Section 13. Combinatorics

Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics. Designs and finite geometries. Algebraic combinatorics. Topological and analytical techniques in combinatorics. Combinatorial geometry. Combinatorial number theory. Additive combinatorics. Polyhedral combinatorics and combinatorial optimization.
Federico Ardila

San Francisco State University / University of Los Andes, USA / Colombia

Federico Ardila investigates objects in algebra, geometry, topology, and applications by understanding their underlying combinatorial structure. His interests include polytopes, matroids, Lie and Coxeter combinatorics, Hopf algebras, and tropical geometry.

Federico is a Professor of Mathematics at San Francisco State University. He is a Fellow of the AMS and he has received the CAREER Award of the NSF, the National Teaching Award of the MAA, and the Programs that Make a Difference Award of the AMS. In Colombia, he is a member of the Academia Colombiana de Ciencias and was awarded the Premios Nacionales de Ciencias y de Matemáticas.

Federico is committed to fostering an increasingly just, equitable, and welcoming community of mathematicians. Having advised more than 50 thesis students, he also co-directs the MSRI-UP program for students from underrepresented ethnic groups and hosts over 200 hours of combinatorics lectures online. His efforts are grounded on the following axioms:

  1. Mathematical potential is equally present among different groups, irrespective of geographic, demographic, and economic boundaries.
  2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
  3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
  4. Every student deserves to be treated with dignity and respect.
Keith Ball

University of Warwick, UK

Survey lecture on convex analysis and its connections to other areas of mathematics

Jointly in sections 8, 10, 12

Keith Ball is a professor at the University of Warwick. His interests are in high-dimensional and discrete geometry, information theory and (more recently) analytic number theory. He was scientific director of the International Centre for Mathematical Sciences in Edinburgh from 2010 to 2014 and holds honorary professorships from the University of Edinburgh and Heriot-Watt University.

Towards the end of his tenure at ICMS he was chair of ERCOM, the umbrella organisation for European mathematics research centres.

He is a Fellow of the Royal Society of London and the Royal Society of Edinburgh and was on the governing council of the Royal Society during 2018-2019.

Among other things his research demonstrated that the central limit theorem of probability is driven by an analogue of the second law of thermodynamics: namely, that entropy increases along the central limit process. He is also known for a popular book on mathematics entitled «Strange Curves, Counting Rabbits...»

Julia Böttcher

London School of Economics, UK

julia Böttcher is a Professor of Mathematics at the London School of Economics and Political Science. Her research is in extremal and probabilistic combinatorics. Jointly with her co-authors she won the Delbert Ray Fulkerson Prize in 2018. She is an Editor in Chief of the Electronic Journal of Combinatorics, a Managing Editor for the Journal of Combinatorial Theory, Series B, and a member of the Editorial Board of Random Structures and Algorithms. After completing a Computer Science degree at Humboldt University Berlin, she obtained a Ph.D. in Mathematics from TU Munich, and was a postdoc at the University of São Paulo. Her move to London with her family was made possible by the LSE agreeing to split a lectureship between her and her husband initially. She has three young children.
Ehud Friedgut

Weizmann Institute, Israel

Ehud Friedgut is a Professor of Mathematics at the Faculty of Mathematics and Computer Science at the Weizmann Institute in Rehovot, Israel.

His main mathematical interests are combinatorics and specifically the application of analytical and algebraic methods as well as discrete Fourier analysis.

He is the father of three children, two of whom are on the autistic spectrum.

Allen Knutson

Cornell University, USA

Allen Knutson is a Professor of Mathematics at Cornell University. His interests include algebraic geometry and algebraic combinatorics, especially within the study of Schubert varieties and Schubert calculus. His early work with T. Tao provided the first of many proofs of Horn’s conjecture on the possible spectra of the sum of Hermitian matrices with known spectra. With E. Miller he pioneered the use of Gröbner degeneration to establish and study combinatorial formulae. He is a former world record holder in juggling, and with T. Lam and D. Speyer connected the mathematical theory thereof to that of positroid varieties, about which he gave the joint AMS/MAA lecture in 2012. His Schubert calculus «puzzles», invented with Tao and C. Woodward and studied more recently with P. Zinn-Justin, have provided the most powerful approach to positive formulae for Schubert calculus beyond the Grassmannian case, and are increasingly connected with geometric representation theory.
Elchanan Mossel

MIT, USA

Survey lecture on combinatorial statistics and its role in the sciences

Jointly in sections 12, 14, 18

Elchanan Mossel is a Professor of Mathematics at the Massachusetts Institute of Technology. His research spans a number of topics across probability, statistics, economics, computer science, and mathematical biology.

He is known for his work in discrete Fourier analysis and its applications to computational complexity and social choice theory and for his research of information flow in biological, economic, and inferential networks.

Mossel held a Sloan Fellowship. He is a fellow of the American Mathematical Society, a Simons Fellow and a Vannevar Bush Fellow.

Sergey Norin

McGill University, Canada

Sergey Norin is an Associate Professor of Mathematics at the Department of Mathematics and Statistics of McGill University. He is primarily interested in structural and extremal graph theory and in applications of graph theory to other areas of mathematics. His results include a graph theoretical version of the Riemann-Roch theorem, a proof of the Lovasz-Plummer conjecture, and partial results towards Hadwiger’s conjecture.

In his spare time, he enjoys playing board games and building LEGO with his son.

Isabella Novik

University of Washington, USA

Isabella Novik is a Professor at the Department of Mathematics of the University of Washington. Novik’s research has focused on problems that come from combinatorics, discrete and polyhedral geometry, and commutative algebra. Her work has been centered on or motivated by problems related to the face numbers of polytopes and simplicial complexes, especially triangulations of spheres and manifolds. She is a recipient of the Haim Nessyahu Prize in Mathematics (2000) and the Alfred P. Sloan Research Fellowship (2006-2008). In 2017, she was also elected a Fellow of the American Mathematical Society. Born in St. Petersburg, Novik caught the «math bug» while participating in Math Olympiads and Math circles.
Mathias Schacht

Universitat Hamburg, Germany

Mathias Schacht is a Professor of Mathematics at the University of Hamburg. He is working in discrete mathematics.

In his research he focuses on problems in graph theory, in extremal and probabilistic combinatorics, and in Ramsey theory.

Together with Vojtěch Rödl he was awarded the George Pólya Prize in Combinatorics of the Society for Industrial and Applied Mathematics in 2012 for the generalisation of Szemerédi’s regularity method to hypergraphs.

Alex Scott

University of Oxford, UK

Alex Scott is a Professor of Mathematics at the Mathematical Institute of the University of Oxford. His interests lie in combinatorics and its connections with probability, computer science and statistical physics. He is known for his work on graphs of large chromatic number, graph partitioning problems, and the Erdos-Hajnal Conjecture.
Asaf Shapira

Tel Aviv University, Israel

Asaf Shapira is a Professor of Mathematics at the School of Mathematical Sciences of Tel Aviv University, Israel.

His fields of interest include extremal graph and hypergraph theory, Ramsey theory, additive number theory and application of these areas to problems in theoretical computer science.

Bernd Sturmfels

MPI Leipzig/ UC Berkeley, Germany/ USA

Survey lecture on applied / computational algebra

Jointly in sections 2, 14

Bernd Sturmfels is a leading experimentalist among mathematicians.

He is well-known for his contributions to computational algebraic geometry, commutative algebra, geometric combinatorics, and their applications, notably in statistics, optimization, and the lifesciences. He has authored 11 books and 270 research articles.

Sturmfels received doctoral degrees in 1987 from the University of Washingtonand the Technical University Darmstadt, and an honorary doctorate in 2015from the Goethe University Frankfurt. He joined UC Berkeley in 1995, where he is a Professor of Mathematics, Statistics and Computer Science. In 2017 he moved to the Max-Planck Institute for Mathematics in the Sciences in Leipzig, where he is a director and the head of the Nonlinear Algebra department. He is also affiliated with the Technical University Berlin and Leipzig University. Hishonors include a David and Lucile Packard Fellowship, a Humboldt Senior Research Prize, the SIAM von Neumann Lecturership, and the George David Birkhoff Prize in Applied Mathematics. He is a fellow of AMS and SIAM,and a member of the Berlin-Brandenburg Academy of Sciences.

Sturmfels is passionate about promoting outward-looking mathematics and the inclusion of talents from all backgrounds. Among his 60 doctoral students and countless postdocs, many are female. He firmly believes in excellence through diversity, and the axioms laid out by Federico Ardila.

Konstantin Tikhomirov

Georgia Institute of Technology, USA

Also in section 8

Konstantin Tikhomirov is an Assistant Professor at the School of Mathematics of Georgia Institute of Technology, USA. His interests include discrete probability, combinatorics, convex geometry, and applications to data analysis. Prior to joining GeorgiaTech, he was an instructor of math at Princeton University, and, in the Fall 2017, the Viterbi Postdoctoral Fellow at the Mathematical Sciences Research Institute in Berkeley.
Lauren Williams

Harvard University, USA

Jointly in sections 7, 11

Lauren Williams is the Robinson Professor of Mathematics at Harvard University and the Seaver Professor at the Radcliffe Institute.

Her research is in algebraic combinatorics. More specifically, she uses algebraic tools (cluster algebras, total positivity, tropical geometry) to study discrete structures in mathematics and physics.

She is a recipient of the AWM-Microsoft Research prize and is an honorary member of the London Mathematical Society.

Melanie Matchett Wood

Harvard University, USA

Interactions between number theory and random structures

Jointly in sections 3, 12

Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study.

Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. In particular,she studies the distribution of number fields and function fields and their fundamental structures, including class groups and the Galois groups of their maximal unramified extensions. In part to understand these distributions, she studies the probability theory of random abelian and non-abelian groups,which also has applications to other randomly arising groups, such as the Jacobians of random graphs and cokernels of random matrices.

She has received a Packard Fellowship for Science and Engineering, the AWM-Microsoft Research Prize in Algebra and Number Theory,an American Institute of Mathematics Five-Year Fellowship, and is a Fellow of the American Mathematical Society.

Thu Sep 16 2021 18:12:48 GMT+0300 (Moscow Standard Time)