Advanced Topics in Theoretical Physics (Spring 2023)
Module 1: Geometric and Topological Methods in Materials
Randal Kamien (Utrecht)
Lectures and exercises: Feb 6, 13, 20, 27
Exam: Mar 6
This course will introduce the geometry and topology of two and three dimensional spaces with a focus on the study of materials such as membranes, liquid crystals, and colloidal systems.
The mathematics and the physics will be codeveloped with one informing the other. Other systems to be studied will depend on class interests and background.
Module 2: Introduction to stochastic thermodynamics
Marc Serra (Leiden)
Lectures and exercises: Mar 13, 20, 27, Apr 3
Exam: Apr 17 (Apr 10 is public holiday)
Location: Gorlaeus EM109
Conventional thermodynamics is immensely successful at describing macroscopic, near equilibrium phenomena. However, many relevant systems, ranging from modern hyper-miniaturised transistors to molecular motors in cells, are both highly fluctuating and far from equilibrium. This course will provide a gentle introduction to the emerging field of stochastic thermodynamics. We will start by discussing the modelling of stochastic processes using Langevin, Itô, and Fokker-Plank representations, including numerical solution techniques and applications to problems such as Brownian motion and stochastic resonance. Then, we will introduce fluctuation theorems and the Jarzynski identity, with applications in the measurement of free energy changes during protein folding. We will briefly discuss notions of coarse graining, including definitions of heat, work and entropy production at the mesoscale, and introduce thermodynamic uncertainty relations. Finally, we will provide a brief overview of the stochastic thermodynamics of information processing — which allows us to solve paradoxes such as the Maxwell demon, and represents an increasingly significant research area.
Module 3: Topological Data Analysis: a physics perspective
Jan Pieter van de Schaar (Amsterdam)
Lectures and exercises: Apr 24, May 8, 15, 22
Exam: Jun 5 (May 1 is UvA holiday, May 29 is a public holiday)
Location: Lectures SP D1.112, the exercise sessions SP G2.02; Exam D1.113
Topological Data Analysis (TDA) is a relatively new approach to analyzing high-dimensional data sets. By focussing on global properties like the shape and connectivity of the data, it probes features very different from local properties, and therefore appears to be a particularly promising approach to identify and constrain scale-dependent and/or non-Gaussian observables . In this Advanced Topics course we aim to introduce its mathematical foundations, including some algebraic topology and discrete Morse theory, and provide some basic examples of applications, all from a physics perspective.
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