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Talk

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

Algebraic geometry of the Lagrangian correspondence of Gaiotto

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Speaker: 
Motohico Mulase
Affiliation: 
UC Davis/MPIM
Date: 
Tue, 2019-08-20 15:00 - 16:00
Location: 
MPIM Lecture Hall
From a consideration of N=2 SUYM in four dimensions, Gaiotto [1] has conjectured that a certain scaling limit of twister lines in the space of G-Higgs bundles converge to an oper. For holomorphic G-Higgs bundles, the conjecture has been settled for an arbitrary simply connected algebraic group G in 2016 in a joint paper with my collaborators [2].

A simplicial and categorical background for Hopf algebras in number theory and physics

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Speaker: 
Ralph Martin Kaufmann
Affiliation: 
Purdue University, West Lafayette/MPIM
Date: 
Thu, 2019-07-25 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

We will discuss how simplicial  and categorical structures lead to Hopf algebras.

tba

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Speaker: 
Wenzhi Luo
Affiliation: 
The Ohio State University
Date: 
Tue, 2019-08-06 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Rationality of Fano 3-folds over nonclosed fields

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Speaker: 
Yuri Prokhorov
Affiliation: 
Steklov Mathematical Institute, Moscow/MPIM
Date: 
Tue, 2019-08-27 14:00 - 15:00
Location: 
MPIM Lecture Hall

The rationality problem for smooth Fano threefolds over algebraically closed fields is basically solved.
In this talk I will discuss rationality  of forms of these  Fanos over nonclosed fields of characteristic 0.
I will concentrate on the case where the  Picard number  equals 1.

The talk is based on joint work with Alexander Kuznetsov (in progress).

Harmonic analysis on GLn over finite fields

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Speaker: 
Shamgar Gurevich
Affiliation: 
University of Wisconsin-Madison/MPIM
Date: 
Tue, 2019-08-20 14:00 - 15:00
Location: 
MPIM Lecture Hall

There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:

Deformations of Abelian categories in algebra, geometry & physics

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Speaker: 
Severin Barmeier
Affiliation: 
Universität Münster/MPIM
Date: 
Tue, 2019-08-13 14:00 - 15:00
Location: 
MPIM Lecture Hall

W. Lowen and M. Van den Bergh developed a deformation theory for Abelian categories, such that deformations of the category of (quasi)coherent sheaves on an affine variety Spec A correspond to deformations of the algebra A, which in turn are controlled by the Hochschild cochain complex equipped with the Gerstenhaber bracket.

Some topics in Kobayashi–Hitchin correspondences

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Speaker: 
Takuro Mochizuki
Affiliation: 
RIMS Kyoto
Date: 
Wed, 2019-07-31 11:30 - 12:30
Location: 
MPIM Lecture Hall

Recently, we studied the Kobayashi–Hitchin correspondences for monopoles and harmonic bundles. In this talk, we would like to discuss some related topics. We plan to explain equivalences between twisted monopoles and twisted difference modules, generalizing the equivalences in the untwisted case. We also plan to discuss some examples of Higgs bundles to which we may apply our equivalences.

Special values of Asai L-functions

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Speaker: 
Baskar Balasubramanyam
Affiliation: 
IISER Puner
Date: 
Thu, 2019-07-18 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Unoriented topological field theory in low dimensions, II

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Speaker: 
Matthew Young
Affiliation: 
MPIM
Date: 
Mon, 2019-07-22 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

This talk is an introduction to unoriented topological field theory. I will give an overview of known examples and highlight some open problems. I will also describe a new class of examples, namely unoriented extensions of twisted Dijkgraaf-Witten theory, and the resulting topological interpretation of the character theory of categorical representations.

Quantum theta functions and signal analysis

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Speaker: 
Yuri Manin
Affiliation: 
MPIM
Date: 
Tue, 2019-07-30 15:00 - 16:00
Location: 
MPIM Lecture Hall

Representations of the celebrated Heisenberg commutation relations and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis).  In this talk I explain how Heisenberg relations bridge the noncommutative geometry and signal analysis.  After providing a brief comparative dictionary of the two languages, I will show e.g.

Knots and q-series, II

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Speaker: 
Don Zagier
Affiliation: 
MPIM
Date: 
Fri, 2019-08-02 10:30 - 11:30
Location: 
MPIM Lecture Hall

Knots and q-series, I

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Speaker: 
Stavros Garoufalidis
Affiliation: 
MPIM
Date: 
Fri, 2019-08-02 09:00 - 10:00
Location: 
MPIM Lecture Hall

Relative shifted symplectic structures

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Speaker: 
Tony Pantev
Affiliation: 
University of Pennsylvania
Date: 
Thu, 2019-08-01 17:30 - 18:30
Location: 
MPIM Lecture Hall

I will discuss the notion of relative shifted symplectic structures on sheaves of derived stacks over locally compact Hausdorff topological spaces. I will describe a general pushforward construction of relative symplectic forms and in the constructible case will
explain explicit techniques for computing such forms. As applications I will discuss a relative lift of recent results of Shende--Takeda on topological Fukaya categories, and a universal construction of symplectic structures on derived irregular character varieties. This
is a joint work with Dima Arinkin and Bertrand Toen.

Asymptotics and lower bounds for complex and real counts of singular surfaces in $\mathbb{P}^3$

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Speaker: 
Hannah Markwig
Organiser(s): 
Universität Tübingen
Date: 
Thu, 2019-08-01 16:30 - 17:20
Location: 
MPIM Lecture Hall

We use tropical geometry and floor decomposed tropical surfaces to study the asymptotics of counts of singular surfaces in $\mathbb{P}^3$ satisfying point conditions. In the real case, we give a lower bound for the number of real singular surfaces satisfying point conditions. This is joint work with Thomas Markwig, Kristin Shaw, Eugenii Shustin.

Aspects of non compact Gromov–Witten–Floer theory

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Speaker: 
Kenji Fukaya
Affiliation: 
Stony Brook
Date: 
Thu, 2019-08-01 15:00 - 15:50
Location: 
MPIM Lecture Hall

Gromov–Witten invariants and Lagrangian Floer theory for compact symplectic manifolds are now very much established as far as general theory concerns. In symplectic geometry, non-compact symplectic manifolds (such as the cotangent bundle) are as important as compact ones. There are many versions and variants for non-compact Gromov–Witten–Floer theory and many of them are still not yet completely established. In this talk, I want to explain some of such versions and issues to study them.

Motivic Donaldson–Thomas invariants of the moduli stacks of parabolic Higgs bundles and bundles with connections

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Speaker: 
Yan Soibelman
Affiliation: 
Kansas State University
Date: 
Tue, 2019-07-30 10:00 - 11:00
Location: 
MPIM Lecture Hall

Using the ideas of motivic integration I will explain how to compute the "number" of semistable Higgs bundles  (maybe with parabolic structure) of fixed rank and degree on a smooth complex curve. Based on that result I am going to discuss a similar problem in the case of bundles with connections. If time permits, I will explain open questions, including a conjectural relation to Satake correspondence for affine Grassmannians over 2-dimensional local rings. This is a joint project with Roman Fedorov and Alexander Soibelman.

Very stable Higgs bundles, the nilpotent cone and mirror symmetry

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Speaker: 
Tamas Hausel
Affiliation: 
IST Austria
Date: 
Thu, 2019-08-01 10:00 - 11:00
Location: 
MPIM Lecture Hall

I will discuss the existence of very stable Higgs bundles how it implies a precise formula for the multiplicity of the components of the nilpotent cone and its relationship to mirror symmetry. Joint project with Nigel Hitchin.

From the Hitchin component to opers

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Speaker: 
Laura Fredrickson
Affiliation: 
Stanford University
Date: 
Wed, 2019-07-31 16:30 - 17:20
Location: 
MPIM Lecture Hall

Let $C$ be a compact Riemann surface.  A holomorphic quadratic differential on $C$ determines a spectral curve $\Sigma$ over $C$.  Given a holomorphic quadratic differential, we can associate two types of differential operators.  One is an oper on $C$, also known as a holomorphic Schrödinger operator.

Weil–Petersson geometry and the BGW KdV tau function

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Speaker: 
Paul Norbury
Affiliation: 
University of Melbourne
Date: 
Wed, 2019-07-31 15:00 - 15:50
Location: 
MPIM Lecture Hall

It was conjectured by Witten and proven by Kontsevich that a generating function for intersection numbers on the moduli space of curves is a tau function of the KdV hierarchy, now known as
the Kontsevich–Witten tau function.  Mirzakhani reproved this theorem via the study of

Lagrangians within Higgs bundles and hyperpolygons

Posted in
Speaker: 
Laura Schaposnik
Affiliation: 
University of Illinois at Chicago
Date: 
Wed, 2019-07-31 10:00 - 11:00
Location: 
MPIM Lecture Hall

Through different group actions, we will construct Lagrangian submanifolds of the moduli space of principal Higgs bundles contained over the singular locus of the Hitchin fibration, as well as of the space of hyperpolygons. As an application, we will consider correspondences between these spaces coming from mirror symmetry as well from other dualities and correspondences. The talk is based on different pieces of work in progress with Steve Rayan, Sebastian Heller, Indranil Biswas, Steve Bradlow and Lucas Branco.

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