# Members Seminar

## Quantum Mechanics -- a Primer for Mathematicians

## A Computer-Checked Proof that the Fundamental Group of the Circle is the Integers

This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed.

## Univalent Foundations Seminar

## Proof of a 35 Year Old Conjecture for the Entropy of SU(2) Coherent States, and its Generalization.

## Algebraic K-Theory Via Binary Complexes

## How to Find Periodic Orbits and Exotic Symplectic Manifolds

## Parallel Repetition of Two Prover Games: A Survey

I will give an introduction to the problem of parallel repetition of two-prover games and its applications and related results in theoretical computer science (the PCP theorem, hardness of approximation), mathematics (the geometry of foams, tiling the space R^n) and, if time allows, physics (Bell inequalities, the EPR paradox).

## Computations of Heegaard Floer Homologies

Heegaard Floer homology groups were recently introduced by Ozsvath and Szabo to study properties of 3-manifolds and knots in them. The definition of the invariants rests on delicate holomorphic geometry, making the actual computations cumbersome. In the lecture we will recall the basic definitions and theorems of the theory, and show how to define the simplest version in a purely combinatorial manner. For a special class of 3-manifolds the more general version will be presented by simple combinatorial ideas through lattice homology of Nemethi.

## Computations of Heegaard Floer Homologies

Heegaard Floer homology groups were recently introduced by Ozsvath and Szabo to study properties of 3-manifolds and knots in them. The definition of the invariants rests on delicate holomorphic geometry, making the actual computations cumbersome. In the lecture we will recall the basic definitions and theorems of the theory, and show how to define the simplest version in a purely combinatorial manner. For a special class of 3-manifolds the more general version will be presented by simple combinatorial ideas through lattice homology of Nemethi.