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Talks and seminars, possibly part of a conference or series.

The Beauville-Voisin conjecture for Hilb(K3) and the Virasoro algebra

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Speaker: 
Andrei Negut
Affiliation: 
MIT
Date: 
Thu, 2019-07-04 10:30 - 12:00
Location: 
MPIM Lecture Hall

We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of K3 surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes. Our approach involves lifting formulas of Lehn and Li-Qin-Wang from cohomology to Chow groups, and using them to solve the problem by invoking the irreducibility criteria of Virasoro algebra modules, due to Feigin-Fuchs. Joint work with Davesh Maulik.

DAHA approach to algebraic knots and links

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Speaker: 
Ivan Cherednik
Affiliation: 
(ETH-ITS/UNC at Chapel Hill)
Date: 
Wed, 2019-07-24 14:00 - 15:00
Location: 
MPIM Seminar Room
Parent event: 
Extra talk

DAHA generally provide refined invariants of colored iterated links, which generalize the
WRT-invariants and HOMFLY-PT polynomials. In the uncolored case and for iterated knots,
they are conjectured to coincide with the stable reduced Khovanov-Rozansky polynomials (the most
powerful numerical invariants we have). The "intrinsic" DAHA conjectures are mostly verified
at the moment; these properties are generally difficult to check topologically. The DAHA super-

Vertex Operator Algebras and Modular Forms

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Speaker: 
Don Zagier
Affiliation: 
MPIM
Date: 
Tue, 2019-07-02 16:30 - 18:00
Location: 
MPIM Lecture Hall

Time: Tuesdays, 4.30 - 6 pm
Place: MPIM Lecture Hall, Vivatsgasse 7
First lecture: on April 2, 2019, end on July 2

Recent developments in Quantum Topology

Posted in
Speaker: 
Stavros Garoufalidis
Affiliation: 
MPIM
Date: 
Tue, 2019-07-02 12:30 - 14:00
Location: 
MPIM Lecture Hall

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

The singular (co)chains and rational homotopy theory, II

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Speaker: 
Felix Wierstra
Affiliation: 
MPIM
Date: 
Mon, 2019-07-01 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The central theme of this talk is the question: How much of the rational homotopy type of a space can we deduce from the (co)chains on the space? More precisely, in this talk we explain what the relationship is between the singular (co)chains and various approaches to the rational homotopy theory. 

The singular (co)chains and rational homotopy theory, I

Posted in
Speaker: 
Felix Wierstra
Affiliation: 
MPIM
Date: 
Mon, 2019-07-01 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The central theme of this talk is the question: How much of the rational homotopy type of a space can we deduce from the (co)chains on the space? More precisely, in this talk we explain what the relationship is between the singular (co)chains and various approaches to the rational homotopy theory. 

On Graphs of Hecke operators and Hall algebras

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Speaker: 
Roberto Alvarenga
Affiliation: 
University of Sao Paolo, Sao Carlos/University of California, Irvine
Date: 
Thu, 2019-06-27 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

In Bombay 1979, Don Zagier observes that if the kernel of certain
operators on automorphic forms turns out to be an unitarizable
representation, over the field of rational numbers $Q$, a formula of Hecke implies the Riemann hypothesis.

Zagier calls the elements of this kernel toroidal automorphic forms.
Moreover, Zagier asks what happens if $Q$ is replaced by a global function field and remarks that  the space of unramified toroidal automorphic forms can be expected to be finite dimensional.

Deformations of VB-groupoids

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Speaker: 
Pier Paolo La Pastina
Affiliation: 
La Sapienza, Rome
Date: 
Thu, 2019-07-04 13:30 - 15:00
Location: 
MPIM Lecture Hall

VB-groupoids can be understood as vector bundles in the category of Lie groupoids. They encompass several classical objects, such as Lie group representations, 2-vector spaces, Lie group actions on vector bundles; moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids, in particular the adjoint representation. In this talk, I will attach to every VB-groupoid a cochain complex controlling its deformations and discuss some features, such as Morita invariance, as well as some examples and applications.

Hochschild cohomology and deformation quantization of affine toric varieties

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Speaker: 
Matej Filip
Affiliation: 
Johannes Gutenberg-Universität Mainz
Date: 
Thu, 2019-06-27 09:15 - 10:15
Location: 
MPIM Lecture Hall
Parent event: 
Extra talk

For an affine toric variety we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Moreover, we show that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization.

Semistability and Approximate Hermitian-Einstein Structures

Posted in
Speaker: 
Johannes Schäfer
Affiliation: 
MPIM
Date: 
Fri, 2019-06-28 10:15 - 11:45
Location: 
MPIM Seminar Room

tba

Posted in
Speaker: 
Rafael Herrera
Affiliation: 
CIMAT, Mexico
Date: 
Wed, 2019-08-07 10:30 - 12:00
Location: 
MPIM Lecture Hall

Frobenius lifts and correspondences on GL_n

Posted in
Speaker: 
Alexandru Buium
Affiliation: 
University of New Mexico/MPIM
Date: 
Wed, 2019-07-03 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Let GL_n be the general linear group scheme over the integers.We show that the p-adic completion of GL_n possessescertain remarkable Frobenius lifts attached to integral symmetric matrices; these Frobenius liftscan be viewed as  arithmetic analogues, for Spec Z,  of the Levi-Civita connection attached to a metric on a manifold. We then show how these Frobeniuslifts admit algebraizations by correspondences on GL_n; the commutatorsof these correspondences can be viewed as an arithmetic analogue, for Spec Z, of Riemannian curvature. 

tba

Posted in
Speaker: 
Ralph Kaufmann
Affiliation: 
Purdue University West Lafayette
Date: 
Tue, 2019-07-09 13:50 - 14:50
Location: 
MPIM Lecture Hall

Vertex Operator Algebras and Modular Forms

Posted in
Speaker: 
Don Zagier
Affiliation: 
MPIM
Date: 
Tue, 2019-06-25 16:30 - 18:00
Location: 
MPIM Lecture Hall

Time: Tuesdays, 4.30 - 6 pm
Place: MPIM Lecture Hall, Vivatsgasse 7
First lecture: on April 2, 2019, end on July 2

Recent developments in Quantum Topology

Posted in
Speaker: 
Stavros Garoufalidis
Affiliation: 
MPIM
Date: 
Tue, 2019-06-25 12:30 - 14:00
Location: 
MPIM Lecture Hall

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

Recent developments in Quantum Topology

Posted in
Speaker: 
Stavros Garoufalidis
Affiliation: 
MPIM
Date: 
Tue, 2019-06-18 12:30 - 14:00
Location: 
MPIM Lecture Hall

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

Vertex Operator Algebras and Modular Forms

Posted in
Speaker: 
Don Zagier
Affiliation: 
MPIM
Date: 
Tue, 2019-06-18 16:30 - 18:00
Location: 
MPIM Lecture Hall

Time: Tuesdays, 4.30 - 6 pm
Place: MPIM Lecture Hall, Vivatsgasse 7
First lecture: on April 2, 2019, end on July 2

Registration

Posted in
Date: 
Mon, 2019-07-08 08:30 - 09:30

Program discussion

Posted in
Date: 
Tue, 2019-07-09 12:00 - 12:30
Location: 
MPIM Lecture Hall

Program discussion

Posted in
Date: 
Mon, 2019-07-08 12:00 - 12:30
Location: 
MPIM Lecture Hall
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