Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
26/03/25	Seminario	16:00	17:00	1201 Dal Passo	Raphael Bousso	UC Berkeley	Colloquium Levi Civita Gravity as a Quantum Computer Note: Sponsored by the European Research Council by the Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models” Sponsored by Miur Prin project contract 2020KR4KN2 “String Theory as abridge between Gauge Theories and Quantum Gravity” Abstract Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity already knows" about its own quantum states (the entropy of a black hole), and about those of all matter (via the covariant entropy bound). The results we are able to extract from classical gravity are inherently non-perturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, and the construction of gravitational holograms in our universe using techniques from single-shot quantum communication protocols.
25/03/25	Seminario	14:30	16:00	1101 D'Antoni	Enrico Fatighenti	Università di Bologna	Geometry Seminar Modular vector bundle on Hyperkahler manifolds Abstract We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3^[2]-type. These are obtained by performing standard linear algebra constructions on the examples studied by O’Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler. Interestingly enough, these constructions are almost never infinitesimally rigid, and more precisely we show how to get (infinitely many) 20 and 40 dimensional families. This is a joint work with Claudio Onorati. Time permitting, I will also present a work in progress with Alessandro D'Andrea and Claudio Onorati on a connection between discriminants of vector bundles on smooth and projective varieties and representation theory of GL(n). Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
18/03/25	Seminario	14:30	15:30	1201 Dal Passo	Gianmaria Verzini	Politecnico di Milano	Seminario di Equazioni Differenziali Singular analysis of a shape optimization problem arising in population dynamic Abstract When analyzing the survival threshold for a species in population dynamics, one is led to consider the principal eigenvalue of some indefinite weighted problems in a bounded domain. The minimization of such eigenvalue, associated with either Dirichlet or Neumann boundary conditions, translates into a shape optimization problem. We perform the analysis of the singular limit of this problem, in case of arbitrarily small favorable region. We show that, in this regime, the favorable region is connected, and it concentrates at points depending on the boundary conditions. Moreover, we investigate the interplay between the location of the favorable region and its shape. Joint works with Lorenzo Ferreri, Dario Mazzoleni and Benedetta Pellacci. NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
18/03/25	Seminario	14:30	16:00	1101 D'Antoni	Grigory Mikhalkin	Université de Genève	Geometry Seminar Vitruvian polygons in symplectic problems Abstract Each angle formed by two rays with integer slopes has two basic integer invariants: its height and its width. An angle is called Vitruvian (after a Roman architect Vitruvius advocating proportions between height and width) if its height divides its length. A Vitruvian polygon is a polygon, such that all of its angles are Vitruvian. Vitruvian polygons form a distinguished class of polygons in Tropical Planimetry. After a breakthrough idea of Galkin and Usnich from 2010, Vitruvian triangles (studied, under a different guise, by Hacking and Prokhorov, buiding up on an earlier work of Manetti to obtain the complete classification of toric degenerations of the plane) started to play a prominent role also in Symplectic Geometry. In the talk, I review some of these applications, as well as a new symplectic application, involving use of Vitruvian quadrilaterals (work in progress, joint with Richard Hind and Felix Schlenk). Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
14/03/25	Seminario	14:30	15:30	1201 Dal Passo	Lydia GÖSMANN	Ruhr-Universität Bochum	Algebra & Representation Theory Seminar (ARTS) "Nakajima varieties of quivers" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Moduli spaces of representations associated to quivers are algebraic varieties encoding the continuous parameters of linear algebraic classification problems. In recent years their topological and geometric properties have been explored to investigate wild quiver classification problems. The goal of this talk is the construction of the Nakajima variety of a quiver as one of these moduli spaces. Starting with basic definitions from the representation theory of quivers, fundamental concepts like doubling and framing are introduced. Via geometric invariant theory Nakajima varieties can be defined. We will discuss their properties focusing on the example of the quiver consisting of one vertex and no arrows. Finally, further relations to recent research interests are explained. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
12/03/25	Seminario	16:00	17:00	1201 Dal Passo	Roberto Volpato	Università of Padova - INFM	Operator Algebras Seminar Topological defects in vertex operators algebras Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) Abstract Topological defects in quantum field theory have received considerable attention in the last few years as generalizations of the concept of symmetry. In the context of two dimensional conformal field theory, the properties of topological defects have been studied since the 90s, in particular in a series of works by Froehlich, Fuchs, Runkel and Schweigert. In this talk, I will discuss some applications of these ideas from physics to the theory of vertex operator (super-)algebras. In particular, I will describe some recent results about topological defects in the Frenkel-Lepowsky-Meurman Monstrous module, as well as in the Conway module, i.e. the holomorphic vertex operator superalgebra at central charge 12 with no weight 1/2 states. Finally, I will speculate about possible generalizations of the Moonshine conjectures. This is partially based on ongoing joint work with Roberta Angius, Stefano Giaccari, and Sarah Harrison.
11/03/25	Seminario	14:30	16:00	1101 D'Antoni	Roberto Volpato	Università di Padova	Geometry Seminar Topological defects and sigma models on K3 surfaces Abstract A famous theorem by Mukai (1988) provides a classification of all possible finite groups admitting a faithful action by symplectic automorphisms on some K3 surface. In 2011, in collaboration with Gaberdiel and Hohenegger, we proposed that a 'physics version' of Mukai theorem should hold for certain two dimensional conformal quantum field theories, called non-linear sigma models (NLSM) on K3, that describe the dynamics of a superstring moving in a K3 surface. In particular, we provided a classification of all possible groups of symmetries of NLSM on K3, that commute with the N=(4,4) algebra of superconformal transformations. This result was later re-interpreted by Huybrechts as a classification of the finite groups of autoequivalences of the bounded derived category of coherent sheaves on a K3 surface. In the last few years, the concept of symmetry group in quantum field theory has been vastly generalized. In the context of two dimensional conformal field theories, these developments suggest that the idea of 'group of symmetries' should be replaced by 'fusion category of topological defects'. We discuss how our previous classification result could be extended to include fusion categories of topological defects in non-linear sigma models on K3. The geometric interpretation of these categories is still mysterious. This is based on joint work in collaboration with Roberta Angius and Stefano Giaccari. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures
11/03/25	Seminario	14:30	15:30	1201 Dal Passo	Michele Palladino	Università dell'Aquila	Seminario di Equazioni Differenziali Optimal Control and Reinforcement Learning Abstract The talk discusses a framework to analyze certain model-based reinforcement learning algorithm. Roughly speaking, this approach consists in designing a model to deal with situations in which the system dynamics is not known and encodes the available information about the state dynamics that an agent has as a measure on the space of functions. In this framework, a natural question is if whether the optimal policies and the value functions converge, respectively, to an optimal policy and to the value function of the real, underlying optimal control problem as soon as more information on the environment is gathered by the agent. We provide a positive answer in the linear-quadratic case and discuss some results also in the control-affine nonlinear case. NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
04/03/25	Seminario	14:30	15:30	1201 Dal Passo	Adriana Garroni	Sapienza, Università di Roma	Seminario di Equazioni Differenziali Grain boundaries in polycrystals: the role of topological defects Abstract Locally periodic structures show regions (grains) with different orientations and at the boundaries between grains there is the appearance of defects. This happens in physical systems (for instance at microscopic scales for metals or patterns in block copolymers) as well as in more geometric models (as local tassellations for partions and clusters, or optimal location problems). In all these cases the energy governing the systems concentrates at the grain boundaries. The understanding of this “surface tesion” is a key ingredient in order to reduce the complexity of the problem and work in a so to say sharp interface model. I will present some recent results in this direction focussing on a two dimensional model for grain boundaries in metals, which account for the elastic long range distorsion due to the presence of crystal defects (dislocations). The latter is inspired to a recent model proposed by Lauteri and Luckhaus. Its asymptotics as the lattice spacing tends to zero produces a sharp interface model for grain boundaries which confirms the Read-Shockley law for small angle grain boundaries. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
04/03/25	Seminario	14:30	16:00	1101 D'Antoni	Nicolas Mascot	Trinity College Dublin	Geometry and Number Theory Seminar Algorithms for plane algebraic curves, with an application to integrating algebraic functions Abstract We will outline an efficient algorithmic approach to the desingularisation of plane algebraic curves. Applications include computing the genus, Riemann-Roch spaces, and testing whether the curve is hyperelliptic. Afterwards, we will see that the (apparently rustic-looking) problem of finding the antiderivative of an algebraic function is actually related to the (much cooler-sounding) ability to test whether certain divisors are torsion in the Picard group of a curve. We will show how to achieve this thanks to the algorithms outlined earlier, which will lead us to a complete integration algorithm for algebraic functions based on arithmetic geometry. The talk will feature many explicit examples. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)