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Abstracts for Physical Math Seminar

Alternatively have a look at the program.

Organizational Meeting for the Summer Term [Math-Phys Seminar]

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Speaker: 
David Aretz and David Prinz
Date: 
Thu, 02/05/2024 - 12:00 - 13:00
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

 

We discuss the schedule for the summer term: Please think of topics that you would like to discuss in the group and a talk that you could present.

Quantum Observables for Free Fermions With Boundary Conditions

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Speaker: 
Stephan Stolz
Affiliation: 
University of Notre Dame
Date: 
Thu, 23/05/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

Costello and Gwilliam developed a systematic approach to perturbative quantization of field theories that describes classical and quantum observables as factorization algebras on the space-time manifold. In the simple case of the linear sigma model whose fields are smooth maps from the real line to an inner product space $V$ (aka the free boson), the algebra of quantum observables is the Weyl algebra of differential operators on $V$. For the free fermion, where $V$ is replaced by its odd analog, the algebra of quantum observables is the Clifford algebra generated by $V$.

The Geometry of Forms on Supermanifolds

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Speaker: 
Simone Noja
Affiliation: 
University of Heidelberg
Date: 
Fri, 31/05/2024 - 11:00 - 12:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

Online-talk.

A K-Theoretic Framework for Neutral Fermionic Topological Phases

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Speaker: 
Luuk Stehouwer
Affiliation: 
Dalhousie University, CA
Date: 
Thu, 06/06/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

Freed and Moore's "Twisted Equivariant Matter" establishes a K-theory-based classification for free fermion symmetry-protected topological phases, building on the work of Kitaev. I present a generalization of their approach which does not assume the protecting symmetry group contains a $U(1)$. I will explain how the tenfold way arises using Wall's classification of $\mathbb{Z}_2$-graded division algebras. If time permits, I will explain how it relates to the tenfold way one can find in Freed-Moore, originally due to Ryu-Schnyder-Furusaki-Ludwig.



 

Spectra, Complex Oriented Cohomology Theories, and Formal Group Laws

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Speaker: 
Alessandro Nanto
Affiliation: 
Universität Bonn
Date: 
Thu, 13/06/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar
This talk is a first introduction to complex oriented cohomology theories. We begin by introducing the 1-category of (symmetric) spectra, giving some basic definitions and properties, and their relationship with generalized cohomology theories, i.e. Brown's representation theorem. Of generalized cohomology theories, we focus then on the class of complex oriented ones. Finally, we introduce the notion of formal group law and sketch its connection to complex oriented cohomology theories.

 

A Soft Introduction to TMF

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Speaker: 
Paolo Tomasini
Affiliation: 
MPIM
Date: 
Thu, 20/06/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar
In this talk we will give a relaxed introduction to TMF. First, we will start with some discussion of elliptic cohomology and the moduli space of elliptic curves. This will lead us to the definition of TMF.
 

The Witten Genus

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Speaker: 
Jonah Epstein
Affiliation: 
Universität Bonn/MPIM
Date: 
Thu, 27/06/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

How geometric field theories represent (generalized, twisted, equivariant) cohomology classes, part I

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Speaker: 
Peter Teichner
Affiliation: 
MPIM
Date: 
Thu, 04/07/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

We discuss the language of functorial field theories, i.e. symmetric monoidal functors on geometric bordism categories, starting with the relation of 1-dimensional Euclidean theories to quantum mechanics. We explain how their concordance classes can lead to generalized cohomology and how this extends to the twisted, equivariant cases.

How geometric field theories represent (generalized, twisted, equivariant) cohomology classes, part II

Posted in
Speaker: 
Peter Teichner
Affiliation: 
MPIM
Date: 
Thu, 18/07/2024 - 12:00 - 13:30
Location: 
MPIM Lecture Hall
Parent event: 
Physical Math Seminar

We discuss the language of functorial field theories, i.e. symmetric monoidal functors on geometric bordism categories, starting with the relation of 1-dimensional Euclidean theories to quantum mechanics. We explain how their concordance classes can lead to generalized cohomology and how this extends to the twisted, equivariant cases.

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