Section 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. p-adic geometry. D-modules and (iso)crystals. Tropical geometry. Derived categories and non-commutative geometry.
Mina Aganagic

UC Berkeley, USA

Also in section 11

Mina Aganagic is a Professor of Mathematics and Physics at the University of California, Berkeley.

She applies string theory to problems in pure mathematics, including enumerative geometry, representation theory, geometric Langlands, and knot theory. She is known for the topological vertex approach to enumerative geometry of toric threefolds (joint with Klemm, Marino and Vafa), for refined Chern-Simons theory which conjecturally computes a refined index of knot homology theories (joint with Shakirov), for work with Andrei Okounkov on elliptic stable envelopes, and for her recent work on a unified geometric approach to knot categorification.

Aravind Asok

University of Southern California, USA

Joint lecture with Jean Fasel

Aravind Asok is a Professor of Mathematics at the University of Southern California.

His interests lie primarily in algebraic geometry and topology, in particular, the study of topology of algebraic varieties, especially using the tools of motivic homotopy theory.

Arend Bayer

University of Edinburgh, UK

Joint lecture with Emanuele-Macrì

Arend Bayer is a Professor of Algebraic Geometry at the School of Mathematics and the Maxwell Institute at The University of Edinburgh. His research focuses on applications of derived categories, in particular to questions of classical flavour in algebraic geometry. Jointly with Macrì, he established wall-crossing as a tool to study birational geometry of moduli spaces and related questions.
Ana Caraiani

Imperial College London, UK

Also in section 3

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.

Alexander Efimov

Steklov Mathematical Institute of RAS and HSE, Russia

Also in section 2

Alexander Efimov is currently a Senior Researcher at the Algebraic Geometry Section of Steklov Mathematical Institute of RAS, Moscow, Russia.

He is also a member of the International Laboratory of Mirror Symmetry and Automorphic Forms, Higher School of Economics, Moscow, Russia. His research interests include algebraic geometry, derived categories, mirror symmetry, and quantum algebra. He is a winner of the 2020 EMS Prize and an invited speaker at the 2020/2021 European Congress of Mathematics.

Barbara Fantechi

SISSA, Italy

Barbara Fantechi is a Professor of Geometry at Sissa, Italy. She works in algebraic geometry with a focus on moduli problems, infinitesimal deformation theory, and enumerative geometry. Her most influential work, joint with Kai Behrend, is the definition of the virtual fundamental class associated with a perfect obstruction theory. She has been a visiting professor jointly at KTH Stockholm and Mittag-Leffler Institute, Hirzebruch Research Chair at MPI Bonn, Chancellor’s Professor at MSRI Berkeley, and has received the Romagnosi Prize from Università di Trento and Tartufari Prize from Accademia dei Lincei, Rome.
Jean Fasel

Institut Fourier, France

Joint lecture with Aravind Asok

Jean Fasel is a Professor of Mathematics at the Institut Fourier in Grenoble. He is interested in motivic homotopy theory, algebraic cycles and their applications to problems of algebro-geometric origins.
Ofer Gabber

Université Paris-Saclay, IHES, CNRS, France

Ofer Gabber is a directeur de recherche at CNRS who contributes to various topics in algebra and algebraic geometry, such as étale cohomology, logarithmic geometry, alterations of schemes and the theory of pseudo-reductive groups.

Recently, Ofer Gabber continues his numerous collaborations with several researchers, in particular, applications of perfectoid techniques in commutative algebra were included in his work with Lorenzo Ramero, or with Adrian Vasiu with whom he worked on the Barsotti-Tate groups.

Ofer Gabber has also made progress on duality in p-adic Hodge theory, as well as results on Picard groups.

Neena Gupta

Indian Statistical Institute, India

Also in section 2

Neena Gupta is an Associate Professor at the Theoretical Mathematics and Statistics Unit of the Indian Statistical Institute, Kolkata, India. Her research interests are in commutative algebra and in affine algebraic geometry.

She is interested in problems on affine fibrations, finite generation of subrings of polynomial rings, cancellation, characterisation and epimorphism problems on affine spaces, locally nilpotent derivations and G_a-actions on affine varieties, and allied topics.

She is known for providing a complete solution to the Zariski Cancellation Problem for affine spaces in positive characteristic. She has developed a general theory on a certain family of affine threefolds which reveals surprising connections between various problems on affine spaces. Solutions to certain central questions in affine algebraic geometry now appear as natural consequences of her theory.

She is a Fellow of the Indian Academy of Sciences and a recipient of the Shanti Swarup Bhatnagar Prize in Mathematical Sciences awarded by the Council of Scientific and Industrial Research (CSIR), Government of India.

Tamas Hausel

Institute of Science and Technology Austria, Klosterneuburg, Austria

Tamas Hausel is a Professor of Mathematics and a group leader at the Institute of Science and Technology Austria. He studies the geometry of moduli spaces in non-Abelian Hodge theory of a curve, moduli spaces of Higgs bundles, character varieties, and other hyperkähler moduli spaces such as Nakajima quiver varieties and toric hyperkähler varieties. He has found several connections of such studies to mirror symmetry, arithmetic, representation theory, algebraic combinatorics, and singularity theory.

Bruno Klingler

Humboldt Universitat zu Berlin, Germany

Also in section 3

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

The University of Duisburg-Essen, Germany

Survey lecture on motivic cohomology

Jointly in sections 2, 3, 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).

Chi Li

Rutgers University, USA

Also in section 5

Chi Li is an associate professor at the Department of Mathematics of Rutgers University — New Brunswick.

He worked at Purdue University between 2015-2020. His interests include canonical metrics in Kähler geometry, stability theory of algebraic varieties, and pluripotential theory.

Emanuele Macrì

Université Paris-Saclay, France

Joint lecture with Arend Bayer

Emanuele Macrì is a Professor of Mathematics at the Laboratoire de mathématiques d’Orsay, Université Paris-Saclay.

His research area is algebraic geometry, mostly concerning derived categories of coherent sheaves and moduli spaces.

Aaron Pixton

University of Michigan, USA

Aaron Pixton is an Assistant Professor at the University of Michigan, Ann Arbor.

He is interested in algebraic geometry, especially enumerative problems and associated moduli spaces. He is particularly interested in cohomology classes on the moduli space of stable curves.

Yuri Prokhorov

Steklov Mathematical Institute of RAS, Russia

Yuri Prokhorov is a Principal Researcher at the Algebraic Geometry Section of Steklov Mathematical Institute in Moscow. He also is a member of the Laboratory of Algebraic Geometry, HSE University and holds a Professorship position at the Faculty of Mathematics and Mechanics of the Lomonosov Moscow State University.

His interests include birational algebraic geometry, classification of algebraic varieties, and the minimal model (Mori) program. In particular, he is known for his works on Fano varieties, Mori fibre spaces, and higher-dimensional Cremona groups.

He is a corresponding member of the Russian Academy of Sciences, an associate member of POSTECH Mathematics Institute (S. Korea), and the winner of the Shuvalov Prize (2002).

Olivier Wittenberg

CNRS & Université Sorbonne Paris Nord, France

Olivier Wittenberg is a CNRS senior scientist currently at Laboratoire Analyse, Géométrie et Applications de l’Université Sorbonne Paris Nord.

His interests include number theory and algebraic geometry, as well as any topic related to algebraic cycles. In recent years he has worked on problems in number theory and in real algebraic geometry emerging from the study of rational points and rational curves on rationally connected varieties.

Peter Zograf

St. Petersburg Department of the Steklov Mathematical Institute and St. Petersburg University, Russia

Jointly in sections 6, 9

Peter Zograf is a Leading Researcher at St.Petersburg Department of the Steklov Mathematical Institute and a Chief Researcher at the Chebyshev Laboratory of St.Petersburg University. His research interests include mathematical physics, geometry of moduli spaces, and enumerative combinatorics.
Wed Nov 17 2021 17:44:40 GMT+0300 (Moscow Standard Time)