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

Reduction of Courant algebroids via graded manifolds

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Speaker: 
Marco Zambon
Affiliation: 
KU Leuven
Date: 
Wed, 20/03/2024 - 10:30 - 12:00
Location: 
MPIM Lecture Hall

Courant algebroids are certain objects in Lie theory that are used to define, for instance, Dirac structures and generalized complex structures. We will use the correspondence between degree 2 symplectic manifolds and Courant algebroids to approach the reduction of Courant algebroids using graded geometry. For this purpose we will consider both graded coisotropic submanifolds and a graded version of moment maps. The resulting reduction procedure, in a particular case, recovers the work of Bursztyn-Cavalcanti-Gualtieri around 2007.

Cycle Integrals of Meromorphic Hilbert Modular Forms

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Speaker: 
Paul Kiefer
Affiliation: 
Universität Bielefeld
Date: 
Wed, 20/03/2024 - 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

When considering the Doi-Naganuma lift, Zagier introduced certain Hilbert cusp forms $\omega_m^{\operatorname{cusp}}$ corresponding to positive integers $m$. A similar construction for negative $m$ yields meromorphic Hilbert modular forms $\omega_m^{\operatorname{mero}}$ with singularities along Hirzebruch-Zagier divisors. We extend the $\xi$-operator of Bruinier-Funke to Hilbert modular surfaces and define a $\xi$-preimage $\Omega_m^{\operatorname{cusp}}$ of $\omega_m^{\operatorname{cusp}}$.

Higher internal category theory

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Speaker: 
Raffael Stenzel
Affiliation: 
MPIM
Date: 
Wed, 20/03/2024 - 11:00 - 12:00
Location: 
MPIM Seminar Room

Results which concern the classification of parametrized structures over a given base by means of internal constructions within that base are fairly ubiquitous in homotopy theory. These internalization results are generally formal consequences of reflection properties of an associated externalization functor (that is, usually, some kind of Yoneda embedding). In this talk, we use a suitable externalization functor to define the $(\infty,2)$-category of $\infty$-categories internal to some base $C$.

Waring's problem: the singular series

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Speaker: 
Steve Fan
Affiliation: 
MPIM
Date: 
Mon, 18/03/2024 - 14:00 - 16:00
Location: 
MPIM Seminar Room

Some Aspects of Vertex Algebras

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Speaker: 
Paolo Tomasini
Affiliation: 
MPIM
Date: 
Wed, 20/03/2024 - 12:00 - 14:30
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Math-Phys Seminar

Vertex algebras are algebraic structures that axiomatize some aspects of conformal field theory. We will review some of the fundamentals of their theory, focusing on the interplay with CFT.

Commutative semirings and bispans

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Speaker: 
Rune Haugseng
Affiliation: 
NTNU Trondheim
Date: 
Wed, 13/03/2024 - 11:00 - 12:00
Location: 
MPIM Seminar Room

Commutative rings are commutative algebra objects in abelian groups, but they can also be viewed as models of a Lawvere theory. If we don't insist on having inverses for addition, this admits a nice description: commutative semirings are product-preserving functors to sets from a category of "bispans" of finite sets. In this talk I will explain an infinity-categorical version of this comparison; in particular, using results of Gepner-Groth-Nikolaus, we can describe connective commutative ring spectra in terms of bispans of finite sets.

Computing Heegaard Floer homology

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Speaker: 
Hongyi Zhou
Affiliation: 
MPIM
Date: 
Tue, 12/03/2024 - 11:45 - 13:00
Location: 
MPIM Lecture Hall

We will discuss standard methods to compute Heegaard Floer homology, both the knot invariant and the three manifold invariant. This talk is meant to serve as a preliminary user guide for people who are interested in applying Heegaard Floer homology in the research.

Waring's problem: the asymptotic formula

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Speaker: 
Doyon Kim
Affiliation: 
Universität Bonn
Date: 
Mon, 11/03/2024 - 14:00 - 16:00
Location: 
MPIM Seminar Room

Tubed embeddings

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Speaker: 
Anton Petrunin
Affiliation: 
Penn State
Date: 
Thu, 21/03/2024 - 16:30 - 18:00
Location: 
MPIM Lecture Hall

We consider the following question:
When does a Riemannian manifold admit an embedding with a uniformly thick tubular neighborhood in another Riemannian manifold of large dimension?

 

Computing modular polynomials by deformation

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Speaker: 
Sabrina Kunzweiler
Affiliation: 
INRIA, France
Date: 
Wed, 27/03/2024 - 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

The classical modular polynomial $\phi_\ell(X,Y) \in \mathbb{Z}[X,Y]$ parametrizes pairs of elliptic curves connected by an isogeny of degree $\ell$.
They play an important role in algorithmic number theory, and are used in many applications, for example in the SEA point counting algorithm.

In this talk, I present a new method for computing modular polynomials. It has the same asymptotic time complexity as the currently best known algorithms, but does not rely on any heuristics.

Semigroups of branched mapping classes: dynamics and geometry

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Speaker: 
Kevin Pilgrim
Affiliation: 
Indiana University, Bloomington/MPIM
Date: 
Thu, 21/03/2024 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Suppose $P \subset S^2$ is a finite subset of the sphere. The  mapping class group $\mbox{Mod}(S^2,P)$ is the countable group of orientation-preserving homeomorphisms $f:(S^2, P) \to (S^2, P)$ with $f(P)\subset P$ , up to isotopy through homeomorphisms fixing $P$ pointwise. If we allow $f$ to be instead a branched covering whose branch values are contained in $P$ with $f(P) \subset P$, we obtain a countable semigroup.

Minimal Kinematics on $\mathcal{M}_{0,n}$

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Speaker: 
Bernd Sturmfels
Affiliation: 
MPI for Mathematics in the Sciences, Leipzig
Date: 
Fri, 26/04/2024 - 11:30 - 13:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Math-Phys Seminar

Minimal kinematics identifies likelihood degenerations where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh. We characterize all choices of minimal kinematics on the moduli space $\mathcal{M}_{0,n}$. These choices are motivated by the CHY model in physics and they are represented combinatorially by 2-trees. We compute 2-tree amplitudes, and we explore extensions to non-planar on-shell diagrams, here identified with the hypertrees of Castravet-Tevelev.

3-braid knots with maximal 4-genus

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Speaker: 
Paula Truöl
Affiliation: 
MPIM
Date: 
Thu, 14/03/2024 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

This talk in the area of low-dimensional topology deals with the problem of determining the topological 4-genus for the special case of 3-braid knots. The 4-genus of a knot is the minimal genus of a "nicely" embedded surface in the 4-dimensional ball with boundary the given knot. Asking whether a knot has 4-genus zero, i.e. whether it bounds a disk in the 4-ball, is a natural generalization in dimension 4 of the question whether it is isotopic to the trivial knot.

The AKSZ construction in derived algebraic geometry as an extended topological field theory

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Speaker: 
Rune Haugseng
Affiliation: 
NTNU
Date: 
Tue, 12/03/2024 - 13:00 - 14:00
Location: 
MPIM Seminar Room

The AKSZ construction, as implemented by Pantev-Toën-Vaquié-Vezzosi in the context of derived algebraic geometry, gives a symplectic structure on the derived stack of maps from an oriented compact manifold to a symplectic derived stack. I  will describe how this gives rise to a family of extended topological field theories, in the sense of symmetric monoidal functors from (∞, n)-categories of cobordisms to some target, which here is a higher category of symplectic derived stacks and iterated Lagrangian correspondences. This is joint work with Damien Calaque and Claudia Scheimbauer.

Conference on "Arithmetic Geometry" in Honour of Gerd Faltings' 70th Birthday

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Organiser(s): 
Christian Blohmann, Christian Liedtke, Wiesława Nizioł
Date: 
Mon, 22/07/2024 - 09:00 - Fri, 26/07/2024 - 15:00
Location: 
MPIM Lecture Hall

Conference on "Arithmetic Geometry" in Honour of Gerd Faltings' 70th Birthday

Speakers:

Bhargav Bhatt (University of Michigan, IAS/Princeton) (tbc)
Jean-Benoit Bost (Université Paris-Saclay)
Ana Caraiani (Imperial College London)
Christopher Deninger (Universität Münster)

Euclidean Quantum Field Theory in One Axiom

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Speaker: 
Werner Nahm
Affiliation: 
Dublin IAS and School of Theoretical Physics
Date: 
Thu, 14/03/2024 - 11:30 - 13:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Math-Phys Seminar

For a given dimension, there is a well-known monoidal category of compact manifolds with Riemannian metric and boundary (possibly empty). The defining operation is the disjoint union and the empty set the neutral object. The category is self-adjoint in the sense that boundary components can be moved between source and target. An equally well-known monoidal category is given by the linear maps of real Hilbert spaces, with tensor products as defining operation and the real numbers as neutral object.

Conformal Field Theory and Conformal Blocks -- Change of date and room --

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Speaker: 
Daniel Bermudez
Affiliation: 
MPIM/Universität Bonn
Date: 
Wed, 06/03/2024 - 11:30 - 14:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Math-Phys Seminar

Tight contact structures on Seifert fibered 3-manifolds

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Speaker: 
Tanushree Shah
Affiliation: 
Vienna
Date: 
Tue, 05/03/2024 - 11:45 - 13:00
Location: 
MPIM Lecture Hall

I will start by introducing contact structures. They come in two flavors: tight and overtwisted. Classification of overtwisted  contact structures is well understood as opposed to tight contact structures. Tight contact structures have been classified on some 3  manifolds like S^3, R^3, Lens spaces, toric annuli, and almost all Seifert fibered manifolds with 3 exceptional fibers. We look at classification on one example of the Seifert fibered manifold with 4 exceptional fibers.

Goodbye

Posted in
Date: 
Fri, 05/04/2024 - 17:00 - 17:30
Location: 
MPIM Lecture Hall

Panel discussion: What to do with a PhD in mathematics?

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Speaker: 
Lynn D’eer, Antje Kiesel, Annette Werner, [TBC]
Date: 
Fri, 05/04/2024 - 15:30 - 17:00
Location: 
MPIM Lecture Hall
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