A Non-Commutative Analog of the 2-Wasserstein Metric for which the Fermionic Fokker-Planck Equation is Gradient Flow for the Entropy
35 years ago Wehrl defined a classical entropy of a quantum density matrix using Gaussian (Schr\"odinger, Bargmann, ...) coherent states. This entropy, unlike other classical approximations, has the virtue of being positive. He conjectured that the minimum entropy occurs for a density matrix that is itself a projector onto a coherent state and this was proved about a year later.
Holant Problems are a broad framework to describe counting problems. The framework generalizes counting Constraint Satisfaction Problems and partition functions of Graph Homomorphisms.
We study the hole probability of Gaussian entire functions. More specifically, we work with entire functions given by a Taylor series with i.i.d complex Gaussian random variables and arbitrary non-random coefficients.
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).