Alternatively have a look at the program.

## Preliminary discussions followed by the talk "Supersymmetric Quantum Mechanics"

Seminar-Webpage: https://davidprinz.org/seminar/

## Supersymmetric Quantum Mechanics, Part 2

## Supersymmetric Quantum Field Theory

## The Atiyah—Singer Index Theorem, Revisited From Supersymmetry

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

## Euclidean Quantum Field Theory in One Axiom

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.

## Some Aspects of Vertex Algebras

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.

## Conformal Blocks and Generalized Theta Functions

Generalized theta functions are the global sections of a determinant bundle over the moduli space of stable vector bundles on a Riemann surface, which generalizes the classical theta function. Motivated by the geometric quantization, we will see that the conformal blocks in CFT are isomorphic to vector spaces of generalized theta functions.

## Fundamental Aspects of Conformal Field Theory and their Mathematical Formulations

I will introduce some aspects of Conformal Field Theory (CFT) like energy-momentum tensor, conformal Ward identities, operator product expansions, and the Virasoro algebra by focusing on computations. Then I attempt to highlight where these fit into the mathematical approaches to CFT.

## Little Group Method

The little group method, or Mackey theory as it is known to Mathematicians, is a way of constructing unitary representations of semi-direct products $G= K\ltimes T$, for $T$ abelian. Physically such unitary irreps should correspond to elementary particles in the case where $G$ is the double cover of the Poincaré group $G = SL_2(\mathbb{C}) \ltimes \mathbb{R}^4$. We will explain the general theory and how the field equations such as the Klein-Gordon or Dirac equation arise from this general framework.

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