Week 03.03.2025 – 09.03.2025

Quantum Chromodynamics (QCD) has been a profound source of inspiration for theoretical physics, driving the development of key concepts such as string theory, effective field theories, instantons, anomalies, and lattice gauge theories. In these lectures, I will explore two distinct regimes of QCD - its infrared (IR) and ultraviolet (UV) limits - and the theoretical tools used to study them.

In the IR regime, where perturbative techniques break down, Effective Field Theories (EFTs) provide a powerful framework. I will introduce the pion EFT as a tool to study non-linearly realized symmetries and soft theorems. In the UV regime, where QCD becomes amenable to perturbative analysis, I will discuss the Operator Product Expansion and renormalization group equations, focusing on their application to deep inelastic scattering, a cornerstone in the discovery of quarks and gluons.

These two regimes illustrate the richness of QCD and its pivotal role in shaping our understanding of fundamental physics.

Propagation and generation of "chaos" is an important ingredient for
rigorous control of applicability of kinetic theory, in general. Chaos
is here understood as sufficient statistical independence of random
variables related to the "kinetic" observables of the system. Cumulant
hierarchy of these random variables thus often gives a way of
controlling the evolution and degree of such independence, i.e., the
degree of "chaos" in the system. In this talk, we will consider two,
qualitatively different, example cases for which kinetic theory is
believed to be applicable: the stochastic Kac model with random velocity
exchange and the discrete nonlinear Schrodinger evolution (DNLS) with
suitable random, spatially homogeneous initial data. In both cases, we
set up suitable random variables and propose methods to control the
evolution of their cumulant hierarchies. The talk is based on joint
works with Sakari Pirnes and Aleksis Vuoksenmaa, and earlier works with
Matteo Marcozzi, Alessia Nota, and Herbert Spohn.

About fifty years ago, Gibbons and Hawking argued that the Euclidean gravitational path integral with suitable boundary conditions can be interpreted as a grand-canonical partition function. Classical gravitational solutions, including black holes, arise as saddles of this path integral, and from the saddle-point action one can extract the black hole entropy. In the talk, I will discuss some recent developments of these ideas. Working in five dimensions, we will see how imposing supersymmetric boundary conditions converts the partition function into an index. Then we will construct a class of saddles of this index which interpolates between supersymmetric black holes and horizonless microstate geometries. I will discuss how the saddle point action can be computed via equivariant localization. Finally, I will comment on the relevance of these findings for black hole microstate counting and holography.