Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
27/05/26	Colloquium	14:30	15:30		Alessandro Carlotto	Università di Trento	Colloquium di Dipartimento The latest on the generic regularity problem for minimal subvarieties Abstract It is well-known that submanifolds of least area for a fixed boundary (Plateau problem) or in a fixed homology class (homological Plateau problem) shall not be smoothly embedded in general, but rather exhibit a singular set (as first noted by Simons and then justified by Bombieri-De Giorgi-Giusti half a century ago). The first singular example(s) of minimizers were in fact extremely rigid: cones with an isolated singularity at the origin. As it is now clear, the occurrence of singularities is an intriguing and partly elusive pathology that may be imputable to diverse causes, ranging from topological obstructions (related e.g. to pioneering work by Thom) to basic complex-analytic phenomena. But how wild may the singular set possibly be, and how frequently will it be observable as one varies the boundary in question or, respectively, the background metric? Over the past five years we have witnessed striking advances on both fronts. In this lecture I will present the general state of the art and my contributions to the latter question(s), known as the generic regularity problem, as well as some surprising geometric applications. Based on joint works with Yangyang Li and Zhihan Wang. NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
22/05/26	Seminario	16:00	17:00	1201 Dal Passo	Olivier SCHIFFMANN	CNRS - Paris Saclay	Algebra & Representation Theory Seminar (ARTS) - joint session with the Topology Seminar - "Khovanov-Lauda-Rouquier type algebras for the projective line" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract   The Khovanov-Lauda-Rouquier (KLR) algebras associated to quivers have been used to categorify positive halves of quantum enveloping algebras of Kac-Moody algebras. Suitable quotients of these algebras, the cyclotomic KLR algebras, categorize highest weight integrable re-presentations, and also lead to interesting knot and link invariants. In this talk, we will present some work which goes towards an analogous theory in which the quiver gets replaced by a smooth projective curve (the case of the projective line is already interesting). <br> This is joint work with Fang Yang. <br>     <em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
22/05/26	Seminario	14:30	15:30	1201 Dal Passo	Xujia CHEN	ISTA, Wien	Algebra & Representation Theory Seminar (ARTS) - joint session with the Topology Seminar - "A product operation on disk fiber bundles and its relation to the Lie bracket in graph homology" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract In this talk we will be concerned with smooth, framed fiber bundles whose fibers are the standard d-dimensional disk, trivialized along the boundary. "Kontsevich's characteristic classes" are invariants defined for these bundles: given such a bundle π : E ⟶ B , we can associate to it a collection of cohomology classes in H^(B). On the other hand, there is a "bracket operation" for these bundles defined by Sander Kupers: namely, given two such bundles π₁ and π₂ as input, we can output a "bracket bundle" [π₁, π₂]. I will talk about this bracket bundle construction and a formula relating the Kontsevich's class of [π₁, π₂] with those of π₁ and π₂ . The main input of the proof is a generalization of the Fulton-MacPherson configuration spaces. This is joint work with Robin Koytcheff and Sander Kupers. N.B.:* this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
19/05/26	Seminario	14:30	15:30	1201 Dal Passo	Lun Guo	South-Central Minzu University, Wuhan	Seminario di Equazioni Differenziali Standing waves for Hartree system with Hardy-Littlewood-Sobolev critical exponent Abstract In this talk, I will give some recent results on the Hartree system with Hardy-Littlewood-Sobolev critical exponent. Under some technical conditions on potentials, we investigate the existence and multiplicity of standing waves by using variational method combined with Brouwer degree theory and Ljusternik-Schnirelmann theory. NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
19/05/26	Seminario	14:30	15:30	2001	Daniele Angella	Università di Firenze	Seminario di Analisi e Geometria Complessa Some problems concerning canonical metrics in Hermitian non-Kähler geometry Abstract We investigate several possible notions of "canonical'' metrics that naturally arise in Hermitian non-Kähler geometry. In particular, we study an analogue of the Yamabe problem in the non-Kähler setting, concerning the existence of Hermitian metrics with constant scalar curvature with respect to the Chern connection. We also develop a moment map interpretation of the Chern scalar curvature in the locally conformally Kähler setting. Another tool for highlighting ''canonical structures'' is the Chern–Ricci flow. The long-time behavior of its solutions is expected to reflect the underlying complex structure, and we present some evidence of this in the case of compact complex surfaces. This talk is based on joint work with Simone Calamai, Mauricio Corrêa, Francesco Pediconi, Cristiano Spotti, Valentino Tosatti, and Oluwagbenga Joshua Windare.
19/05/26	Seminario	14:30	16:00	1101 D'Antoni	Xavier Roulleau	Université d'Angers	Geometry Seminar Point and line arrangements: moduli spaces and operator actions Abstract Point and line arrangements in the plane arise in various contexts, including topology (Zariski pairs), algebra (freeness), and combinatorics. Notably, Hirzebruch utilized these configurations to construct specific ball-quotient surfaces. In this talk, I will introduce operators acting on these arrangements and their corresponding parameter spaces. We shall see how certain elliptic modular surfaces and modular curves can be recovered as parameter spaces of point arrangements under the action of these operators. *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
13/05/26	Seminario	11:00	12:00	2001	Manuel Garzon Martinez	Universidad de Sevilla	Seminario di Sistemi Dinamici Low-energy dynamics in generic potential fields Abstract The question of whether a Hamiltonian system is typically integrable or chaotic is a central topic in dynamical systems, which traces back to the pioneering works of Poincaré in Celestial Mechanics. A satisfactory picture of the typical dynamics of such systems did not emerge until the 1970s, when Markus and Meyer established that a generic (in the Baire category sense) Hamiltonian system on a compact symplectic manifold is neither integrable nor ergodic. On the contrary, the case of natural Hamiltonian systems is much less studied, in spite of its central relevance in mathematical physics. Specifically, a natural Hamiltonian corresponds to the situation in which the symplectic manifold is the cotangent bundle of a manifold M , and the Hamiltonian is given by the sum of a fixed kinetic energy term and a potential field V in C^{infty}(M ; R). It is known that a generic potential field on a compact manifold is non-ergodic. Moreover, near the potential maximum, the system may exhibit positive topological entropy under (non-generic) suitable conditions. Nevertheless, the fundamental question of whether motion at low energy levels is typically integrable or chaotic remains open to date. This difficulty arises because standard transversality methods are no longer applicable, raising the conjecture of whether classical results on generic non-integrability extend to the setting of potential fields. In this talk we shall show that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential V on T^2 exhibits an arbitrarily high number of hyperbolic periodic orbits and a positive-measure set of invariant tori. To put this result in perspective, the existence of hyperbolic periodic orbits is the natural starting point to establish the presence of chaos in dynamical systems. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).
08/05/26	Seminario	16:00	17:00		Christophe HOHLWEG	Université du Quebec, Montreal	Algebra & Representation Theory Seminar (ARTS) "Weak order on groups generated by involution" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract   An involution system (<em>W</em>,<em>S</em>), that is a group <em>W</em> generated by a set of involutions <em>S</em>, is naturally endowed with a weak order arising from orienting its Cayley graph. If (<em>W</em>,<em>S</em>) is a Coxeter system, Björner showed that the weak order is a complete meet-semilattice. This fact has many important consequences for Coxeter systems and their related structures. <br>   In this talk, we discuss the following question: For which involution systems is the weak order a complete meet-semilattice? <br>   The class of involution systems that satisfies this condition is larger than the class of Coxeter systems (it contains, for instance, cactus groups). In the case of an involution system with sign character, we provide a finite presentation by generators and relations and a classification in rank 3. If time allows, we will also discuss open problems (e.g. in relation to automatic structures, geometric representations,…). <br>   This is joint work with Fabricio Dos Santos and Aleksandr Trufanov. <br>     <em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>
08/05/26	Seminario	14:30	15:30	1201 Dal Passo	Francesco BRENTI	Università di Roma "Tor Vergata"	Algebra & Representation Theory Seminar (ARTS) "Combinatorics of Cuntz algebra" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract C^-algebras are fundamental objects in the mathematical descriptions of quantum mechanics and field theory. Cuntz algebras are a family of C^-algebras first defined in [Comm. Math. Phys. 57 (1977), 173-185]. In this talk I will survey the main combinatorial concepts and results arising from, and related to, these algebras. In particular, I will define certain permutations and review the state of the art on their characterization, enumeration, and construction. I will also explain how these results can be applied to the construction of subgroups of the automorphism, and outer automorphism, groups of these algebras. I will conclude with some open problems and directions for further research.. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
06/05/26	Seminario	16:00	17:00	1201 Dal Passo	Pieter Naaijkens	Cardiff University	Operator Algebras Seminar Local topological order and boundary algebras Abstract Topologically ordered phases of matter have interesting features, such as the existence of quasi-particles with braid statistics. These quasi-particles can be studied using an AQFT-inspired approach along the lines of the celebrated Doplicher-Haag-Roberts programme on superselection sectors. In this talk I will introduce an axiomatisation, called local topological order, of such quantum models. These axioms are defined in terms of nets of (ground state) projections satisfying certain conditions. They allow us to define a physical boundary algebra, and I will outline how in concrete models (such as Kitaev's toric code or Levin-Wen models) the bulk superselection sector (''DHR'') category can be recovered from the boundary algebra, giving a mathematical framework for topological holography. If time permits, I will explain how these axioms can be extended to included models with topological boundaries, and outline how this can be used to study, for example, Walker-Wang bulk-boundary systems. Based on joint work with Corey Jones, Dave Penneys and Daniel Wallick (arXiv:2307.12552 and arXiv:2506.19969)