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Mathematical Challenges in Quantum Mechanics - Online Seminars
from
Saturday, November 1, 2025 (9:00 AM)
to
Saturday, May 30, 2026 (11:00 PM)
Monday, October 27, 2025
Tuesday, October 28, 2025
Wednesday, October 29, 2025
Thursday, October 30, 2025
Friday, October 31, 2025
Saturday, November 1, 2025
Sunday, November 2, 2025
Monday, November 3, 2025
Tuesday, November 4, 2025
Wednesday, November 5, 2025
11:30 AM
MCQM PhD Lecture: Simon Larson
MCQM PhD Lecture: Simon Larson
11:30 AM - 12:30 PM
Title: TBA Abstract: TBA
2:30 PM
MCQM Seminar: Phan Thành Nam
MCQM Seminar: Phan Thành Nam
2:30 PM - 3:30 PM
Title: Weyl's law: from music to quantum mechanics Abstract: I will discuss the spectral theory of Schrödinger operators, ranging from the general question “Can we hear the shape of a drum?” to semiclassical approximations. In particular, I will focus on Weyl’s law and explore several open problems, including the Lieb–Thirring conjecture (on the semiclassical constant), the Pólya conjecture (on the first-order term of Laplacian eigenvalues), Weyl’s conjecture (on the second-order term of Laplacian eigenvalues), and the Hardy–Landau conjecture (related to the Gauss circle problem).
Thursday, November 6, 2025
Friday, November 7, 2025
Saturday, November 8, 2025
Sunday, November 9, 2025
Monday, November 10, 2025
Tuesday, November 11, 2025
Wednesday, November 12, 2025
Thursday, November 13, 2025
Friday, November 14, 2025
Saturday, November 15, 2025
Sunday, November 16, 2025
Monday, November 17, 2025
Tuesday, November 18, 2025
Wednesday, November 19, 2025
Thursday, November 20, 2025
Friday, November 21, 2025
Saturday, November 22, 2025
Sunday, November 23, 2025
Monday, November 24, 2025
Tuesday, November 25, 2025
Wednesday, November 26, 2025
Thursday, November 27, 2025
Friday, November 28, 2025
Saturday, November 29, 2025
Sunday, November 30, 2025
Monday, December 1, 2025
Tuesday, December 2, 2025
Wednesday, December 3, 2025
Thursday, December 4, 2025
Friday, December 5, 2025
Saturday, December 6, 2025
Sunday, December 7, 2025
Monday, December 8, 2025
Tuesday, December 9, 2025
Wednesday, December 10, 2025
Thursday, December 11, 2025
Friday, December 12, 2025
Saturday, December 13, 2025
Sunday, December 14, 2025
Monday, December 15, 2025
Tuesday, December 16, 2025
Wednesday, December 17, 2025
11:30 AM
MCQM PhD Lecture: Chris Bourne
MCQM PhD Lecture: Chris Bourne
11:30 AM - 12:30 PM
Title: Gapped Hamiltonians and topological phases Abstract: Starting from the quantum Hall effect and, more recently, topological insulators, there is a vast physical and mathematical literature on 'topological phases of matter'. For this PhD Lecture, we will give a gentle introduction to this topic. We explain how topological quantities can be assigned to Hamiltonians with a spectral gap and how this quantity may change depending on symmetries of the underlying system.
2:00 PM
MCQM Seminar: Gian Michele Graf
MCQM Seminar: Gian Michele Graf
2:00 PM - 3:00 PM
Title: An elementary derivation of the periodic table of topological matter Abstract: Band insulators and superconductors are of topological interest, depending on the dimension of physical space and on their symmetry classes. Within the context of the independent particle approximation, their topological content is summarised by a periodic table (due to Kitaev and precursors) that lists the index groups for each dimension and each of 10 classes. Various derivations of the table have been provided. The talk is about one more, prompted by the striking feature that groups are constant along the diagonals of the table. That observation calls for a corresponding proof, which will be provided by an isomorphism between groups that are diagonal neighbours. The details of the isomorphisms depend on the pair of classes involved. For instance, if the domain of that map relates to a non-chiral class (and hence the codomain to a chiral class in the next lower dimension), the map itself can be understood quite simply by way of an analogy: A real bundle on a circle can be pictured as a strip, either as a Möbius strip or an ordinary one. The isomorphism is the one mapping the bundle to the clutching map that comes from cutting the circle. (Joint work with F. Santi).
Thursday, December 18, 2025
Friday, December 19, 2025
Saturday, December 20, 2025
Sunday, December 21, 2025
Monday, December 22, 2025
Tuesday, December 23, 2025
Wednesday, December 24, 2025
Thursday, December 25, 2025
Friday, December 26, 2025
Saturday, December 27, 2025
Sunday, December 28, 2025
Monday, December 29, 2025
Tuesday, December 30, 2025
Wednesday, December 31, 2025
Thursday, January 1, 2026
Friday, January 2, 2026
Saturday, January 3, 2026
Sunday, January 4, 2026
Monday, January 5, 2026
Tuesday, January 6, 2026
Wednesday, January 7, 2026
11:30 AM
MCQM PhD Lecture: María Ángeles García-Ferrero
MCQM PhD Lecture: María Ángeles García-Ferrero
11:30 AM - 12:30 PM
Title: TBA Abstract: TBA
2:30 PM
MCQM Seminar: Pedro Caro
MCQM Seminar: Pedro Caro
2:30 PM - 3:30 PM
Title: An inverse problem for data-driven prediction in quantum mechanics Abstract: Data-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the influence of the same Hamiltonian. The difficulty of this problem comes from the ignorance of the exact Hamiltonian ruling the dynamic. In order to address this problem, Alberto Ruiz and I have formulated an inverse problem consisting in determining the Hamiltonian of a quantum system from the knowledge of the state at some fixed finite time for each initial state. We focus on the simplest case where the Hamiltonian is given by −∆ + V , where the electric potential V is non-compactly supported. During the talk I will present several uniqueness results for time-dependent potentials V = V(t, x) and stationary potentials V = V(x), and the difference between them. Roughly speaking, these results are uniqueness theorems, that explain why the Hamiltonians ruling the dynamics of all quantum particles are determined by the corresponding initial and final states of all these particles. As a consequence, one expects to be able to solve the data-driven prediction problem in quantum mechanics. The theorems I will discuss are the results of collaborations with Alberto Ruiz, and Manuel Cañizares, Ioannis Parissis and Athanasios Zacharopoulos.
Thursday, January 8, 2026
Friday, January 9, 2026
Saturday, January 10, 2026
Sunday, January 11, 2026
Monday, January 12, 2026
Tuesday, January 13, 2026
Wednesday, January 14, 2026
Thursday, January 15, 2026
Friday, January 16, 2026
Saturday, January 17, 2026
Sunday, January 18, 2026
Monday, January 19, 2026
Tuesday, January 20, 2026
Wednesday, January 21, 2026
Thursday, January 22, 2026
Friday, January 23, 2026
Saturday, January 24, 2026
Sunday, January 25, 2026
Monday, January 26, 2026
Tuesday, January 27, 2026
Wednesday, January 28, 2026
Thursday, January 29, 2026
Friday, January 30, 2026
Saturday, January 31, 2026
Sunday, February 1, 2026
Monday, February 2, 2026
Tuesday, February 3, 2026
Wednesday, February 4, 2026
Thursday, February 5, 2026
Friday, February 6, 2026
Saturday, February 7, 2026
Sunday, February 8, 2026
Monday, February 9, 2026
Tuesday, February 10, 2026
Wednesday, February 11, 2026
Thursday, February 12, 2026
Friday, February 13, 2026
Saturday, February 14, 2026
Sunday, February 15, 2026
Monday, February 16, 2026
Tuesday, February 17, 2026
Wednesday, February 18, 2026
Thursday, February 19, 2026
Friday, February 20, 2026
Saturday, February 21, 2026
Sunday, February 22, 2026
Monday, February 23, 2026
Tuesday, February 24, 2026
Wednesday, February 25, 2026
11:30 AM
MCMQ Seminar: Giorgio Cipolloni
MCMQ Seminar: Giorgio Cipolloni
11:30 AM - 12:30 PM
Title: The mystery of universality of random matrices Abstract: Over the past fifteen years, our understanding of universality in random matrix theory has undergone a remarkable transformation. For many models of large random matrices, it is now known that both eigenvalue statistics and eigenvector structures exhibit universal behavior that depends only on the symmetry class and not on the fine details of the matrix entries. This universality lies at the heart of deep conjectures in mathematical physics—connecting topics as diverse as quantum chaos, number theory, and high-dimensional statistics. We will survey these advances with a focus on Wigner matrices, Hermitian or symmetric random matrices with i.i.d. entries up to the symmetry constraint.
2:30 PM
MCQM Seminar: Antti Knowles
MCQM Seminar: Antti Knowles
2:30 PM - 3:30 PM
Title: Localization and delocalization in random graphs Abstract: A disordered quantum system is mathematically described by a large Hermitian random matrix. One of the most remarkable phenomena expected to occur in such systems is a localization-delocalization transition for the eigenvectors. Originally proposed in the 1950s to model conduction in semiconductors with random impurities, the phenomenon is now recognized as a general feature of wave transport in disordered media, and is one of the most influential ideas in modern condensed matter physics. A simple and natural model of such a system is given by the adjacency matrix of a random graph. In this talk, I review recent results on the localization and delocalization for the Erdös-Renyi model of random graphs. In the first part of the talk, I explain the emergence of fully localized and fully delocalized phases, which are separated by a mobility edge. In the second part of the talk, I explain how optimal delocalization bounds can be obtained using a dynamical Bernoulli flow method. Based on joint work with Johannes Alt, Raphael Ducatez, and Joscha Henheik.
Thursday, February 26, 2026
Friday, February 27, 2026
Saturday, February 28, 2026
Sunday, March 1, 2026
Monday, March 2, 2026
Tuesday, March 3, 2026
Wednesday, March 4, 2026
Thursday, March 5, 2026
Friday, March 6, 2026
Saturday, March 7, 2026
Sunday, March 8, 2026
Monday, March 9, 2026
Tuesday, March 10, 2026
Wednesday, March 11, 2026
Thursday, March 12, 2026
Friday, March 13, 2026
Saturday, March 14, 2026
Sunday, March 15, 2026
Monday, March 16, 2026
Tuesday, March 17, 2026
Wednesday, March 18, 2026
Thursday, March 19, 2026
Friday, March 20, 2026
Saturday, March 21, 2026
Sunday, March 22, 2026
Monday, March 23, 2026
Tuesday, March 24, 2026
Wednesday, March 25, 2026
11:30 AM
MCQM PhD Lecture: Dominik Sulz
MCQM PhD Lecture: Dominik Sulz
11:30 AM - 12:30 PM
Title: Numerical methods for quantum dynamics using Gaussian wave packets Abstract: This talk aims to provide an introduction to numerical methods for quantum dynamics using Gaussian wave packets. Solving the time-dependent Schrödinger equation in high dimensions remains one of the most significant challenges in quantum dynamics due to the so-called 'curse of dimensionality'. Gaussian wave packets provide a mesh-free ansatz to approximate the wave function and therefore are a powerful tool for high-dimensional numerical simulations. We will discuss the underlying geometry of the Gaussian manifold and apply the Dirac-Frenkel time-dependent variational principle to derive efficient equations of motion. A particular focus will be placed on the semiclassical regime: we discuss how Gaussian methods handle the occurring high oscillations of the wave function—a fundamental numerical difficulty.
2:30 PM
MCQM Seminar: Clotilde Fermanian Kammerer
MCQM Seminar: Clotilde Fermanian Kammerer
2:30 PM - 3:30 PM
Title: Semiclassical propagators and systems of PDEs Abstract: In this talk, we will describe different phenomena that arise when analyzing systems of coupled semiclassical PDEs. We will discuss approximations of the propagator in the semiclassical limit, methods and example.
Thursday, March 26, 2026
Friday, March 27, 2026
Saturday, March 28, 2026
Sunday, March 29, 2026
Monday, March 30, 2026
Tuesday, March 31, 2026
Wednesday, April 1, 2026
Thursday, April 2, 2026
Friday, April 3, 2026
Saturday, April 4, 2026
Sunday, April 5, 2026
Monday, April 6, 2026
Tuesday, April 7, 2026
Wednesday, April 8, 2026
11:30 AM
MCQM PhD Lecture: Hui Zhu
MCQM PhD Lecture: Hui Zhu
11:30 AM - 12:30 PM
Title: Wave Kinetic Theory Beyond the Periodic Setting Abstract: In analogy with Boltzmann’s kinetic theory, wave kinetic theory seeks to describe the statistical behavior of large ensembles of interacting waves. For spatially periodic waves in Euclidean space, significant recent progress has been achieved in a series of works by Deng and Hani. By contrast, much less is understood in non-periodic or more general geometric settings, where only partial or non-optimal results are currently available. In this talk, I will provide an informal and intuitive introduction to the theory and its underlying motivations, and highlight several open problems. The aim is to convey some of the key ideas and conceptual framework of wave kinetic theory. zoom link: https://uniroma1.zoom.us/j/84486358253?pwd=b9ohHb3EifQFpBDV2BsA5iAua2kkvq.1
2:30 PM
MCQM Seminar: Yu Deng
MCQM Seminar: Yu Deng
2:30 PM - 3:30 PM
Title: Mathematical theory of wave turbulence Abstract: The theory of wave turbulence describes the statistical behavior of wave interactions (as in nonlinear dispersive equations) in the "large box" kinetic limit. The central concept of the subject is the wave kinetic equation, which has wide applications in different areas of physics and science. In this talk we will discuss recent progress on derivation of wave kinetic equations for various dispersive models. This is based on joint works with Zaher Hani (University of Michigan). zoom link: https://uniroma1.zoom.us/j/89192434578?pwd=ORArvOFbSZBCJCVFp2wOp7sXGfbi9Y.1
Thursday, April 9, 2026
Friday, April 10, 2026
Saturday, April 11, 2026
Sunday, April 12, 2026
Monday, April 13, 2026
Tuesday, April 14, 2026
Wednesday, April 15, 2026
Thursday, April 16, 2026
Friday, April 17, 2026
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Tuesday, April 21, 2026
Wednesday, April 22, 2026
Thursday, April 23, 2026
Friday, April 24, 2026
Saturday, April 25, 2026
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Tuesday, April 28, 2026
Wednesday, April 29, 2026
Thursday, April 30, 2026
Friday, May 1, 2026
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Monday, May 4, 2026
Tuesday, May 5, 2026
Wednesday, May 6, 2026
Thursday, May 7, 2026
Friday, May 8, 2026
Saturday, May 9, 2026
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Monday, May 11, 2026
Tuesday, May 12, 2026
Wednesday, May 13, 2026
Thursday, May 14, 2026
Friday, May 15, 2026
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Monday, May 18, 2026
Tuesday, May 19, 2026
Wednesday, May 20, 2026
11:30 AM
MCMQ PhD Lecture: Tom Wessel
MCMQ PhD Lecture: Tom Wessel
11:30 AM - 12:30 PM
Title: Response theory for gapped many-body quantum lattice systems Abstract: This talk provides an introduction to adiabatic and response theory for quantum lattice systems. After a brief motivation and discussion of response theory, we introduce the algebraic description of fermionic lattice systems and discuss the challenges in rigorously justifying response theory. We then outline the construction of non-equilibrium almost stationary states and how they are used to justify response theory and Kubo’s formula. While a complete proof would exceed the available time, we highlight some of the technical tools, in particular the quasi-local inverse Liouvillian and Lieb-Robinson bounds. We conclude with a brief overview of recent advances in the field, including extensions to infinite volume systems, systems with a gap in the bulk, and locally gapped systems. zoom link: https://uniroma1.zoom.us/j/82533447845?pwd=TGxIDMGoKwkPNMg8xv90axIvnQDvc1.1
2:30 PM
MCQM Seminar: Marcello Porta
MCQM Seminar: Marcello Porta
2:30 PM - 3:30 PM
Title: Validity of linear response for gapless many-body quantum systems Abstract: In this talk I will discuss the transport properties of interacting fermionic lattice models, at low temperature, exposed to external perturbations slowly varying in space and in time. For weak enough perturbations, the linear response of physical observables is typically computed using Kubo formula, obtained truncating the Duhamel expansion for the time-dependent dynamics at first order. A first nontrivial question is to explicitly compute Kubo formula, and to understand its dependence on the parameters of the model. A second, complementary question is to understand the rigorous validity of Kubo formula, namely to prove that all higher order corrections in the Duhamel expansion are subleading, uniformly in the size of the system. Both questions become particularly hard for gapless systems, which are relevant for describing metals. In this talk, I will present a rigorous derivation of Kubo formula for interacting one-dimensional Fermi systems, in the absence of a spectral gap. Our result provides an explicit expression for the linear response of the current and of the density operators, as well as rigorous quantitative estimates for all higher order corrections. The proof is based on the combination of a number of ingredients: the rewriting of the real-time Duhamel expansion in terms of Euclidean correlation functions; the renormalization group analysis of Euclidean multipoint correlation functions, which provides sharp estimates for such correlations on large scales; the use of conservation laws and of the associated Ward identities, to determine the explicit form of the leading term, and to prove a key cancellation for all higher order terms which reproduces a prediction of bosonization. Based on a joint work with Giuseppe Scola and with Harman Preet Singh. zoom link: https://uniroma1.zoom.us/j/82890763353?pwd=9TfCxvy1SN5DQS0zvHfySuoYYPh6yJ.1
Thursday, May 21, 2026
Friday, May 22, 2026
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Tuesday, May 26, 2026
Wednesday, May 27, 2026
Thursday, May 28, 2026
Friday, May 29, 2026
Saturday, May 30, 2026
