Morris Brooks: The effective mass of the Fröhlich polaron at strong coupling

In this talk we investigate the Fröhlich polaron in the strong coupling limit, which is a model describing the interactions of a charged particle, e.g. an electron, with a polarizable environment. Notably, the model is simple enough to allow for rigorous mathematical proofs, while giving rise to a multitude of interesting and non-trivial phenomena, such as an effectively increased mass of the electron. In particular, we will discuss a recent proof concerning the validity of the celebrated Landau-Pekar formula for the effective mass of the Fröhlich polaron at strong couplings, which has been an outstanding open problem in mathematical physics conjectured by Spohn in 1987.

Luca Fresta: Random Operators via SUSY: rigorous results on Green's function and density of state

The SUSY method has long been a powerful tool in the physics literature for studying disordered quantum systems. It enables the computation of averages of products of resolvents by expressing them as correlation functions of interacting quantum field theories involving both bosons and fermions. However, these theories typically feature highly oscillatory integrals, and this has hindered rigorous progress using standard constructive techniques.

In this talk, I will present rigorous results on the average Green's function and the density of states for two classes of random operators: random Schrödinger operators and random band matrices. 

Based on joint work with G. Antinucci, M. Disertori, and M. Porta.

Hal Tasaki: Topological index and phase transition in the S=1 quantum Heisenberg Antiferromagnetic chain

After briefly reviewing the modern study of quantum antiferromagnetic chains with emphasis on the Haldane conjecture, the AKLT model, and the notion of symmetry-protected topological (SPT) phases, I discuss my elementary index theorem that applies to the realistic S=1 Heisenberg antiferromagnetic chain.  The index theorem shows that the ground state of the model is topologically nontrivial if it has a unique gapped ground state.  I will also discuss the relation between my index and that of Pollmann, Turner, Berg, and Oshikawa and that of Ogata.

Arnaud Triay: The dilute Bose gas at positive temperature

In their celebrated paper of 1957, Lee, Huang and Yang computed the excitation spectrum of dilute Bose gases. I will talk about a series of recent works where we justified this formula by proving an expansion of the free energy for low temperature hence capturing the effects of the quantum fluctuations.