ricevo e con piacere inoltro saluti alessandra

---------- Forwarded message --------- From: Serena Cenatiempo serena.cenatiempo@gssi.it Date: Fri, 28 Apr 2023 at 08:02 Subject: Course by Daniel Ueltschi (U Warwick) / May, 2-12 2023

Dear all,

This is a gentle reminder for the course by Daniel Ueltschi http://ueltschi.org/ (University of Warwick) on *Equilibrium Quantum Lattice Systems, *which will be held at the GSSI Main Lecture Hall from May 2nd to May 12th, according to the following calendar:

Tue May 2nd, Wed May 3rd, Thu May 4th,

Mon May 8th, Tue May 10th, Thu May 11th,

from 9 to 11.

It will also be streamed online at the link: https://zoom.us/j/97365002731?pwd=cmR1Y0RIV3lxTlJ5QWVJUlN0akNvQT09

ID riunione: 973 6500 2731 Passcode: MATHatGSSI

A detailed list of topics covered in the class follows below, and it is also available at the page: https://indico.gssi.it/event/478/.

For any further information, please do not hesitate to contact me.

With best wishes, Serena

----------------------------

*Equilibrium Quantum Lattice Systems* Daniel Ueltschi http://ueltschi.org/ (University of Warwick)

Tentative list of topics covered in the class:

1. *Spin systems* Hilbert spaces, spin operators, symmetries, hamiltonians. Finite-volume Gibbs states. Correlation functions. Thermodynamic limit of the free energy.

2. *Two results for quantum spins* o No long-range order in two dimensions, in systems with continuous

symmetry. o Long-range order in dimensions three and higher.

3. *Fermionic and bosonic systems* Fock space, creation and annihilation operators. Bose-Einstein

condensation. Hubbard model.

4. *Infinite-volume Gibbs states* Tangent functionals to the free energy. KMS condition. Extremal state decomposition.

5. *Probabilistic representations of quantum lattice systems* Feynman-Kac representation of Bose and spin systems. Loop representations. Poisson-Dirichlet conjecture.

-------------------------------------------------- Serena Cenatiempo Gran Sasso Science Institute (GSSI) Viale Crispi n.7, 67100 - L'Aquila (Italy)

phone: +39 0862 428 0276 email: serena.cenatiempo[at]gssi[dot]com homepage: http://www.serenacenatiempo.it/