researchseminars.org

Karim Adiprasito (Department of Mathematical Sciences, University of Copenhagen)
2021-11-01 15:00 - 16:30 UTC | https://stable.researchseminars.org/talk/IMSAC/1/
Title: Lefschetz theorems beyond Hodge structures (https://stable.researchseminars.org/talk/IMSAC/1/)
by Karim Adiprasito (Department of Mathematical Sciences, University of Copenhagen) as part of IMSAC Distinguished Lecture Series

Abstract
One of the key developments in combinatorics and algebra of recent years has been the discovery of Lefschetz principles beyond Hodge structures, resolving several long-standing conjectures. I will provide an overview over recent developments, and discuss joint work with Johanna Steinmeyer, Stavros Papadakis and Vasiliki Petrotou.

Karim Adiprasito (Department of Mathematical Sciences, University of Copenhagen)
2021-11-02 15:00 - 16:30 | https://stable.researchseminars.org/talk/IMSAC/2/
Title: Lefschetz theorems beyond Hodge structures (https://stable.researchseminars.org/talk/IMSAC/2/)
by Karim Adiprasito (Department of Mathematical Sciences, University of Copenhagen) as part of IMSAC Distinguished Lecture Series

Abstract
One of the key developments in combinatorics and algebra of recent years has been the discovery of Lefschetz principles beyond Hodge structures, resolving several long-standing conjectures. I will provide an overview over recent developments, and discuss joint work with Johanna Steinmeyer, Stavros Papadakis and Vasiliki Petrotou

Don Zagier (International Centre for Theoretical Physics)
2021-10-29 14:30 - 16:00 | https://stable.researchseminars.org/talk/IMSAC/3/
Title: From Knots to Number Theory II (https://stable.researchseminars.org/talk/IMSAC/3/)
by Don Zagier (International Centre for Theoretical Physics) as part of IMSAC Distinguished Lecture Series

Abstract
First talk: https://www.youtube.com/watch?v=Moq1pJp0f9g

Abstract
During the course of the last few years a number of startling connections between quantum invariants of knots and 3-manifolds and high-level number theory have emerged. Already the rigidity theorems of 3-dimensional hyperbolic topology, which have been known for many years, had a quite non-trivial arithmetic content, with the volume of every hyperbolic 3-manifold being linked via the dilogarithm to the so-called Bloch group and algebraic K-theory, and another connection comes from the Kashaev invariant, which is linked via his famous conjecture to the hyperbolic volume but also belongs to the so-called Habiro ring, which is a beautiful number-theoretical object that is not yet well known to number theorists. The more recent developments that I will describe concern even deeper links to algebraic number theory (construction of non-trivial units) and algebraic K-theory, to a generalization of the classical Habiro ring to Habiro rings associated to arbitrary algebraic number fields, and above all to surprising “quantum modularity” properties of the Kashaev invariant and its generalizations leading to a new type of object in the theory of modular forms. All of the work that will be reported on is joint with Stavros Garoufalidis, and some of it also with Rinat Kashaev and with Peter Scholze.

The lectures are intended for a general mathematical audience and do not require any prior knowledge of knot theory, K-theory, modular forms theory, or any other theory.

Dennis Gaitsgory (Harvard University)
2021-11-08 15:00 - 16:30 | https://stable.researchseminars.org/talk/IMSAC/4/
Title: Geometric Langlands I (https://stable.researchseminars.org/talk/IMSAC/4/)
by Dennis Gaitsgory (Harvard University) as part of IMSAC Distinguished Lecture Series

Abstract
We will start these series by reviewing the general framework of geometric Langlands correspondence, and state the main conjectures in the de Rham and Betti settings. We will also recall V. Lafforgue’s theorem about the spectral decomposition in the classical Langlands over function fields. We will then proceed to the formulation of “restricted” Langlands correspondence, which unifies the different contexts. We will state the restricted version of the geometric Langlands conjecture, and explain its relation with the classical Langlands conjecture via the operation of categorical trace.

Dennis Gaitsgory (Harvard University)
2021-11-10 15:00 - 16:30 | https://stable.researchseminars.org/talk/IMSAC/5/
Title: Geometric Langlands II (https://stable.researchseminars.org/talk/IMSAC/5/)
by Dennis Gaitsgory (Harvard University) as part of IMSAC Distinguished Lecture Series

Abstract: TBA
