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

"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).

tba

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Speaker: 
Adam Morgan
Affiliation: 
MPIM
Date: 
Wed, 2019-12-18 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Boundary-adapted arithmetic random waves

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Speaker: 
Oleksiy Klurman
Affiliation: 
KTH Stockholm/MPIM
Date: 
Tue, 2019-11-12 14:00 - 15:00
Location: 
MPIM Lecture Hall
In this talk, we test M. Berry's ansatz on nodal deficiency in presence of boundary.

General quantization scheme for symplectic manifolds which admit Kähler structures

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Speaker: 
Jørgen Ellegaard Andersen
Affiliation: 
QGM Aarhus
Date: 
Wed, 2019-10-23 10:30 - 12:00
Location: 
MPIM Lecture Hall

We will consider arbitrary holomorphic families of Kähler structures on a fixed prequantizable symplectic manifold and provided the corresponding family of Kähler quantisations for level k form a vector bundle over the chosen family of Kähler structures, we will for large enough k construct a large family of Hitchin connections in this bundle. We will also consider a natural family of Hermitian structures on the bundle of quantum spaces and understand which (unique) Hitchin connection is compatible with a given one of these Hermitian structures.

Lattice points, Ehrhart theory, and the relation to volumes

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Speaker: 
Reinier Kramer
Affiliation: 
MPIM
Date: 
Tue, 2019-10-22 10:00 - 11:30
Location: 
MPIM Seminar Room

Continuing from the previous session, we will define the valuation for exponential sums, a discrete analogue of exponential integrals, and obtain another version of Brion's theorem. We continue to Ehrhart theory, showing polynomiality of lattice counts for polytopes with fixed cones of feasible directions. Finally, we relate exponential sums and exponential integrals via an Euler-Maclaurin type formula.

Automorphisms and Periods of Cubic Fourfolds

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Speaker: 
Zhiwei Zheng
Affiliation: 
MPIM
Date: 
Thu, 2019-10-24 10:30 - 12:00
Location: 
MPIM Lecture Hall

Cubic fourfold plays a central role in algebraic geometry because of its close relation to hyper-Kahler geometry. In this talk I will start with this relation and discuss the Hodge theory and moduli theory for cubic fourfolds. Then I will introduce an application of the above theories, namely, a complete classification of the symplectic automorphism groups of smooth cubic fourfolds. This work can be regarded as a higher dimensional analogue of Mukai's celebrated result on classification of finite symplectic automorphism groups of K3 surfaces. This is a joint work with Radu Laza.

New guests at the MPIM

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Speaker: 
Emiliano Ambrosi, William Olson, Wee Chaimanowong
Date: 
Thu, 2019-10-24 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Splitting theorems for configuration spaces

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Speaker: 
Tashi Walde
Affiliation: 
MPIM
Date: 
Wed, 2019-10-23 16:15 - 17:45
Location: 
MPIM Seminar Room

Formal groups

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Speaker: 
Gerd Faltings
Affiliation: 
MPIM
Date: 
Mon, 2019-10-21 13:30 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
IMPRS Minicourse

Trisections in CP^2, I

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Speaker: 
Peter Lambert-Cole
Affiliation: 
Georgia Institute of Technology (GIT)/MPIM
Date: 
Mon, 2019-10-28 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In the first hour, I will describe the standard trisection of CP^2 and how to put complex curves in CP^2 into bridge position with respect to this trisection.  Time permitting, I will also present trisections of projective surfaces obtained as a branched covers over these curves.  In the second hour, I will describe how to compute the homology and intersection form from a trisection diagram.

Some recent results of free boundary minimal hypersurfaces

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Speaker: 
Zhichao Wang
Affiliation: 
Peking University/MPIM
Date: 
Thu, 2019-10-24 13:00 - 14:00
Location: 
MPIM Lecture Hall

In this talk, I will introduce some recent developments of free boundary minimal hypersurfaces, including compactness, generic finiteness and index estimates. As an application, we also give the existence of infinitely many minimal hypersurfaces with non-empty free boundary under some weak assumptions. Part of the work is joint with Q.Guang, M.Li and X.Zhou.

Trisections in CP^2, II

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Speaker: 
Peter Lambert-Cole
Affiliation: 
Georgia Institute of Technology (GIT)/MPIM
Date: 
Mon, 2019-10-28 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

In the first hour, I will describe the standard trisection of CP^2 and how to put complex curves in CP^2 into bridge position with respect to this trisection.  Time permitting, I will also present trisections of projective surfaces obtained as a branched covers over these curves.  In the second hour, I will describe how to compute the homology and intersection form from a trisection diagram.

Resonant spaces for volume-preserving Anosov flows

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Speaker: 
Mihajlo Cekic
Affiliation: 
MPIM
Date: 
Thu, 2019-11-21 13:00 - 14:00
Location: 
MPIM Lecture Hall

Cohomology of arithmetic groups - A specific -highly non trivial- example

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Speaker: 
Günter Harder
Affiliation: 
MPIM
Date: 
Tue, 2019-10-22 16:30 - 18:00
Location: 
MPIM Lecture Hall

Mapping class groups of highly connected manifolds, II

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Speaker: 
Manuel Krannich
Affiliation: 
University of Cambridge, UK
Date: 
Mon, 2019-10-21 16:30 - 17:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The classical mapping class group Γ(g) of a surface of genus g shares many features with its higher dimensional analogue Γ(g,n)—the group of isotopy classes of diffeomorphisms of #ᵍ(Sⁿ x Sⁿ)—but some aspects become easier in high dimensions. This enabled Kreck in the 70’s to describe Γ(g,n) for n>2 in terms of an arithmetic group and the group of exotic spheres. His answer, however, left open two extension problems which were later understood in some dimensions, but remained unsettled in most cases.

Mapping class groups of highly connected manifolds, I

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Speaker: 
Manuel Krannich
Affiliation: 
University of Cambridge, UK
Date: 
Mon, 2019-10-21 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

The classical mapping class group Γ(g) of a surface of genus g shares many features with its higher dimensional analogue Γ(g,n)—the group of isotopy classes of diffeomorphisms of #ᵍ(Sⁿ x Sⁿ)—but some aspects become easier in high dimensions. This enabled Kreck in the 70’s to describe Γ(g,n) for n>2 in terms of an arithmetic group and the group of exotic spheres. His answer, however, left open two extension problems which were later understood in some dimensions, but remained unsettled in most cases.

Specializations of the Burau representation at roots of unity

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Speaker: 
Tyakal Venkataramana
Affiliation: 
TIFR/MPIM
Date: 
Tue, 2019-10-22 14:00 - 15:00
Location: 
MPIM Lecture Hall

The Burau representation and its specialisations at roots of unity are closely related to monodromy representations associated to families of cyclic coverings of a fixed degree of the projective line. If the number of ramifications is small relative to the degree, Deligne and Moscow constructed non arithmetic monodromy using these families. We show

Quasi Isometries

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Speaker: 
Shi Wang
Affiliation: 
MPIM
Date: 
Thu, 2019-10-24 10:15 - 11:45
Location: 
MPIM Seminar Room

Estimates for the Artin conductor

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Speaker: 
Amalia Pizarro
Affiliation: 
Universidad de Valparaíso/MPIM
Date: 
Wed, 2019-10-23 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

By using geometry of numbers, Minkowski showed that there exists a constant C such that if D_K is the discriminant of a number field K, then |D_K|>C^[K:Q]. In 1978, from the existence of  infinite class field towers, Martinet constructed  sequences of number fi elds of growing degree and  bounded root discriminant.

It is natural to ask if it is possible to extends the previous results to the Artin conductor.

Trisections and branched covers of S^4, I

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Speaker: 
Alexandra Kjuchukova
Affiliation: 
MPIM
Date: 
Mon, 2019-10-14 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar
I will give a generalization of triplane diagrams to describe embeddings of surfaces in S^4 which have isolated cone singularities. Given a singular surface F\subset S^4, a triplane diagram for F allows us to produce a trisection of a dihedral cover of S^4 branched along F.
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