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Kommende Vorträge

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Ausführliche Liste aller demnächst stattfindenden Vorträge und Seminare. Für eine Übersicht konsultieren Sie bitte auch den Kalender.

Oberseminar Arithmetic Geometry and Representation Theory

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Organiser(s): 
Prof. Dr. J. Fintzen, Prof. Dr. T. Kaletha, Prof. Dr. P. Scholze
Datum: 
Fre, 11/10/2024 - 14:05 - Fre, 19/12/2025 - 16:00
Location: 
MPIM Lecture Hall

https://people.mpim-bonn.mpg.de/scholze/veranstaltungen.html

On the categorical spectrum of topological quantum field theories

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Speaker: 
David Reutter
Zugehörigkeit: 
University of Hamburg
Datum: 
Die, 08/07/2025 - 14:00 - 15:00
Location: 
MPIM Lecture Hall

As originally suggested by Kitaev, invertible topological quantum field theories of varying dimensions should assemble into a spectrum/generalized homology theory. A candidate for such a spectrum of invertible TQFTs was proposed by Freed and Hopkins, with the defining property that (isomorphism classes of) n-dimensional invertible TQFTs are completely determined by their partition functions on closed n-manifolds.

More generally, not-necessarily-invertible TQFTs should assemble into a `categorical spectrum', an analogue of a spectrum with non-invertible cells at each level.

An algebraic theory of planon-only fracton orders

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Speaker: 
Agnes Beaudry
Zugehörigkeit: 
UC Boulder
Datum: 
Die, 08/07/2025 - 15:30 - 16:30
Location: 
MPIM Lecture Hall

In this talk, I will describe an algebraic theory for planon-only abelian fracton orders. These are three-dimensional gapped phases with the property that fractional excitations are abelian particles restricted to move in parallel planes. The fusion and statistics data can be identified with a finitely generated module over a Laurent polynomial ring together with a U(1)-valued quadratic form. These systems thus lend themselves to an elegant algebraic theory which we expect will lead to easily computable phase invariants and a classification.

A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from discrete higher gauge theory

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Speaker: 
João Faria Martins
Zugehörigkeit: 
University of Leeds
Datum: 
Die, 08/07/2025 - 16:45 - 17:45
Location: 
MPIM Lecture Hall

Quinn's Finite Total Homotopy TQFT is a topological quantum field theory defined for any dimension n of space, depending on the choice of a homotopy finite space B. For instance, B can be the classifying space of a finite group or a finite 2-group.

Mapping the landscape of frustration-free models

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Speaker: 
Emil Prodan
Zugehörigkeit: 
Yeshiva University
Datum: 
Die, 08/07/2025 - 18:00 - 19:00
Location: 
MPIM Lecture Hall

Frustration-free models are of great interest because they are amenable to specialized techniques and their understanding is more complete among the general quantum spin models. In this talk, I will establish an almost bijective relation between frustration-free families of projections and a subclass of hereditary subalgebras defined by an intrinsic property. This relation sets further synergies between frustration-free models and open projections in double duals, and subsets of pure states spaces. These connections enable a better understanding of the class of frustration-free models.

C*-categorical prefactorization algebras for superselection sectors and topological order

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Speaker: 
Alexander Schenkel
Zugehörigkeit: 
University of Nottingham
Datum: 
Mit, 09/07/2025 - 14:00 - 15:00
Location: 
MPIM Lecture Hall

I will present a geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the n-dimensional lattice $Z^n$. I will show that, under certain assumptions which are implied by Haag duality, the monoidal C*-categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of $Z^n$.

Quantizing homotopy types

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Speaker: 
Constantin Teleman
Zugehörigkeit: 
UC Berkeley
Datum: 
Mit, 09/07/2025 - 15:30 - 16:30
Location: 
MPIM Lecture Hall

Kontsevich (90’s) proposed a topological quantization of (sigma-models into) finite homotopy types to top dimensions (d, d+1). Its enhancement to a `fully extended’ TQFT was described later (Freed, Hopkins, Lurie and the speaker) in the target category of iterated algebras. Independently, Chas and Sullivan constructed a (partially defined) 2-dimensional TQFT (d=1) with target compact oriented manifolds.

Gauging categorical symmetries

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Speaker: 
Nils Carqueville
Zugehörigkeit: 
University of Vienna
Datum: 
Mit, 09/07/2025 - 16:45 - 17:45
Location: 
MPIM Lecture Hall

Orbifold data are categorical symmetries that can be gauged in oriented defect topological quantum field theories. We review the general construction and apply it to 2-group symmetries of 3-dimensional TQFTs; upon further specialisation this leads to equivariantisation of G-crossed braided fusion categories. We also describe a proposal, via higher dagger categories, to gauging categorical symmetries in the context of other tangential structures. This is based on separate projects with Benjamin Haake and Tim Lüders.

Reflection positivity and invertible phases of 2d quantum many-body systems

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Speaker: 
Nikita Sopenko
Zugehörigkeit: 
IAS
Datum: 
Mit, 09/07/2025 - 18:00 - 19:00
Location: 
MPIM Lecture Hall

Reflection positivity is a property that is usually taken as an assumption in the classification of topological phases of matter via continuous quantum field theories. For general quantum many-body systems, this property does not hold. This raises the question of whether it somehow emerges in the effective theory from the microscopic description, thereby justifying the field-theoretic approach.

(Seminar SAG) On the exceptional locus of O’Grady’s nonsymplectic resolutions

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Speaker: 
Luigi Martinelli
Zugehörigkeit: 
Bielefeld
Datum: 
Don, 10/07/2025 - 10:30 - 12:00
Location: 
MPIM Lecture Hall

In this talk, we focus on some singular moduli spaces of sheaves on a K3 surface. More precisely, for any integer n > 1, we consider the moduli space M(n) associated with the Mukai vector 2(1,0,1-n). Looking for new deformation classes of hyper-Kähler manifolds, O’Grady constructed an explicit resolution of every M(n). O’Grady’s resolution is crepant and does give a hyper-Kähler manifold only if n=2. If n>2, it turns out that no crepant resolution exists for M(n), but one may still look for a categorical crepant resolution.

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