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

Homotopy versus Isotopy: Spheres with Duals in 4-Manifolds, II

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Speaker: 
Rob Schneiderman and Peter Teichner
Affiliation: 
City University of New York / MPIM
Date: 
Mon, 2019-08-19 16:30 - 17:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar
This will be an experimental “Jazz session” where both of us will be explaining our recent results together.
We’ll also be encouraging audience participation and are aiming not only at 4-manifolds experts.

Homotopy versus Isotopy: Spheres with Duals in 4-Manifolds, I

Posted in
Speaker: 
Rob Schneiderman and Peter Teichner
Affiliation: 
City University of New York / MPIM
Date: 
Mon, 2019-08-19 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar
This will be an experimental “Jazz session” where both of us will be explaining our recent results together.
We’ll also be encouraging audience participation and are aiming not only at 4-manifolds experts.

"Pentagramma Mirificum". Hirzebruch lecture by Sergey Fomin on Friday, November 8, University Club Bonn

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Speaker: 
Sergey Fomin
Affiliation: 
University of Michigan
Date: 
Fri, 2019-11-08 18:00 - 19:00
Location: 
University Club Bonn

Pentagramma Mirificum (the miraculous pentagram) is a beautiful geometric construction studied by Napier and Gauss. Its algebraic description yields the simplest instance of cluster transformations, a remarkable family of recurrences which arise in diverse mathematical contexts, from representation theory and enumerative combinatorics to theoretical physics and classical geometry (Euclidean, spherical, or hyperbolic). The lecture will explore some of the most basic and concrete examples of cluster transformations, and briefly discuss their properties such as periodicity, integrability, Laurentness, and positivity. 

Sergey Fomin studied at St. Petersburg State University where he received his doctorate in 1982 with Leonid Ossipov and Anatoli Verschik. He was a lecturer at St. Petersburg Electrotechincal University (LETI) from 1982 to 1991. From 1992 to 2000 he was on the faculty at the Massachusetts Institute of Technology (Assistant Professor 1993, Associate Professor 1996) before moving to a position at the University of Michigan in 1999, where he has been Robert M. Thrall Collegiate Professor since 2007. He was also a scientist at the Institute of Computer Science and Automation of the Russian Academy of Sciences in St. Petersburg from 1991 to 2005. He was a visiting scientist at the Mittag-Leffler-Institut (1992, 2005), MSRI, the Isaac Newton Institute in Cambridge, the University of Strasbourg (IRMA), the Hausdorff Institute in Bonn, and the Erwin Schrödinger Institute for Mathematical Physics in Vienna. In 2012 he became a fellow of the American Mathematical Society. He was invited speaker at the International Congress of Mathematicians 2010 in Hyderabad. In 2018 he received the Leroy P. Steele Prize of the American Mathematical Society.

His research is on combinatorics with applications to geometry, algebra, and representation theory, where he introduced cluster algebras with Andrei Zelevinsky. He has also worked in ennumerative geometry (Schubert calculus) and mathematical physics (e.g. Yang-Baxter equation, Bethe ansatz).

Spaces, Categories, and the Cobar Construction

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Speaker: 
Mahmoud Zeinalian
Affiliation: 
The Graduate Center, CUNY Mathematics/MPIM
Date: 
Thu, 2019-08-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar
In topology, there are two ways to think about fiber bundles on connected spaces. Generally speaking, parallel transport along loops starting and ending at a basepoint gives rise to a map of groups from the loop space (i.e., the space of loops) to the group of automorphisms of the fiber. This map determines, and is determined by, the bundle. A bundle also determines, and is determined by, a map of spaces from its base to the classifying space of the automorphisms of its fibre. 

Thinking of fiber bundles in two ways establishes a duality between connected spaces and groups. Every space has a loop space, which is a group, and every group has a classifying space, which is a space. Moreover, the classifying space of the loop space of a space is the space itself, and the loop space of the classifying space of the group is the group itself.

In algebra, one half of this duality assigns to a coalgebra (an avatar of a space) an algebra (an avatar of a group). This assignment, known as the cobar construction, was introduced in a 1956 paper of Frank Adams under the assumption of simply-connectedness. A deeper look at the categorical meaning of the construction reveals that the simply-connectedness assumption can be removed. This is joint work with Manuel Rivera which started when he visited the Max-Planck-Institute for a week in 2016. Some newer results are with Manuel Rivera and Felix Wierstra whom I met at Max-Planck last year.

The Hodge and de Rham Chern characters of holomorphic connections, II

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Speaker: 
Mahmoud Zeinalian
Affiliation: 
CUNY/MPIM
Date: 
Mon, 2019-08-12 16:30 - 17:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Joint with Cheyne Glass, Micah Miller, and Thomas Tradler.

In the first part of the talk, I will describe the formulae for the Hodge and de Rham characteristic classes of holomorphic bundles solely in terms of their clutching functions. To do so, I define a map of simplicial presheaves, the Chern character, that assigns to every sequence of composable isomorphisms of vector bundles with holomorphic connections that do not necessarily preserve the connections, an appropriate sequence of holomorphic forms. We then apply this map of simplicial presheaves to the Cech nerve of a cover of a complex manifold and assemble the data by passing to the totalization. In this way, we obtain a map of simplicial sets that on the vertices produces an explicit formula for the Hodge Chern character of a bundle in terms of its clutching functions. On the edges, we obtain similar invariants associated to isomorphisms between bundles. Similarly, we obtain suitable Hodge and de Rham Chern characters in the equivariant setting.

The Hodge and de Rham Chern characters of holomorphic connections, I

Posted in
Speaker: 
Mahmoud Zeinalian
Affiliation: 
CUNY/MPIM
Date: 
Mon, 2019-08-12 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Joint with Cheyne Glass, Micah Miller, and Thomas Tradler.

In the first part of the talk, I will describe the formulae for the Hodge and de Rham characteristic classes of holomorphic bundles solely in terms of their clutching functions. To do so, I define a map of simplicial presheaves, the Chern character, that assigns to every sequence of composable isomorphisms of vector bundles with holomorphic connections that do not necessarily preserve the connections, an appropriate sequence of holomorphic forms. We then apply this map of simplicial presheaves to the Cech nerve of a cover of a complex manifold and assemble the data by passing to the totalization. In this way, we obtain a map of simplicial sets that on the vertices produces an explicit formula for the Hodge Chern character of a bundle in terms of its clutching functions. On the edges, we obtain similar invariants associated to isomorphisms between bundles. Similarly, we obtain suitable Hodge and de Rham Chern characters in the equivariant setting.

tba

Posted in
Speaker: 
David Gay
Affiliation: 
University of Georgia/MPIM
Date: 
Thu, 2019-08-29 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Colloquium
Parent event: 
MPI-Oberseminar

Persistent homology (from a mathematical point of view)

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Speaker: 
Grégory Ginot
Affiliation: 
Université Paris 13, Institut Galilée/MPIM
Date: 
Thu, 2019-08-22 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

The goal of the talk is to present the basics of persistent homology which is one of the primary tools in  applied algebraic topology and topological data analysis.
We hope to explain the mathematical ideas behind it, some of its current challenges and relations to sheaf theory.

Fibre surfaces, knots, and elastic strings

Posted in
Speaker: 
Filip Misev
Affiliation: 
MPIM
Date: 
Thu, 2019-08-08 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Colloquium
Parent event: 
MPI-Oberseminar

tba

Posted in
Speaker: 
Xianchang Meng
Organiser(s): 
Universität Göttingen/MPIM
Date: 
Wed, 2019-08-28 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

On a mean value result for a product of L-functions

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Speaker: 
Nicole Raulf
Affiliation: 
Université de Lille
Date: 
Wed, 2019-08-21 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

The asymptotic behaviour of moments of L-functions is of special interest to number theorists and there
are conjectures that predict the shape of the moments for families of L-functions of a given symmetry type.
However, only some results for the first few moments are known. In this talk we will consider the asymptotic
behaviour of the first moment of the product of a Hecke L-function and a symmetric square L-function
in the weight aspect. This is joint work with  O. Balkanova, G. Bhowmik, D. Frolenkov. 

Higher structures in rational homotopy theory, II

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Speaker: 
José Manuel Moreno-Fernandez
Affiliation: 
MPIM
Date: 
Mon, 2019-08-05 16:30 - 17:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar
I will explain how L-infinity structures on the rational homotopy groups relate to higher Whitehead products, how A-infinity structures in cohomology algebras relate to Massey higher products (no need for rational coefficients here) and give an extension of the classical Milnor-Moore theorem for rational spaces to the infinity-algebras setting.
 

Higher structures in rational homotopy theory, I

Posted in
Speaker: 
José Manuel Moreno-Fernandez
Affiliation: 
MPIM
Date: 
Mon, 2019-08-05 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar
I will explain how L-infinity structures on the rational homotopy groups relate to higher Whitehead products, how A-infinity structures in cohomology algebras relate to Massey higher products (no need for rational coefficients here) and give an extension of the classical Milnor-Moore theorem for rational spaces to the infinity-algebras setting.
 

From almost purity to functional analysis

Posted in
Speaker: 
Peter Scholze
Affiliation: 
Universität Bonn/MPIM
Date: 
Wed, 2019-08-07 14:30 - 15:45
Location: 
MPIM Lecture Hall
Parent event: 
Special colloquium

Faltings' almost purity theorem asserts that, in p-adic geometry, things become simpler when passing to certain highly ramified, largely non-geometric, coverings. The coverings in question are somewhat akin to covering an interval by a Cantor set. I will show how embracing this idea has led us (with Dustin Clausen) to recast the basic notions of topology, leading to a better setup in which to do algebra with topological groups.

Perturbing an isoradial triangulation

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Speaker: 
Jeanne Scott
Affiliation: 
Universidad de los Andes
Date: 
Tue, 2019-09-24 14:00 - 15:00
Location: 
MPIM Lecture Hall

The theory of random Delaunay triangulations of the plane has been proposed by
David-Eynard and others as a discrete model for 2-dimensional quantum gravity: In this model
the role of a continuous metric is played by a Delaunay triangulation while flat metrics
correspond to isoradial triangulations (on which one can define a theory of discrete analyticity).
Like the continuous case, the partition function for this discrete theory is given by a suitably
normalized determinant of a Beltrami-Laplace operator which varies with the choice of
triangulation. An elegant formula of Richard Kenyon expresses this determinant as a finite sum
of local contributions when the triangulation is both isoradial and periodic. In joint work with
François David we consider smooth perturbations of a periodic isoradial triangulation and obtain
an asymptotic expansion for the second variation of the log-determinant of the discrete
Beltrami-Laplace operator. This result can be interpreted as a discretization of the formula for
the second variation (of the logarithm) of the continuous partition function know from conformal
field theory; using this interpretation we can identify the central charge in this discrete setting.

"surprise"

Posted in
Speaker: 
surprise
Date: 
Tue, 2019-07-30 17:30 - 18:30
Location: 
MPIM Lecture Hall

Algebraic geometry of the Lagrangian correspondence of Gaiotto

Posted in
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]. Later, it was noticed in [3] that the analysis method established in [2] can be applied to the scaling limit of Gaiotto for more general stable Higgs bundles when G = SL(n), and a correspondence between certain holomorphic Lagrangians in the moduli of Higgs bundles and the moduli of holomorphic connections on a curve was discovered.
 
In this talk, I will review the known results and present the Lagrangian correspondence in the language of algebraic geometry, in the spirit of Variation of Hodge Structures of Simpson [4], modeled after SL(n)-opers.
 
[1] D. Gaiotto: Opers and TBA (2014)
[2] O. Dumitrescu, L.Fredrickson, G. Kydonakis, R. Mazzeo, M. Mulase, and A. Neitzke: From the Hitchin section to opers through nonabelian Hodge, J. Diff. Geom., to appear
[3] B. Collier and R. Wentworth: Conformal limits and the Bialyncki-Birula stratification of the space of lambda-connections, Adv. Math., to appear
[4] C. Simpson: Iterated destabilizing modifications for vector bundles with connections (2010)
 

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

Posted in
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.

In particular, we will focus on Joyal duality to give a simple explanation of the co-product given by Goncharov
for multi-zeta values and its graphical depiction. In this setting, co-actions also appear naturally. We further show that
his type of Hopf algebracomes from a categorical setup, where the product is a monoidal product and the co-product is
dual to the partial productthat is  given by composition of morphisms, providing a simple "raison d'être" for these
"prima vista" complicated co-products. In this setting, we see the analogous structure of the Hopf algebra of Goncharov
and those of Connes and Kreimer.

On Hecke eigenvalues of Maass cusp forms

Posted in
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

For a Hecke-Maass newform F of level N and with pth Hecke eigenvalue a(p) where p is a prime, the generalized Ramanujan conjecture
asserts that a(p) is bounded by 2 in the absolute value for ( p, N) = 1. In this talk we will survey the recent results and developments
centered on this intriguing problem.

Rationality of Fano 3-folds over nonclosed fields

Posted in
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).

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