Alternatively have a look at the program.

## Organizational Meeting for the Summer Term [Math-Phys 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

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

Online-talk.

## A K-Theoretic Framework for Neutral Fermionic Topological Phases

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

## A Soft Introduction to TMF

## The Witten Genus

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

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

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.

## Towards non-perturbative quantization and the mass gap problem for the Yang-Mills Field

In 2000 Jaffe and Witten stated the long standing problem of exact quantization for the 4D Yang-Mills field on the Minkowski space and the existence of a mass gap in the theory as one on the Clay Institute Millenium problems. In this talk I shall explain how to reduce the problem of quantization of the Yang-Mills field Hamiltonian to a problem for defining a probability measure on an infinite-dimensional space of gauge equivalence classes of connections, the so called Yang-Mills measure associated to a 3D Yang-Mills theory on a Euclidean space.

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