04&07/03/2024 : Stefan Teufel @ PoliMi

Monday, March 4, 2024 – 14:15 and Thursday, March 7, 2024 – 10:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 “Nave”, Campus Leonardo


SPEAKER: Stefan Teufel (Eberhard Karls Universität Tübingen)


Quantisation of Hall conductivity in infinite interacting fermion systems

Understanding the exact quantisation of the experimentally observed Hall
conductivity has led to many interesting developments also in mathematical
physics and to two Nobel prizes in physics. Although the problem is now more
than 40 years old, significant progress has been made on a rigorous level for
interacting systems in the last ten years. In my talk I will briefly review
some of the mathematical highlights of this development and then present a new result: We consider infinite systems of interacting electrons on a lattice
governed by a translation-invariant Hamiltonian with a unique gapped ground
state. Using the NEASS approach, we show that the Hall conductivity of such a
system at zero temperature is given by a many-body version of the famous
double-commutator formula without power-law corrections. We also show that this formula takes only quantised values. The main novelty compared to
existing mathematical results is that we consider the conductivity instead of
the conductance, and that working directly in infinite volume simplifies and
clarifies some arguments, provided one is willing to work in the C^*-algebraic
framework used in the mathematical description of such systems.

In the first lecture I will mainly talk about the history of the problem and set up the mathematical framework. In the second lecture I will present the new results. The latter are based on joint work with Giovanna Marcelli, Tadahiro Miyao, Domenico Monaco and Marius Wesle.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

06/02/2024: Marco Olivieri @ PoliMi

Tuesday, February 6, 2024 – 14:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 “Nave”, Campus Leonardo


SPEAKER: Marco Olivieri (University of Copenhagen)


A novel method for the derivation of the free energy expansion of the Bose gases

We present an innovative method to derive the expansion of the free energy
density of a dilute Bose gas in thermodynamic regime in dimension three. In the first part of the talk, we give a gentle introduction on the thermodynamic limit as the optimal tool for the macroscopic derivation of the thermodynamics from the quantum statistical mechanics. In the second part of the talk, we will focus our attention on the macroscopic behavior of Bose gases, which have a phase transition to Bose Einstein condensates for low temperature. We then study a gas of many bosons interacting through a spherical, pairwise, positive potential. Using a combination of the renormalization of the potential, the Neumann localization and Bogoliubov diagonalization, we derive a lower bound for the second order expansion of the free energy.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on thetopics presented at the talk.

Lecture Series: Alessandro Giuliani @ PoliMi

Monday, Jan 15, 2024 – 15:00 Aula Seminari III piano (III fl)
Wednesday, Jan 17, 2024 – 15:00 Sala Consiglio (VII fl)
Mathematics Department, Politecnico di Milano
Ed. 14 (Nave), Campus Leonardo, Milano, Italy


SPEAKER: Alessandro Giuliani (Università degli Studi di Roma Tre)


Universality of the critical conductivity of the Haldane-Hubbard model

The Haldane model is a standard tight binding model describing electrons hopping on a hexagonal lattice subject to a transverse, dipolar, magnetic field. We consider its interacting version and study the critical case at the transition between the trivial and the “topological” insulating phases. In previous works,
we proved the quantization of the critical longitudinal conductivity for weak enough interaction strength. We now report a recent extension of the result to the critical transverse conductivity, which turns out to be quantized at half-integer values, irrespective of the interaction strength. Proofs are based on a combination of constructive Renormalization Group methods and exact lattice Ward Identities. Joint works with S. Fabbri, V. Mastropietro, M. Porta, R. Reuvers.

The talk will be divided in two parts: in part 1, motivations, main results and main ideas of the proof will be stated and explained. Part 2 will be more technical and will discuss in more detail some selected aspects of the proof.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Lecture Series: Nicola Pinamonti @ PoliMi

Monday, Nov 20, 2023 - 15:15 Sala Consiglio (VII fl)
Tuesday, Nov 21, 2023 - 11:15 Sala Consiglio (VII fl)
Thursday, Nov 23, 2023 - 14:15 Sala Seminari MOX (VI fl)
Mathematics Department, Politecnico di Milano
Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Nicola Pinamonti (University of Genova)


Aspects of free and interacting quantum field theories on curved backgrounds

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

30/10/2023: Alain Joye @ PoliMi

Monday, October 30, 2023 - 16:15
Sala Consiglio
Mathematics Department, Politecnico di Milano
VII Floor, Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Alain Joye (Université Grenoble Alpes)


Quantum Walks: Deterministic and Random

The concept of quantum walks on a graph has gained popularity in the scientific literature in recent years, likely due to its intersection between theoretical computer science, physics, and mathematics. After providing an overview of some popular quantum walks to illustrate their significance in these fields, we will focus on the quantum walks commonly referred to as “coined quantum walks” in the literature. Taking a discrete dynamical system perspective on these quantum walks, we will then discuss some of their transport properties in various regimes, both random and deterministic. This discussion will highlight the differences and similarities between coined quantum walks and classical random walks.

This initiative is part of the “PhD Lectures” activity of the project
“Departments of Excellence 2023-2027”, consisting of seminars open to
Ph.D. students, followed by meetings with the speaker to discuss and go into
detail on the topics presented at the talk.

12/07/2023: Giuseppe De Nittis @ PoliMi

July 12, 2023 - 15:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Giuseppe De Nittis (Pontificia Universidad Católica de Chile)


About the notion of eigenstates in C*-algebras and some application to quantum mechanics

This talk is concerned with the notion of eigenstates of an operator in an abstract C*-algebra. After reviewing some basic and structural results, I will explore the possibility of reinterpreting certain typical concepts of quantum mechanics (dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.


This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

12/07/2023: Massimo Moscolari @ PoliMi

July 12, 2023 - 11:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Massimo Moscolari (Politecnico di Milano)


On the bulk-edge correspondence for (interacting) fermion systems

I will first show that for general 2d random ergodic magnetic Schrödinger operators the bulk magnetization equals the total edge current at any temperature. The equality between the bulk and edge quantum transport indices can be then obtained as a corollary of our purely analytical argument by imposing a gap condition and by taking a “zero temperature” limit. After that, I will briefly show how to extend the equality of bulk magnetization and total edge current to lattice fermion systems with short-range interactions and above a certain critical temperature. The talk is based on joint works with Horia Cornean, Jonas Lampart, Stefan Teufel and Tom Wessel.


This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

17/07/2023: Angelo Lucia @ PoliMi

July 17, 2023 - 16:00
Sala Consiglio, seventh floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Angelo Lucia (Universidad Complutense de Madrid)


Thermalization of quantum memories

Quantum memories are quantum spins systems designed to protect a quantum state from external noise. Contrary to the classical case, there are reasons to conjecture that there are no two-dimensional quantum memories that survive for long period of times at non-zero temperature.

In this talk, I will discuss a way to rigorously prove this conjecture, by estimating the mixing time of a class of
Quantum Markovian Semigroups. I will then present some recent results, regarding the case of so-called Kitaev’s quantum double models, for which we can perform such estimate and confirm the conjecture.


This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

25/05/2023: Hynek Kovarik @PoliMi

May 25, 2023 - 14h30
Aula Seminario III Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

SPEAKER: Hynek Kovarik (Università degli studi di Brescia)


Resolvent expansion and time decay of the wave functions of magnetic Hamiltonians in dimension two

I this talk I will present some results on the resolvent expansions of magnetic Hamiltonians at the threshold of the essential spectrum. I will show, in particular, that the nature of the expansion of a two-dimensional magnetic Hamiltonian is completely determined by the flux of the associated magnetic field. Applications to time decay of the wave functions will be discussed as well.

20/02/2023: Jan Derezinski @ Polimi

February 20, 2023
Aula Consiglio VII Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

SPEAKER: Jan Derezinski (University of Warsaw)


Schrödinger operators with singular boundary conditions

In order to define a differential operator on a domain with boundary one often needs to specify boundary conditions. In the presence of singular terms this can be quite tricky. It may lead to interesting and surprising phase diagrams. I will illustrate this with the so-called perturbed Bessel operators, that is one-dimensional Schrödinger operators on the half-line of the form $ – \partial_x^2 + (m^2 – 1/4) 1/x^2 + Q(x) $.


The talk will be based on my joint work with Jeremy Faupin.