- Alex Lubotzky (Israel)
- Andrei Okounkov (Russia/USA)
- Assaf Naor (USA)
- Carlos Gustavo Moreira (Brazil)
- Catherine Goldstein (France)
- Christian Lubich (Germany)
- Geordie Williamson (Australia/Germany)
- Gil Kalai (Israel)
- Greg Lawler (USA)
- Lai-Sang Young (USA)
- Luigi Ambrosio (Italy)
- Michael Jordan (USA)
- Nalini Anantharaman (France)
- Peter Kronheimer (USA) and Tom Mrowka (USA)
- Peter Scholze (Germany)
- Rahul Pandharipande (Switzerland)
- Ronald Coifman (USA)
- Sanjeev Arora (USA)
- Simon Donaldson (UK/USA)
- Sylvia Serfaty (France/USA)
- Vincent Lafforgue (France)
Click the sections to view invited speakers and panels list.
1. Logic and Foundations
Model theory. Set theory. Recursion theory. Proof theory. Applications.
Connections with sections 2, 3, 13, 14 and 16.
- Jochen Koenigsmann (UK)
- Joris van der Hoeven (France), Lou van den Dries (USA) and Matthias Aschenbrenner (USA)
- Maryanthe Malliaris (USA)
- Stephen Jackson (USA)
- Ulrich Kohlenbach (Germany)
Groups (finite, infinite, algebraic) and their representations. Rings (both commutative and non commutative),
fields and modules. General algebraic structures, algebraic K-theory, category theory. Computational aspects of algebra and applications.
Connections with sections 1, 3, 4, 5, 6, 7, 13, 14.
- Christof Geiss (Mexico) – joint with section 7
- Ivan Panin (Russia)
- Moritz Kerz (Germany)
- Osamu Iyama (Japan)
- Pham Huu Tiep (USA/Vietnam)
- Sonia Natale (Argentina)
3. Number Theory
Algebraic number theory. Galois groups of local and global fields and their representations. Arithmetic of algebraic
varieties and Diophantine equations. Geometry of numbers, Diophantine approximation, and transcendental numbers.
Modular and automorphic forms, modular curves, and Shimura varieties. Langlands program. p-adic analysis. Zeta and L functions.
Analytic number theory. Probablistic method in number theory. Number theory and physics. Computational number theory and applications.
Connections with sections 1, 2, 4, 7, 11, 12, 13, 14.
- Adrian Iovita (Canada/Italy), Fabrizio Andreatta (Italy) and Vincent Pilloni (France)
- Bjorn Poonen (USA)
- Georgios Pappas (USA) – joint with section 4
- Jack Thorne (UK)
- Jacob Tsimerman (Canada)
- James Maynard (UK)
- Kaisa Matomäki (Finland) and Maksym Radziwill (Canada)
- Laurent Fargues (France) – joint with section 4
- Maryna Viazovska (Switzerland) – joint with section 13
- Miguel Walsh (Argentina) – joint with section 9
- Ritabrata Munshi (India)
- Wei Zhang (USA)
- Yves André (France)
4. Algebraic and Complex Geometry
Algebraic varieties, their cycles, cohomologies, and motives. Schemes and stacks. Geometric aspects of commutative algebra.
Arithmetic geometry. Rational points. Low-dimensional and special varieties. Singularities. Birational geometry and minimal
models. Moduli spaces and enumerative geometry. Transcendental methods and topology of algebraic varieties. Complex
differential geometry, Kähler manifolds and Hodge theory. Relations with mathematical physics and representation theory.
Computational methods. Real algebraic and analytic sets. Rigid and p-adic analytic spaces. Tropical geometry.
Derived categories and non-commutative geometry.
Connections with sections 2, 3, 5, 6, 7, 8, 11, 13, 14.
- András Némethi (Hungary) – joint with section 6
- Carolina Araujo (Brazil)
- Caucher Birkar (UK)
- Chenyang Xu (China)
- Dan Abramovich (USA)
- Georgios Pappas (USA) – joint with section 3
- JongHae Keum (South Korea)
- Jungkai Alfred Chen (Taiwan) and Meng Chen (China)
- Krzysztof Kurdyka (France) and Wojciech Kucharz (Poland)
- Laurent Fargues (France) – joint with section 3
- Lucia Caporaso (Italy)
- Mihnea Popa (USA)
- Paul Hacking (USA) and Sean Keel (USA)
- Sébastien Boucksom (France) – joint with section 8
- Serge Cantat (France) – joint with section 9
- Zhiwei Yun (USA) – joint with section 7
Local and global differential geometry. Geometric partial differential equations and geometric flows.
Geometric structures on manifolds. Riemannian and metric geometry. Kähler geometry. Geometric aspects of group theory.
Symplectic and contact manifolds. Convex geometry. Discrete geometry.
Connections with sections 2, 4, 6, 7, 8, 9, 10, 11, 12, 13.
- Aleksandr Logunov (Israel/Russia) and Eugenia Malinnikova (Norway) – joint with section 10
- Anna Wienhard (Germany)
- Bo Berndtsson (Sweden) – joint with section 8
- Ciprian Manolescu (USA) – joint with section 6
- Denis Osin (USA)
- Emmy Murphy (USA) – joint with section 6
- Ivan Smith (UK)
- Mahan Mj (India)
- Nicolas Bergeron (France)
- Pedro Salomão (Brazil) and Umberto Hryniewicz (Brazil)
- Song Sun (USA)
- Tobias Ekholm (Sweden) – joint with section 6
Algebraic, differential and geometric topology. Stable and unstable homotopy theory. Operands and higher categories. K-theory. Motivic homotopy theory. Floer and gauge theories. Low dimensional manifolds including knot theory. Aspects of Teichmüller theory. Symplectic and contact manifolds. Topological quantum field theories.
Connections with sections 2, 4, 5, 7, 8, 9, 11.
- Alan Reid (USA)
- András Némethi (Hungary) – joint with section 4
- Andreas Thom (Germany) – joint with section 8
- Arthur Bartels (Germany)
- Bernardo Uribe Jongbloed (Colombia)
- Ciprian Manolescu (USA) – joint with section 5
- Emmy Murphy (USA) – joint with section 5
- Fanny Kassel (France)
- John Pardon (USA)
- Koji Fujiwara (Japan)
- Robert Lipshitz (USA) and Sucharit Sarkar (USA)
- Thomas Willwacher (Switzerland) – joint with section 11
- Tobias Ekholm (Sweden) – joint with section 5
7. Lie Theory and Generalizations
Algebraic and arithmetic groups. Structure, geometry, and representations of Lie groups and Lie algebras.
Related geometric and algebraic objects, symmetric spaces, buildings, vertex operator algebras, quantum groups.
Non-commutative harmonic analysis. Geometric methods in representation theory. Discrete subgroups of Lie groups.
Lie groups and dynamics, including applications to number theory.
Connections with sections 2, 3, 4, 5, 6, 8, 9, 11, 12, 13.
- Akshay Venkatesh (USA)
- Christof Geiss (Mexico) – joint with section 2
- Dipendra Prasad (India)
- Eva Viehmann (Germany)
- Michael Finkelberg (Russia)
- Olivier Schiffmann (France)
- Tomoyuki Arakawa (Japan)
- Tsachik Gelander (Israel)
- Vyacheslav Futorny (Brazil)
- Xuhua He (USA)
- Zhiwei Yun (USA) – joint with section 4
8. Analysis and Operator Algebras
Classical analysis. Real and Complex analysis in one and several variables, potential theory, quasiconformal mappings.
Harmonic analysis. Linear and non-linear functional analysis, operator algebras, Banach algebras, Banach spaces.
Non-commutative geometry, spectra of random matrices. Asymptotic geometric analysis. Metric geometry and applications.
Geometric measure theory.
Connections with sections 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16.
- Adrian Ioana (USA)
- Alexei Poltoratski (USA)
- András Máthé (UK)
- Andreas Thom (Germany) – joint with section 6
- Bill Johnson (USA)
- Bo Berndtsson (Sweden) – joint with section 5
- Christopher Bishop (USA)
- Ciprian Demeter (USA)
- Dinh Tien-Cuong (Singapore)
- Dmitry Chelkak (France/Russia) – joint with section 12
- Guido de Philippis (Italy) – joint with section 10
- Lewis Bowen (USA) – joint with section 9
- Mouhamed Moustapha Fall (Senegal)
- Richard Haydon (UK) and Spiros Argyros (Greece)
- Ruy Exel (Brazil)
- Sébastien Boucksom (France) – joint with section 4
- Stefanie Petermichl (France)
- Svitlana Mayboroda (USA)
- Wilhelm Winter (Germany)
- Yasuyuki Kawahigashi (Japan) – joint with section 11
9. Dynamical Systems and Ordinary Differential Equations
Topological and symbolic dynamics. Geometric and qualitative theory of ordinary differential equations and smooth dynamical systems.
Bifurcations and singularities. Hamiltonian systems and dynamical systems of geometric origin. One-dimensional and holomorphic dynamics.
Strange attractors and chaotic dynamics. Lyapunov exponents. Multidimensional actions and rigidity in dynamics.
Ergodic theory including applications to combinatorics and combinatorial number theory. Infinite dimensional dynamical systems and
partial differential equations.
Connections with sections 5, 7, 8, 10, 11, 12, 13, 15, 16.
- Andrés Koropecki (Brazil) and Meysam Nassiri (Iran)
- Andrés Navas (Chile)
- Bassam Fayad (France) and Raphael Krikorian (France)
- Carlangelo Liverani (Italy) – joint with section 11
- Feliks Przytycki (Poland)
- Jairo Bochi (Chile)
- Jiangong You (China)
- Konstantin Khanin (Canada) – joint with section 11
- Laura DeMarco (USA)
- Lewis Bowen (USA) – joint with section 8
- Lorenzo J. Díaz (Brazil)
- Martin Möller (Germany)
- Michael Hochman (Israel)
- Miguel Walsh (Argentina) – joint with section 3
- Rafael Potrie (Uruguay)
- Sébastien Gouëzel (France)
- Serge Cantat (France) – joint with section 4
- Stéphane Nonnenmacher (France) – joint with section 10
10. Partial Differential Equations
Solvability, regularity, stability and other qualitative properties of linear and non-linear equations and systems.
Asymptotics. Spectral theory, scattering, inverse problems. Variational methods and calculus of variations.
Optimal transportation. Homogenization and multiscale problems. Relations to continuous media and control.
Modeling through partial differential equations. Stochastic partial differential equations.
Connections with sections 5, 8, 9, 11, 12, 15, 16, 17.
- Alexander Kiselev (USA)
- Aleksandr Logunov (Israel/Russia) and Eugenia Malinnikova (Norway) – joint with section 5
- Clément Mouhot (UK) – joint with section 11
- Colin Guillarmou (France)
- Diego Córdoba (Spain)
- Guido De Philippis (Italy) – joint with section 8
- Helena Nussenzveig Lopes (Brazil)
- Jean-Marc Delort (France)
- Maria Esteban (France) – joint with section 17
- Massimiliano Gubinelli (Germany) – joint with section 12
- Mohamed Majdoub (Saudi Arabia/Tunisia)
- Nader Masmoudi (USA)
- Pierre-Emmanuel Jabin (France) – joint with section 17
- Stéphane Nonnenmacher (France) – joint with section 9
- Yvan Martel (France)
- Yoshikazu Giga (Japan)
11. Mathematical Physics
Dynamical systems, including integrable systems. Equilibrium and non-equilibrium statistical mechanics,
including interacting particle systems. Partial differential equations including fluid dynamics, wave equation,
Boltzmann equation and material science. General relativity. Stochastic models and probabilistic methods including
random matrices and stochastic (partial) differential equations. Algebraic methods, including operator algebras,
representation theory and algebraic aspects of quantum field theory. Quantum mechanics and spectral theory,
including quantum chaos. Quantum information and computation. Quantum many-body theory and condensed matter physics.
Quantum field theory including gauge theories and conformal field theory. Geometry and topology in physics
including string theory and quantum gravity.
Connections with sections 2, 4, 5, 6, 7, 8, 9, 10, 12.
- Alexander Belavin (Russia)
- Benjamin Schlein (Switzerland)
- Carlangelo Liverani (Italy) – joint with section 9
- Claudio Landim (Brazil) – joint with section 12
- Clément Mouhot (UK) – joint with section 10
- Fabio Toninelli (France)
- Hugo Duminil-Copin (France/Switzerland) – joint with section 12
- Konstantin Khanin (Canada) – joint with section 9
- Philippe Di Francesco (France/USA)
- Mariya Shcherbina (Ukraine)
- Rinat Kashaev (Switzerland)
- Simone Warzel (Germany)
- Thomas Willwacher (Switzerland) – joint with section 6
- Yasuyuki Kawahigashi (Japan) – joint with section 8
- Yuji Tachikawa (Japan)
12. Probability and Statistics
Stochastic processes. Interacting particle systems. Random media. Random matrices, conformally invariant models.
Stochastic networks. Stochastic geometry. Statistical inference. High-dimensional data analysis. Spatial methods.
Connections with sections 3, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17.
- Allan Sly (USA)
- Andrea Montanari (USA)
- Bálint Tóth (Hungary/UK)
- Byeong U. Park (South Korea)
- Claudio Landim (Brazil) – joint with section 11
- Dmitry Chelkak (France/Russia) – joint with section 8
- Hugo Duminil-Copin (France/Switzerland) – joint with section 11
- Jason Miller (UK)
- Jonathan Taylor (USA)
- Josselin Garnier (France) – joint with section 17
- Liza Levina (USA)
- Massimiliano Gubinelli (Germany) – joint with section 10
- Noureddine El Karoui (USA)
- Paul Bourgade (USA)
- Peter Bühlmann (Switzerland)
- Richard Kenyon (USA) – joint with section 13
- Sem Borst (Netherlands) – joint with section 17
- Vladimir Koltchinskii (USA)
Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics.
Designs and finite geometries. Relations with linear algebra, representation theory and commutative algebra.
Topological and analytical techniques in combinatorics. Combinatorial geometry. Combinatorial number theory.
Additive combinatorics. Polyhedral combinatorics and combinatorial optimization.
Connections with sections 1, 2, 3, 4, 7, 9, 12, 14.
- Alexander Postnikov (USA)
- Balázs Szegedy (Hungary)
- Gábor Tardos (Hungary)
- Igor Pak (USA)
- József Balogh (USA) and Robert Morris (Brazil)
- June Huh (USA)
- László Babai (USA) – joint with section 14
- Maryna Viazovska (Switzerland) – joint with section 3
- Nicholas Wormald (Australia)
- Peter Keevash (UK)
- Richard Kenyon (USA) – joint with section 12
14. Mathematical Aspects of Computer Science
Complexity theory and design and analysis of algorithms. Formal languages. Computational learning.
Algorithmic game theory. Cryptography. Coding theory. Semantics and verification of programs.
Symbolic computation. Quantum computing. Computational geometry, computer vision.
Connections with sections 1, 2, 3, 4, 12, 13, 15.
- Aleksander Madry (USA)
- Andris Ambainis (Latvia)
- Benjamin Rossman (Canada)
- David Steurer (USA) and Prasad Raghavendra (USA)
- László Babai (USA) – joint with section 13
- Neeraj Kayal (India)
- Piotr Indyk (USA)
- Virginia Vassilevska-Williams (USA)
- Yael Tauman Kalai (USA)
15. Numerical Analysis and Scientific Computing
Design of numerical algorithms and analysis of their accuracy, stability, convergence and complexity. Approximation theory.
Applied and computational aspects of harmonic analysis. Numerical solution of algebraic, functional, stochastic,
differential, and integral equations.
Connections with sections 8, 9, 10, 12, 14, 16, 17.
- Anna-Karin Tornberg (Sweden)
- Barbara Wohlmuth (Germany)
- Manuel Castro (Spain) – joint with section 17
- Mike Giles (UK)
- Pingwen Zhang (China)
- Qiang Du (USA) – joint with section 17
- Raimund Bürger (Chile) – joint with section 17
- Shi Jin (China/USA) – joint with section 17
- Siddhartha Mishra (Switzerland)
- Tao Tang (China)
16. Control Theory and Optimization
Minimization problems. Controllability, observability, stability. Robotics. Stochastic systems and control.
Optimal control. Optimal design, shape design. Linear, non-linear, integer, and stochastic programming.
Inverse problems. Applications.
Connections with sections 9, 10, 12, 15, 17.
- Claudia Sagastizábal (Brazil)
- Emmanuel Trélat (France)
- Jean Bernard Lasserre (France)
- Matti Lassas (Finland)
- Philippe Toint (Belgium)
- Rekha Thomas (USA)
17. Mathematics in Science and Technology
Mathematics and its applications to physical sciences, engineering sciences, life sciences, social and economic
sciences, and technology. Bioinformatics. Mathematics in interdisciplinary research. The interplay of mathematical
modeling, mathematical analysis, and scientific computation, and its impact on the understanding of scientific
phenomena and on the solution of real life problems.
Connections with sections 9, 10, 11, 12, 14, 15, 16.
- Amit Singer (USA)
- Andrea Bertozzi (USA)
- Josselin Garnier (France) – joint with section 12
- Manuel Castro (Spain) – joint with section 15
- Maria Esteban (France) – joint with section 10
- Pierre Degond (UK)
- Pierre-Emmanuel Jabin (USA) – joint with section 10
- Qiang Du (USA) – joint with section 15
- Raimund Bürger (Chile) – joint with section 15
- Richard James (USA)
- Selim Esedoglu (USA)
- Sem Borst (USA) – joint with section 12
- Shi Jin (China/USA) – joint with section 15
18. Mathematics Education and Popularization of Mathematics
Range of research and key issues in mathematics education, from elementary school to higher education.
Modern developments in effective popularization of mathematics, from publications, to museums, to online communication.
Connections with sections 17 and 19.
Panel: Use of Lesson Study to support quality mathematics teaching
- Luis Radford (Canada)
- Mamokgethi Phakeng (South Africa)
- Mariana Bosch (Spain)
Akihiko Takahashi (USA) – moderator, Maitree Inprasitha (Thailand), Mercy Kazima (Malawi), Rongjin Huang (USA)
and Stéphane Clivaz (Switzerland).
Panel: Math museums: a worldwide explosion
Robert Firmhofer (Poland) – moderator, Albrecht Beutelspacher (Germany), Chidchanok Lursinsap (Thailand),
Cindy Lawrence (USA), Deborah Raphael (Brazil) and Sujatha Ramdorai (Canada).
Panel: New avenues for raising public awareness of mathematics
Simon Pampena (Australia) – moderator, Mariana Pereira (Uruguay), Nikolai Andreev (Russia),
Rogério Martins (Portugal), Tadashi Tokieda (USA).
19. History of Mathematics
Historical studies of all of the mathematical sciences in all periods and all cultural settings.
Connections with all the other sections, especially section 18.
- Tatiana Roque (Brazil)
- David Rowe (Germany)
- Jan von Plato (Finland)