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 (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  (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/

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Prof. Alessandra Faggionato


Department of Mathematics
University "La Sapienza"
Piazzale Aldo Moro, 5
00185 - Rome

Office 5, Phone  (0039)  06 49913252
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