Q-Math Seminar
Marco Díaz Maceda (CUNEF)
Multisymplectic formalism for manifolds with boundaries
Wednesday the 18th of March, 2026, 11:00, Room 2.2.D08
In this seminar, I will present a new formalism for studying the field theories on manifolds with boundary. Based on the ideas of relative cohomology [Margalef-Bentabol & Villaseñor, 2021], I will extend the definition of multisymplectic structures to manifolds with boundary. We will see how this structure reproduces the field equations of variational principles with boundary. I will explain how to generalize the observables, the graded Poisson brackets, and the conserved charges to manifolds with boundary. Moreover, I will present the Lagrangian formalism, deriving the Poincaré–Cartan form and the Euler–Lagrange equations. Finally, I will illustrate the formalism with several examples.Link for online session: http://meet.google.com/nia-eqqt-utk
Gonzalo Vázquez-Villar (UC3M, Signal Processing Group)
Non-Asymptotic Bounds for Quantum Hypothesis Testing
Wednesday the 11th of March, 2026, 11:00, Room 2.2.D08
Quantum hypothesis testing, the task of distinguishing quantum states through measurement, is central to quantum information theory, with applications ranging from quantum communication to quantum error correction. In this talk, we formalize the binary quantum hypothesis testing problem in both non-asymptotic and asymptotic settings. A central tool in our analysis is the Nussbaum-Szkoła mapping, which transforms the quantum problem into a classical surrogate test. Using this mapping, we derive rigorous non-asymptotic converse bounds on the error probabilities of quantum hypothesis testing and provide a unified treatment of three key asymptotic regimes: small, moderate, and large deviations. Furthermore, we show that the M-ary quantum hypothesis testing problem admits an exact binary formulation, reducing the analysis of its minimum average error probability to a single binary hypothesis test with a structured alternative hypothesis. Overall, this talk illustrates how classical methodologies can provide both intuitive insight and powerful analytical tools for understanding quantum hypothesis testing and related quantum information processing tasks.Link for online session: http://meet.google.com/ejj-hfpf-xuw
Pieter Naaijkens (U. Cardiff, UK)
Superselection theory for stacked systems
Wednesday the 18th of February, 2026, 11:00, Room 2.2.D08
In this talk I will introduce the theory of quantum superselection sectors from an algebraic perspective. We will then consider the DHR superselection sector theory for stacked topologically ordered systems. It is relatively easy to construct sectors of the stacked system from sectors of the individual layers. The question if all sectors of the stacked system are obtained in this way is more subtle. I will show that under physically reasonable conditions, this is the case and we can give a complete characterisation of the sector theory of the stacked system. I will then discuss some applications to invertible phases and the colour code. Based on joint work with Sven Bachmann, Alan Getz and Naomi Wray.Link for online session (Active on request): https://meet.google.com/ksm-xzou-bgp
Daniel Burgarth (Friedrich-Alexander-Universität Erlangen)
Orbital Angular Momentum - a journey through 100 years of quantum mechanics with a surprising twist
Monday the 10th of November, 2025, 13:00, Room 2.2.D08
I provide a historical view on how the integer quantization of orbital angular momentum was discovered and how it is taught till date. Then I explain a recent twist to the story (https://arxiv.org/abs/2506.03254, joint work with Paolo Facchi).Link for online session (Active on request): https://meet.google.com/oma-cnyg-tjy
Alberto Ruiz-de-Alarcón (CUNEF Universidad)
Topologically-ordered 2-d quantum phases and the Haag duality property
Tuesday the 4th of November, 2025, 13:00, Room 2.2.D08
Topologically ordered two-dimensional quantum many-body systems have attracted considerable attention because of their striking emergent phenomena, such as ground-state degeneracy depending on topology, the absence of local order parameters, or long-range entanglement. A particularly important feature is the appearance of quasiparticle excitations with nontrivial braid statistics, called anyons, which are actually expected to classify all non-chiral two-dimensional gapped quantum phases. However, a fully rigorous understanding remains incomplete. A key insight established by Naaijkens is that a strong notion of locality, known as Haag duality, implies the existence of anyons (specifically, that one can derive a C*-braided tensor category for certain equivalence classes of irreducible representations of the quasi-local observable C*-algebra). More recently, Ogata introduced a weaker but phase-stable version, known as approximate Haag duality. An open problem has been to establish this property in quantum spin systems beyond the few known cases: one-dimensional systems and two-dimensional Abelian quantum double models. In this talk, I will present a construction of topologically ordered two-dimensional tensor-network states based on biconnected C*-weak Hopf algebras, which serve as renormalization fixed-point representatives of all known non-chiral phases (i.e. encompassing Levin-Wen string-net models), and sketch a proof of the fact that these states satisfy (approximate) Haag duality. Based on arXiv:2204.05940 and arXiv:2509.23734.Link for online session (Active on request): https://meet.google.com/ait-uyoc-krg
Ernesto Estrada (IFISC)
Towards Network Geometrodynamics. Directed Networks.
Friday the 10th of October, 2025, 11:00, NOTICE THE UNUSUAL LOCATION: ICMAT Aula Gris 2.
I will start by motivating the problems emerging for the analysis of diffusion on directed and mixed graphs. Then, I will introduce a model or reaction-diffusion on networks where the diffusive part is controlled by the standard graph Laplacian operator and the reaction one by an imaginary potential. This results in a Hermitian reaction-diffusion operator, which is mathematically identical to the 'magnetic' Laplacian of the graph. By solving the abstract Cauchy problem of the reaction-diffusion based on this operator I will prove how the capacity of the whole network to transporting mass between two vertices is a (real-valued) Euclidean distance in the graph. Although the embedding of the graph induced by this distance is in a complex Euclidean space, we can define some real, Hermitian and complex angles between different planes defined on the graph. In particular, I will focus on the meaning and applications of the Kahler angles formed between pairs of vertices in the graph.Link for online session (Active on request): https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380