The Mathematical Physics Summer School for masters students and beginning PhD students is organized by SwissMAP and offers introductory lectures to different aspects of mathematical physics.
Confirmed speakers:
- Anton Alekseev (University of Geneva)
- Edward Mazenc (ETH Zurich)
- Nikita Nikolaev (University of Birmingham)
- Elise Raphael (University of Geneva)
- Alexander Thomas (Lyon 1)
- Fridrich Valach (University of Hertfordshire)
Mini-courses topics
- Introduction to Cohomology
- The Stokes Phenomenon
- Conformal field theory
Conformal field theory is an exciting area at the interface of mathematics and theoretical physics. It plays a central role in string theory and provides an invaluable description of statistical systems near their critical points; on the mathematical side it is (among other things) related to representation theory or the theory of special functions. After a brief physical motivation, this minicourse aims to introduce the basic concepts and lay foundations for this wide field, as well as explore connections to the above areas.
- Characteristic classes and their applications in Physics
- Multiple Zeta Values: from number theory to physics
- Hamiltonian reduction - symmetries in symplectic geometry
The first part of these lectures is an introduction to symplectic geometry and the Hamiltonian formalism of Classical Mechanics. In the second part, we will discuss the theory of symplectic quotients, or Hamiltonian reduction, which corresponds to the study of reduced phase spaces in the presence of some symmetry.
- A First Glimpse at Large N Matrices
We will focus our two lectures on two beautiful results in the
field of random matrix theory. First, we will derive Wigner‘s famous
semi-circle law describing the eigenvalue distribution of hermitian
matrices whose entries are i.i.d. Gaussian-distributed variables. We
will see how many things simplify in the limit of large rank N, and why
that is analogous to a „classical limit“ in physical theories. The
second lecture introduces the basics of a diagrammatic calculus known as Feynman diagrams, allowing us to explore large N matrices beyond the Gaussian regime. It will provide a first glimpse into why theoretical
physicists care about large N gauge theories, and briefly sketch their
connection to string theory.
Registration deadline: June 30, 2025
Participants whose registration is accepted will have their local expenses covered (accommodation in shared room and meals). Travel expenses are not covered.
Please note that we accept in priority participants based in Swiss institutions.
