Q-Math Seminar
About the Q-Math Seminar
The Q-Math Seminar is a series of seminars regularly held at the Mathematics Department of Universidad Carlos III de Madrid and the ICMAT. This is an activity carried out by the members of the Q-Math Research Group The topics discussed usually in the seminar are related with mathematical aspects of quantum theory and include:
- Differential Geometry
- Functional Analysis
- Operator Theory
- Quantum Information Theory
Upcoming seminars
Ángel González-Prieto (UCM)
Topological Quantum Field Theories for Character Groupoids
Tuesday the 6th of May, 2025, 11:00, NOTICE THE UNUSUAL TIME:Room 2.2.D08
Given a compact manifold M, the space of representations of its fundamental group into a group G plays a central role in modern geometry, reflecting deep connections between the topology of M and the representation theory of G. When G is finite, this space naturally acquires the structure of a groupoid—known as the character groupoid—whose combinatorics are rich and intricate.In this talk, we construct a Topological Quantum Field Theory (TQFT) that computes the number of points of these character groupoids, extending the celebrated Dijkgraaf–Witten theory. As we shall see, this TQFT provides a complete encoding of the classical representation theory of finite groups. We will also address the case where G is an algebraic group, for which the space of representations becomes the so-called character stack. We will explain how the TQFT developed in the finite case extends naturally to this algebraic setting, leading to a far-reaching generalization of character theory in terms of algebraic K-theory and character sheaves.Link for online session (Active on request): https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380
Ernesto Estrada (IFISC)
Geometry induced by Hermitian adjacency matrices of directed graphs
Tuesday the 20th of May, 2025, 12:00, NOTICE THE UNUSUAL PLACE AND TIME: ICMAT Aula Gris 2
I will introduce several geometric measures for mixed graphs represented by complex-valued Hermitian adjacency matrices. Such matrices can be interpreted as tight-binding Hamiltonian operators on a graph, similar to the magnetic tight-binding model for solids. In the talk I will define the communicability function of mixed graphs based on the exponential of the Hermitian adjacency matrix. Then, I will define a Euclidean distance between the vertices of the mixed graphs. Further I introduce Kähler and Hermitian angles between different planes among the position vectors and holomorphic and projection planes, respectively. I will prove several mathematical relations and inequalities between all these geometric parameters. Finally, I will show some applications of these geometric parameters for the characterization of ecological food webs, networks of co-purchasing of political books, a neuronal network, an Internet (Russian) trolls network, and a software collaboration graph..Link for online session (Active on request): https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380