Tentative schedule for Week 2. Titles, abstracts, slides to be added after the talks.

09:00-09:30 • Registration + Welcome

09:30-09:50 • Daniele**Ferretti** • *Efimov effect in a three-dimensional zero-range hamiltonian*

09:55-10:15 • Joachim**Kerner** • *On Bose–Einstein condensation in the random Kac–Luttinger model*

10:20-10:40 • Cristina**Caraci** • *Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime*

10:45-11:15 • Coffee break

11:15-11:35 • Luc**Vinet** • *Two or three things about inhomogeneous spin/fermionic chains*

11:40-12:00 • Georgios**Athanasopoulos** • *The exact solution of the 2D classical and 1D quantum Ising models via the Kac-Ward method*

12:05-12:25 • Jürg**Fröhlich** • *The problem of the unsolved problems*

12:30-14:30 • Lunch in**Ristorante San Trovaso**

14:30-17:30 • Constanza**Rojas-Molina** • Afternoon session on *Current challenges in disordered quantum systems*.

17:30-18:15 • Annalisa**Panati** • *A brief history of Venice*

18:15 • Welcome party

09:30-09:50 • Daniele

09:55-10:15 • Joachim

10:20-10:40 • Cristina

10:45-11:15 • Coffee break

11:15-11:35 • Luc

11:40-12:00 • Georgios

12:05-12:25 • Jürg

12:30-14:30 • Lunch in

14:30-17:30 • Constanza

One of the main features of disordered quantum systems is the absence of wave propagation, known as Anderson localization. Since the seminal work of P.W. Anderson, in the late 1950s, the mathematical physics community has devoted much effort to give a rigorous description of this phenomenon. Today, much is known about these systems, however the story is far from over. Once localization for one-particle systems is well understood, the next natural question is, what is the fate of localization in many-body systems? And what about the absence of localization, the thorny issue known as delocalization?
In this session we will briefly introduce the topic and review some of the approaches that have been developed to tackle both these questions, and proceed to a panel discussion, followed by Q&A and a discussion on current trends on the field, including an introduction to a promising approach to disordered (and deterministic) systems. We hope this will encourage questions and stimulate discussions with the audience.
Planning: Brief introduction to Anderson localization. Part I: Panel discussion on the topic of many-body systems with disorder with Chiara Boccato (Milano), Joachim Kerner (Hagen) and Frédéric Klopp (Paris).
Part II: Current trends in the field: an introduction to the method of the Landscape function by Filoche-Mayboroda by Severin Schraven (Munich).
Coffee break 15:30-16:00. |

17:30-18:15 • Annalisa

18:15 • Welcome party

09:30-09:50 • Jakob **Björnberg** • *Dimerization in mirror models and O(n)-invariant spin chains*

09:55-10:15 • Armen**Shirikyan** • *Markovian reduction for dynamical systems driven by a stationary noise*

10:20-10:40 • Constanza**Rojas-Molina** • *Fractional random Schrödinger operators: Spectral and dynamical properties*

10:45-11:15 • Coffee break

11:15-11:35 • Gaia**Pozzoli** • *From waiting times to the Ziv-Merhav algorithm as entropy estimators*

11:40-12:00 • Frédéric**Klopp** • *Harper's equation at non real coupling*

12:05-12:25 • Michael**Aizenman** • *Entanglement area-type bounds for pure states of rapid decorrelatkon*

12:30-14:30 • Lunch in**OKE Zattere**

14:30-17:30 • Serena**Cenatiempo** • Afternoon session on *Quantum fields with relativity*.

09:55-10:15 • Armen

10:20-10:40 • Constanza

10:45-11:15 • Coffee break

11:15-11:35 • Gaia

11:40-12:00 • Frédéric

12:05-12:25 • Michael

12:30-14:30 • Lunch in

14:30-17:30 • Serena

With the participation of Michael Aizenman, Jan Dereziński, Jürg Fröhlich, and Manfred Salmhofer. Here are Jan's slides and Manfred's slides.
Coffee break 15:30-16:00. |

09:30-09:50 • Vedran **Sohinger** • *A microscopic derivation of Gibbs measures for the 1D focusing quintic nonlinear Schrödinger equation*

09:55-10:15 • Volker**Betz** • *The polaron problem, self-attracting Brownian motion and the Gaussian correlation inequality*

10:20-10:40 • Chiara**Boccato** • *The free energy of the Bose gas at low density*

10:45-11:15 • Coffee break

11:11-11:35 • Matteo**Gallone** • *Prethermalization and conservation laws in time quasi-periodically driven quantum systems*

11:40-12:00 • Sascha**Lill** • *Momentum distribution of Fermi gases*

12:05-12:25 • Annalisa**Panati**

12:30-14:30 • Lunch in**Ristorante San Trovaso**

14:30-17:30 • Christian**Hainzl** • Afternoon session on *Correlation energy of Fermi gases via bosonic methods*.

09:55-10:15 • Volker

10:20-10:40 • Chiara

10:45-11:15 • Coffee break

11:11-11:35 • Matteo

11:40-12:00 • Sascha

12:05-12:25 • Annalisa

12:30-14:30 • Lunch in

14:30-17:30 • Christian

I will consider a system of fermions and explain how bosonization methods are used to understand the correlation energy. These methods, originally used for bosonic systems, are equally useful for large density Coulomb systems as well for a low density Fermi gases. Here are Christian's slides.
Coffee break 15:30-16:00. |

09:30-09:50 • no talks

09:55-10:15 • Jan**Dereziński** • *Point-splitting and dimensional regularization in quantum mechanics. Point potentials in any dimension*

10:20-10:40 • Christian**Hainzl** • *The free energy of dilute Bose gases at low temperatures*

10:45-11:15 • Coffee break

11:15-11:35 • Serena**Cenatiempo** • *Upper bound for the ground state energy of a dilute Bose gas of hard spheres*

11:40-12:00 • Simone**Warzel** • *The Parisi Formula for the QSK*

12:05-12:25 • Manfred**Salmhofer**

12:30-14:30 • Lunch in**OKE Zattere**

14:30-17:30 • Bruno**Nachtergaele** and Alessandro **Pizzo** • Afternoon session on *Recent spectral results on quantum lattice systems*.

09:55-10:15 • Jan

10:20-10:40 • Christian

10:45-11:15 • Coffee break

11:15-11:35 • Serena

11:40-12:00 • Simone

12:05-12:25 • Manfred

12:30-14:30 • Lunch in

14:30-17:30 • Bruno

Here are Bruno's slides.
Coffee break 15:30-16:00. |

09:30-09:50 • Amanda **Young**

09:55-10:15 • Oliver**Siebert** • *Lieb-Robinson bounds for a class of continuum fermions and the thermodynamic limit*

10:20-10:40 • Anastasiia**Trofimova** • *Exact loop densities in the O(1) dense loop model*

10:45-11:15 • Coffee break

11:15-11:35 • Severin**Schraven** • *Two-sided Lieb-Thirring bounds*

11:40-12:00 • Daniele**Toniolo** • *Stability of slow hamiltonian dynamics and dynamical generation of alpha-Rényi entropies*

12:05-12:25 • Bruno**Nachtergaele** • *Charge gap > neutral gap*

12:30-14:30 • Lunch in**Ristorante San Trovaso**

14:30-15:00 • Daniel**Ueltschi** • *Venice and the crusades*

15:00-15:30 • Annalisa**Panati** • *The battle of Lepanto*

15:30-16:00 • Coffee and Prosecco break

16:00-16:30 • Anastasiia**Trofimova** • *Murano glass*

16:30-17:00 • Vedran**Sohinger** • *Zadar*

18:30 • Unofficial conference dinner

09:55-10:15 • Oliver

10:20-10:40 • Anastasiia

10:45-11:15 • Coffee break

11:15-11:35 • Severin

11:40-12:00 • Daniele

12:05-12:25 • Bruno

12:30-14:30 • Lunch in

14:30-15:00 • Daniel

15:00-15:30 • Annalisa

15:30-16:00 • Coffee and Prosecco break

16:00-16:30 • Anastasiia

16:30-17:00 • Vedran

18:30 • Unofficial conference dinner