Mathematical Challenges in Quantum Mechanics - Online Seminars

1 Nov 2025, 09:00 → 30 May 2026, 23:00 Europe/Rome

Online

The series of online seminars Mathematical Challenges in Quantum Mechanics (MCQM) focuses on current topics of mathematical physics, with special attention to the mathematical aspects of quantum mechanics. It aims to bring together the Italian community working on mathematical methods for quantum theory.             

The seminars take place on Wednesday afternoon, usually at 14:30 Italian time, on a monthly basis. The preliminary schedule for the 2025-26 seminar series is as follows:

 

• November 5th, 2025 – Phan Thành Nam (Ludwig-Maximilians Universität München)
• December 17th, 2025 – Gian Michele Graf (ETH Zürich)
• January 7th, 2026 – Pedro Caro (BCAM)
• February 25, 2026 – Antti Knowles (Université de Genève)
• March 2026 – Clotilde Fermanian Kammerer (Université d'Angers)
• April 2026 – TBA
• May 2026 – TBA

 

Each seminar will be accompanied by a lecture addressed to PhD students and young researchers, aimed at introducing the broad topic of the seminar and presenting some perspectives of the open problems and mathematical challenges in the field. The lecture is usually held on the same day of the seminar, at 11.30 Italian time.

 

Titles and abstracts of the MCQM Seminars and PhD lectures are available at this page and this page respectively. To receive the zoom link to attend the seminars and/or the PhD lectures please register here. 

 

The online seminars are part of a long-running series of events organized over the years by the Italian community working on mathematical methods for quantum physics, including the following School and Workshops:        

MCQM - Mathematical Challenges in Quantum Mechanics    
MCQM25 - L'Aquila, February 9-14, 2025    
MCQM22 - Como, June 13-18, 2022        
MCQM18 - Rome, February 19-24, 2018         
MCQM16 - Bressanone, February 8-13, 2016

Organizing committee
Lucrezia Cossetti (Bilbao) 
Marco Falconi (PoliMi) 
Luca Fresta (Roma Tre) 
Emanuela L. Giacomelli (UniMI) 
Domenico Monaco (Sapienza) 
Marco Olivieri (Barcelona)

 

MCQM PhD Lectures 2022/23

• MCQM PhD Lecture_Boni_Quantum graphs_2023-05-17.pdf
• MCQM_PhDLecture_Gontier_2022-12-14.pdf
• MCQM_PhDLecture_Koenig_2022-11-09.pdf
• MCQM_PhDLecture_Shapiro_2023-01-10.pdf

MCQM PhD Lectures 2023/24 TalkEntropies_Capel_highlighted.pdf TalkEntropies_Capel.pdf

MCQM PhD Lectures 2024/25

• 2024-01-15_Hinrichs.pdf
• 2024-11-06_Alvarez_bibliography.pdf
• 2024-12-18_Lucia_slides.pdf
• 2025-04-09_Merz.pdf
• 2025-05-14_Ranallo.pdf

MCQM PhD Lectures 2025/26 2025-11-05_MCQM_PhDLecture_Larson_Spectral Theory Of Schrödinger Operators.pdf

MCQM Seminars 2022/23 hiro.pdf MCQM_Seminar_Cances_2022-12-14.pdf

Wednesday, 5 November

1 MCQM PhD Lecture: Simon Larson

Title: TBA

Abstract: TBA

2 MCQM Seminar: Phan Thành Nam

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).

Wednesday, 17 December

3 MCQM PhD Lecture: Chris Bourne

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.

4 MCQM Seminar: Gian Michele Graf

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).

Wednesday, 7 January

5 MCQM PhD Lecture: María Ángeles García-Ferrero

Title: TBA

Abstract: TBA

6 MCQM Seminar: Pedro Caro

Wednesday, 25 February

7 MCQM Seminar: Antti Knowles