Period Integrals in Mathematical Physics
(by Johannes Brödel)
Numerous calculations in mathematical physics lead to periods: those are numbers, which can be represented as an integral of an algebraic differential form over a cycle in certain algebraic varieties. In the proseminar, we are going to explore various types of periods appearing in several fields of mathematical physics. While setting the mathematical foundations for periods and exploring their relation to various known special functions in a first part, the second part of the proseminar is devoted to understanding how the analytical properties of periods can be put to work in order to simplify calculations in classical mechanics, quantum field theory and string theory.
Slots & Requirements: There will be approximately 14 slots for Master students and 7 slots for advanced Bachelor students. For some of the topics, knowledge of QFT and/or GR is required.
Topic Assignment Meeting: Tuesday, Dec. 17th, 4pm, HIT E41.1
Introduction to Conformal Field Theory
(by Matthias Gaberdiel)
The proseminar will be based on the book ``Introduction to Conformal Field Theory with Applications to String Theory'' by Ralph Blumenhagen & Erik Plauschinn (Springer 2009).
Slots & Requirements: There will be approximately 18 slots for Master students and 2 slots for advanced Bachelor students.
Topic Assignment Meeting: tba
Introduction to General Relativity
(by Peter Hintz)
This proseminar is for advanced Bachelor students who wish to take a first step into general relativity. The mathematical background on tensors and differential geometry will be developed alongside the physics of special relativity, general relativity, stars, black holes, and cosmology. A main source for the seminar will be the book ``A First Course in General Relativity'' (Cambridge University Press) by Bernard Schutz.
Slots & Requirements: There will be approximately 16 slots for Bachelor students (typically in their third year) and 4 slots for Master students.
Topic Assignment Meeting: tba
Quantum Phase Transitions
(by Chitra Ramasubramanian)
In this Proseminar, we will explore the world of quantum phase transitions both in and out of equilibrium. These transitions at zero temperature occur as a result of competing ground state phases, when a control parameter in the Hamiltonian in tuned. As one approaches the quantum critical point, critical fluctuations grow along with long-range many-body quantum entanglement. The Proseminar aims to get an overview of the basic theory of quantum phases and their phase transitions. We will explore different kinds of quantum transitions, as well as dissipative phase transitions, their observable properties and relevance for experiments in condensed matter physics and other fields of physics. We will also potentially highlight the state of the art in the fields. To prepare for their topics, students will use graduate level books, review articles as well as papers published in scientific journals.
Slots & Requirements: There will be approximately 18 slots for Master students.
Topic Assignment Meeting: tba
