the challenges I faced when learning something. Teaching is also adventurous, as the same explanation or method almost never works for different students, and there are endless opportunities for innovation in communication. This way, teaching keeps me on my toes and makes learning exciting.

Der Beitrag 10 out of 200: For a better tomorrow – Anmol Kabra applies machine learning to sustainability problems erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag 10 out of 200: Teaching the teachers – Zirhumanana Balike Dieudonné takes math to rural areas erschien zuerst auf Heidelberg Laureate Forum.

]]>**What are your name and your nationality?**

My name is Zirhumanana Balike Dieudonné. I am from the Democratic Republic of the Congo (DRC).

**Where did you study and where are currently based?**

Most recently (June 2019), I have earned my master’s degree in Mathematical Sciences at the *African Institute for Mathematical Sciences* (AIMS) in Senegal. Prior to this, I started my studies at the *Institut Supérieur Pédagogique de Bukavu* (Higher Pedagogic Institute from Bukavu) where I earned my Bachelor in Mathematical Physics (2014) and two years later I got a postgraduate degree in Mathematics applied to Pedagogy. I am currently based in the Democratic Republic of the Congo.

**What is your current position?**

I am currently a part-time tutor at the Institut Supérieur Pédagogique de Bukavu and provide training to secondary school teachers in my village. I am looking forward to starting my Ph.D. studies as soon as possible.

**What is the focus of your research? What is your research project?**

My research focuses on modeling natural phenomena like the movement of molecules in cells or the spreading of epidemics. My current projects include the modeling of molecules in tilings by Markov chains and the modeling of Ebola outbreak in the east part of DRC (in the context of war and ignorance of population) by using a SIR model.

**Why did you become a mathematician?**

Since secondary school, I enjoyed mathematics thanks to various reading material although I did not get good professors. I then enrolled in the department of mathematics primarily because I expected to relieve the lack of mathematics teachers in my village. Finally, I realized that most of – if not all – solutions to our daily problems lie in mathematics.

**What are some fundamental challenges you have faced in your academic career?**

Moving from mathematical physics to mathematics applied to pedagogy was a big challenge because there is a gap between these two fields. During my master studies, I had the challenge of meeting deadlines because of the amount of daily work.

**What do you feel the greatest pressures facing scientists today?**

The main challenge for scientists today is to provide solutions to the daily problems of our society. Time is faster than scientific findings. Therefore, the quicker time passes, the more dated scientists’ findings are to solve the new challenges.

**What are you doing besides research?**

I like to read psychological and self-management books, I like jogging and watching or playing football. I also like to hear stories from older people (especially from my father!) in my village.

**How did you hear about the HLF and why did you apply?**

I read about in the chat group of my university and received much information from a former attendee (Deborah Kanubala from Ghana). I applied because I saw that the HLF is involved in the diffusion of sciences through their yearly forums, which is particularly what I am doing in my village. I thought it would be a nice opportunity to meet other people with the same challenges and learn more from them but also share my experience with them.

**What do you expect from this meeting?**

I hope to meet experienced researchers in my domain and chat with them about their strategies in research. Since the forum will gather many young researchers, I am excited to meet them and discuss during this forum about our common centers of interest.

I respect all the laureates attending the forum but I am particularly delighted to meet Martin Hairer. I have read some of his publications and I guess he is one of the most important mathematicians of this century, a kind of Einstein in Mathematics. I would like to know exactly what has not yet been done to complete the solution of Navier Stokes equations. I would like to know if the unicity of the solution to the Navier stochastic equation has been demonstrated analytically and what the major application of these results in our current context should be.

**Who were your most important mentors and what lessons did they pass on to you?**

I owe a lot to all my teachers for the sacrifices they made to make me mature scientifically. However, one teacher particularly nourished my mind: Mushiwalyahyage. I learned much from his way of teaching mathematics, I realized how passionate I should be for teaching mathematics. From him, I got the energy to teach mathematics with a new view of my students.

**You are teaching math especially in rural areas of your country. What do you find most rewarding doing so?**

When you teach in rural areas in a country like the DRC, what you gain is the number of young people you can reach; not money. As far as I am concerned, teaching in my village has allowed me to motivate some talented young people to love mathematics more and more. Today, many of them are ready to enroll in the mathematics or physics departments, but the financial resources are lacking. Before, no young people in my village could even accept a scholarship in these areas. Today the situation has changed and this is quite motivating for me.

Der Beitrag 10 out of 200: Teaching the teachers – Zirhumanana Balike Dieudonné takes math to rural areas erschien zuerst auf Heidelberg Laureate Forum.

]]>Der Beitrag Abelian Groups erschien zuerst auf Heidelberg Laureate Forum.

]]>Most of Abel’s work in mathematics was done within a 6-7 year period, and covered topics including polynomial equations, elliptic functions and calculus. Many concepts in mathematics are named after Abel (so many, in fact, that Wikipedia has a dedicated List of things Named after Abel).

One of the first things on this list that I encountered when studying maths at uni was the notion of an **abelian group** – and to explain what one is, I’ll need to start by defining one of the most useful abstract ideas in pure maths: the theory of groups.

You’re probably very used to working with groups, but maybe don’t realise it yet. A group is a set of objects – they could be numbers, letters, permutations (as we met in my previous blog post), matrices, symmetries, or even moves on a Rubik’s cube. The main thing we need for them to be a group is this: if we take two things from in the group, and combine them using a specified rule, the result of doing that should also be something in the group.

For example, if we take two whole numbers, like 2 and 5, and add them together, the result will also be a whole number: 7. We could then take 7 and combine it with some other number, like 1, and we’d still get another number. This property is called being **closed** – a group, considered with the specific operation you have chosen to be the way of combining things in the group, will only ever give you things from within the group.

The definition of the operation is also in some sense part of the definition of the group. For example, I could take the same base set as in the previous example (whole numbers), and instead of adding them together, I could use multiplication. When writing this, we can use the notation (ℤ, +) to mean the whole numbers under addition, and (ℤ, ×) to mean the whole numbers under multiplication. The different operations give different structures – you don’t get the same result if you combine the same two elements using different operations.

**Interesting side fact:** the use of the symbol ℤ to mean the whole numbers comes from German: it stands for both Zahlen, meaning “numbers”, and zählen, meaning “to count”. This double-letter font is called ‘blackboard bold’, and mathematicians use blackboard bold symbols to represent important concepts – like the ‘counting numbers’, or integers.

There’s a few more things we need to make something definitely a group. For example, in the case of integers under +, we have a special element in the group: 0. This has the property that if you combine it with another element of the group, using the group operation, it doesn’t change the element. So, 7 + 0 = 7. 0 here is called the **identity element** of the group – it doesn’t change anything. For something to definitely be a group, we need the identity element to exist and be unique in the group.

It’s also more obvious how the structure of (ℤ, +) differs from (ℤ, ×) when you think about identity elements: in (ℤ, +), 0 is the identity, but in (ℤ, ×) the identity element would be the number 1 – if you multiply something by 1, it doesn’t change.

There are a couple more conditions we need to satisfy to be sure we have a group. Since our definition of the integers includes negative numbers, we find that there are some special pairs of elements in the group: elements which we can combine with others and come out with the identity element as the result! 4 + (-4) = 0. We say -4 is the **inverse** of 4 in the group (ℤ, +), and for something to be a group, you need every element in there to have an inverse (including the identity element – but that should be its own inverse: 0+0=0).

You might have spotted an issue here: (ℤ, +) definitely has this property – whatever number you can name, I can find its inverse easily by putting a minus symbol in front. But this doesn’t work with (ℤ, ×). The inverse of a number N under the operation ×, which we can combine with it to get the identity 1, is given by 1/N. For example, 2 × ½ = 1. But these inverses – which will be fractions, and not whole numbers – are not elements of the group. This means (ℤ, ×) isn’t actually a group! This type of structure, which is less strict than a group, is called a **monoid**.

We’re not quite done yet: there’s one more property we need our set and operation to have in order to be a group, and that’s called **associativity**. It’s a slightly funny one to define, but it essentially means that if you combine two elements using the operation, and then combine the result with another element, it doesn’t matter which order you apply the two operations in. That is: (a+b)+c = a+(b+c).

This works for our group (ℤ, +) of integers under addition: (1+2)+3 = 1+(2+3) = 6 whichever way you look at it. With this property of associativity, any set and operation which are closed, have an identity and all elements have inverses, that’s the definition of a group.

There are plenty of examples of group structures all around us. You probably look at one every day: a clock face. The numbers on a 12-hour clock form a finite set, and you can combine them by adding times: 4 o’clock plus 5 hours is 9 o’clock, and it wraps around: 10 o’clock plus 5 hours is 3 o’clock. You always get something in the group, 12 o’clock is the identity element (12 hours after 5 o’clock, it’s still 5 o’clock), and you can find the inverse of something by counting backwards.

An even simpler example of a group structure can be found on your coffee tray, next to a hot drink: a battenberg cake. In this group, there are two elements: pink cake, and yellow cake, and the definition of the group operation is laid out as a table in the cake’s cross-section. The top row and left column show what happens if you add pink, and the bottom row and right column are what happens if you add yellow. Pink is the identity element: pink + pink = pink, and yellow + pink = pink + yellow = yellow.

The identity is its own inverse, but we also have an inverse for yellow: yellow + yellow = pink (bottom right corner). This has the same structure as one of the simplest groups, and it’s denoted ℤ_{2}. It’s the only group that has two elements – any other group with exactly two elements is equivalent to it.

You might find another example of a group around the house too – a Rubik’s cube, which has an underlying group describing how it moves. The elements of the group are moves on the cube, and they can be combined by simply performing one after the other. This group is also finite, but it’s got more than two elements (it’s actually got 43,252,003,274,480,856,000 elements, but who’s counting) – and because it’s finite, starting from a solved cube and repeating the same move over and over will get you back to a solved state eventually. The fascinating group underlying the Rubik’s cube is the reason why it’s pictured at the top of the Wikipedia page for Group Theory.

Maybe you’re still wondering what an abelian group is! We’ve seen various properties that groups can have – being finite, or infinite, or having a certain number of elements. Another property possessed by some but not all groups is that of being abelian. To understand this, we need to think about how the group operation works.

A property of some group operations, which might seem so obvious that you may not even notice it, is that it doesn’t matter which way round the two elements are when you combine them. If you want 2 + 4, you can write it as 4 + 2 and you get the same result, and it’s 6 but nobody cares how you got there. And if I take two numbers on a clock and add them the other way round – 5 hours after 3 o’clock, or 3 hours after 5 o’clock, it’s still 8 o’clock whichever way you work it out.

But this doesn’t always work. The moves on a Rubik’s cube give you a different result if you do them in a different order (go and find one now and try it, if you don’t believe me). Multiplying two matrices together – and certain sets of matrices form a group under standard matrix multiplication – gives a different result if you do it in a different order. Some operations give the same result either way round, and we say they **commute**.

There are some groups in which only some pairs of elements commute – for example, the identity commutes with everything in a group. But if a group has the property that all of its elements commute with all the others, it’s called an **abelian group**. Group theorist Camille Jordan named them as a nod to Abel’s work on groups of polynomials which commute. Unusually, despite being named after a person, abelian groups aren’t usually spelled with a capital A – showing just how ubiquitous they are.

Abelian groups are generally easier to understand and work with than general groups, and finite abelian groups have been thoroughly studied. Infinite abelian groups, however, are still not completely understood, and are an area of current research. This means mathematicians today are still researching them – and every time a mathematician studies a group with elements which all commute, they remember Niels Henrik Abel.

Der Beitrag Abelian Groups erschien zuerst auf Heidelberg Laureate Forum.

]]>