Section 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. P-adic analysis. Modular and automorphic forms, modular curves, and Shimura varieties. Langlands program. Zeta and L-functions. Analytic, additive and probabilistic number theory. Computational number theory and applications. Relations with logic and with physics.
Raphaël Beuzart-Plessis

Aix Marseille Université, France

Also in section 7

Raphaël Beuzart-Plessis is Chargé de Recherches at CNRS and Université d’Aix-Marseille. His primary interests lie in the field of automorphic forms and the Langlands program particularly through the use of trace formulas and other tools of harmonic analysis.
Ana Caraiani

Imperial College London, UK

Also in section 4

Ana Caraiani is a Royal Society University Research Fellow and Professor in Pure Mathematics at Imperial College London. Her research lies at the interface between the Langlands program and arithmetic geometry.

She has contributed to the theory of Shimura varieties, to the p-adic Langlands program, and to modularity lifting theorems. She has been awarded a Whitehead Prize (2018), an EMS Prize (2020), a Leverhulme Prize (2020), and is a Fellow of the AMS.

Samit Dasgupta

Duke University, USA

Joint lecture with Mahesh Kakde

Samit Dasgupta is a Professor in the Department of Mathematics at Duke University. His interests include special values of L-functions, Stark's conjectures, modular forms and their Galois representations, and the explicit construction of class fields of number fields. In particular, he is known for his joint works proving the Gross-Stark conjecture and the Brumer-Stark conjecture (away from p=2) as well as constructing class fields of totally real fields. In other works, Prof. Dasgupta has studied Darmon's constructions of Stark-Heegner points and Greenberg's exceptional zero conjectures for p-adic L-functions. Dasgupta is a prior recipient of a Sloan Research Fellowship and a CAREER award from the National Science Foundation. Professor Dasgupta's web site is available at the following link.
Alexander Gamburd

CUNY Graduate Center, USA

Alexander Gamburd is Presidential Professor of Mathematics at the Graduate Center, City University of New York.

His interests include spectral problems in number theory, probability and combinatorics, and their relations to equidistribution and pseudorandomness. In particular, he is known for the development, jointly with Jean Bourgain, of the Bourgain-Gamburd expansion machine.

He is a recipient of the Presidential Early Career Award for Scientists and Engineers, the Sloan Foundation Research Fellowship, and the von Neumann Fellowship at the Institute for Advanced Study.

Philipp Habegger

University of Basel, Switzerland

Philipp Habegger is a Professor of Mathematics at the Department of Mathematics and Computer Science of the University of Basel. His interests lie in number theory and more specifically diophantine geometry, diophantine approximation, and their connection with o-minimal geometry. He is known for his work on unlikely intersections, height functions, their interactions and applications to diophantine equations. Habegger spent a year as a von Neumann Fellow at the Institute for Advanced Study in Princeton and has held positions at the Goethe University Frankfurt and the Technical University of Darmstadt.
Atsushi Ichino

Kyoto University, Japan

Atsushi Ichino is an Associate Professor of Mathematics at the Department of Mathematics of Kyoto University. His interests include periods of automorphic forms, special values of L-functions, and representation theory of p-adic groups. In particular, he is known for the Ichino-Ikeda conjecture, which is a refinement of the global Gan-Gross-Prasad conjecture relating periods and L-values. He is also known for extending Langlands’ conjecture on Plancherel measures to express formal degrees of discrete series representations in terms of arithmetic invariants.
Tasho Kaletha

University of Michigan, USA

Also in section 7

Tasho Kaletha is a Professor of Mathematics at the Department of Mathematics of the University of Michigan.

His interests include the representation theory of real and p-adic reductive groups, the theory of automorphic representations, and the Langlands functoriality and reciprocity conjectures. In particular, he has been interested in explicit realizations of the local Langlands correspondence and in the finer properties of inner forms of reductive groups. Before joining the University of Michigan, he studied at the Universities of Bonn and Chicago and held post-doctoral positions at Princeton University and Harvard University.

Mahesh Kakde

Indian Institute of Science, Bangalore, India

Joint lecture with Samit Dasgupta

Mahesh Kakde is a Professor in the Mathematics Department at the Indian Institute of Science, Bangalore. His research is motivated by conjectures on special values of L-functions, more precisely, the Equivariant Tamagawa Number Conjecture. His recent joint works resolved the Gross-Stark conjecture, the Brumer-Stark conjecture and the tower of fields conjecture of Gross leading to explicit p-adic analytic construction of abelian extensions of totally real number fields. His earlier works include resolution of the main conjecture of non-commutative Iwasawa theory for totally real fields and the introduction of higher codimension Iwasawa theory.

Bruno Klingler

Humboldt Universitat zu Berlin, Germany

Also in section 4

Bruno Klingler is a Professor of Mathematics at Humboldt University, Berlin. His interests include complex and arithmetic geometry, in particular, Hodge theory and periods.
Dimitrios Koukoulopoulos

Universite de Montreal, Canada

Dimitrios Koukoulopoulos is a Professor of Mathematics at the Department of Mathematics and Statistics of the Université de Montréal, where he holds the Courtois Chaire II in fundamental mathematics. He works in analytic number theory, with a focus on multiplicative and probabilistic aspects of number theory, the anatomy of integers and permutations, sieve methods, diophantine approximation and additive combinatorics. In particular, he is known for a proof of the Duffin-Schaeffer conjecture in metric diophantine approximation, jointly with James Maynard; a new proof of the strongest known form of the prime number theorem for arithmetic progressions; a proof that a positive proportion of 0,1 polynomials are irreducible over the rationals, jointly with Lior Bary-Soroker and Gady Kozma.
Marc Levine

The University of Duisburg-Essen, Germany

Survey lecture on motivic cohomology

Jointly in sections 2, 4, 6

Marc Levine was born in Detroit, Michigan.

He is a Senior Professor in the Faculty of Mathematics at the University of Duisburg-Essen.

He works in algebraic geometry and algebraic topology, specialising in motivic cohomology, algebraic K-theory, algebraic cobordism, motives and motivic homotopy theory, with an interest in applications to basic problems in algebraic geometry and arithmetics.

He is a member of the Leopoldina-German National Academy of Science and the Academia Europaea, and is a recipient of the Wolfgang Paul Award (2001) and the Senior Berwick Prize (2018). He also held a Humboldt Professorship at the University of Duisburg-Essen (2009-2014).

David Loeffler

University of Warwick, UK

Joint lecture with Sarah Zerbes

David Loeffler is a number theorist at the University of Warwick, working on special values of L-functions and their connections to Galois cohomology and Iwasawa theory. He is perhaps best known for his work on Euler systems, carried out jointly with his wife Sarah Zerbes, for which the two of them were awarded a Philip Leverhulme Prize and a London Mathematical Society Whitehead Prize. In his spare time, he enjoys hiking, rock-climbing, and cave exploration. He has taken part in several expeditions to discover new caves in the Alps and in China.
Lillian Pierce

Duke University, USA

Also in section 8

Lillian Pierce is the Nicholas J. and Theresa M. Leonardy Professor of Mathematics at Duke University.

Her interests range across analytic number theory and harmonic analysis. She is known for her work on class groups of number fields, character sums, the circle method, and oscillatory integrals. Pierce has been awarded a Presidential Early Career Award for Scientists and Engineers and a Sloan Research Fellowship. She is a Fellow of the American Mathematical Society.

Joseph H. Silverman

Brown University, USA

Survey lecture on arithmetic dynamics

Also in section 9

Joseph H. Silverman is a Professor of Mathematics at Brown University.

His interests include elliptic curves, arithmetic geometry, arithmetic dynamics, and cryptography.

In particular, he is known for his numerous books on these subjects, and for being one of the founders of the field of arithmetic dynamics, a subject in which number theory and dynamical systems on algebraic varieties are intertwined. He is also a co-inventor, with Jeffrey Hoffstein and Jill Pipher, of NTRU, the first practical lattice-based public key cryptosystem.

He is a Fellow of the American Mathematical Society and a recipient of the AMS Steele prize.

Sug Woo Shin

UC Berkeley/KIAS, USA/Korea

Sug Woo Shin is a Professor of Mathematics at UC Berkeley and a visiting KIAS scholar at the Korea Institute for Advanced Study. He was a Sloan Fellow (2013-17) and a Miller Professor (2021). His research centers around the Langlands program and related topics such as Shimura varieties, Galois representations, automorphic forms, and the trace formula. He has made contributions to the global Langlands correspondence, the Langlands-Kottwitz method and its variants for Shimura varieties, as well as equidistribution problems for families of automorphic forms.
Ye Tian

Chinese Academy of Sciences, China

Ye Tian is a Professor of Mathematics at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

His interests include the arithmetic of elliptic curves, Iwasawa theory, Birch and Swinnerton-Dyer Conjecture, Goldfeld Conjecture, etc. In particular, he is known for his work on congruent number problem and CM p-converse theorem. In 2013, Ye Tian was awarded the Ramanujan Prize by ICTP and IMU, and the Morningside Gold Medal by ICCM.

Melanie Matchett Wood

Harvard University, USA

Interactions between number theory and random structures

Jointly in sections 12, 13

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.

Sarah Zerbes

ETH Zurich, Switzerland

Joint lecture with David Loeffler

Sarah Zerbes works in algebraic number theory; her main mathematical interests are Iwasawa theory and special values of L-functions. Born in Germany, she moved to the UK as an undergraduate student and completed her Ph.D. in 2005 at the University of Cambridge, under the supervision of John Coates. Since then, she has held positions at the University of Exeter and at University College London, and she will be moving to ETH Zürich in January 2022.

For her work on the Birch—Swinnerton-Dyer conjecture and its generalizations she was awarded an LMS Whitehead Prize and a Philip Leverhulme Prize, both of which she received jointly with her husband and close collaborator David Loeffler. In her spare time, Sarah enjoys rock and ice climbing, mountaineering, literature and learning to speak Latin.

Xinwen Zhu

California Institute of Technology, USA

Also in section 7

Xinwen Zhu is a professor at Caltech. His research interests lie in representation theory and arithmetic algebraic geometry. In particular, he is working at the interface of geometric and arithmetic Langlands program, by applying techniques from the geometric theory to arithmetic theory. He has been awarded an AMS centennial fellowship (2013), a Sloan fellowship (2015), an ICCM Gold Medal (2019), and a New Horizons Prize (2020).
Tue Oct 05 2021 16:02:35 GMT+0300 (Moscow Standard Time)