Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
20/03/24	Seminario	16:00	17:00	1201 Dal Passo	Jacopo Bassi	Università di Roma Tor Vergata	Operator Algebras Seminar How far is SL(3,Z) from being hyperbolic? Abstract Motivated by the problem of determining whether biexactness, the (AO)-property and von Neumann solidity are equivalent properties for a discrete countable group, I will discuss few recent results regarding analytic properties of SL(3,Z), related to hyperbolicity. I will focus on the role of measurable dynamics and proximality arguments in this context. Partly based on joint works with F. Radulescu and T. Amrutam. Some references: https://arxiv.org/abs/2305.16277 https://arxiv.org/abs/2111.13885 https://arxiv.org/abs/2403.05948
19/03/24	Seminario	14:30	16:00	1101 D'Antoni	Leo Herr	University of Utah	The rhizomic topology and tropical abelian varieties Abstract The log etale topology is a natural analogue of the etale topology for log schemes. Unfortunately, very few things satisfy log etale descent -- not even vector bundles or the structure sheaf. We introduce a new rhizomic topology that sits in between the usual and log etale topologies and show most things do satisfy rhizomic descent! As a case study, we look at tropical abelian varieties and give some exotic examples.
15/03/24	Seminario	16:00	17:00	1201 Dal Passo	Christophe HOHLWEG	Université du Quebec à Montréal	Algebra & Representation Theory Seminar (ARTS) "Shi arrangements in Coxeter groups" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Given an arbitrary Coxeter system (W,S) and a nonnegative integer m, the m-Shi arrangement of (W,S) is a subarrangement of the Coxeter hyperplane arrangement of (W,S). The classical Shi arrangement (m=0) was introduced in the case of affine Weyl groups by Shi to study Kazhdan-Lusztig cells for W. As two key results, Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W and that the union of their inverses form a convex subset of the Coxeter complex. The set of m-low elements in W was introduced to study the word problem of the corresponding Artin-Tits (braid) group and they turn out to produce automata to study the combinatorics of reduced words in W. In this talk, I will discuss how to Shi's results extend to any Coxeter system and show that the minimal elements in each Shi region are in fact the m-low elements. This talk is based on joint work with Matthew Dyer, Susanna Fishel and Alice Mark.
15/03/24	Seminario	14:30	15:30		Anna MICHAEL	Universität Magdeburg	Algebra & Representation Theory Seminar (ARTS) "Folded galleries - a museum tour through 192 years of math history" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Folded galleries, as introduced by Peter Littelmann in the 1990s, are combinatorial objects related to certain (subsets of) elements of Coxeter groups. They have shown to have versatile applications in algebra and geometry, making them an object of interest for current research. In this talk we will retrace the roots of their invention 192 years back in history, contemplate colorful illustrations of examples, and discover open questions for future applications. N.B.: the talk will be colloquium-style and aimed at a wide audience: no prerequisite of deep algebraic nor group theoretic knowledge is required.
13/03/24	Seminario	16:00	17:00	1201 Dal Passo	Boris Bolvig Kjær	University of Copenhagen	Operator Algebras Seminar The double semion model in infinite volume Abstract According to physics literature, topologically ordered gapped ground states of 2-dimensional spin systems can be described by a topological quantum field theory. Many examples arise from microscopic models with local commuting projector Hamiltonians, namely Levin-Wen models. In this talk, I will describe the general framework for classifying infinite volume gapped ground states (by Naaijkens, Ogata, et.al.) in the simple context of abelian Levin-Wen models. This framework is heavily inspired by the DHR analysis in relativistic quantum field theory. It applies to the doubled semion model whose anyon theory is a braided fusion category equivalent to the representation category of the twisted Drinfeld double of Z_2. Based on joint work with Alex Bols and Alvin Moon, https://arxiv.org/abs/2306.13762. Seminar schedule here: https://sites.google.com/view/oastorvergata/home-page.
12/03/24	Seminario	16:00	17:00	1201 Dal Passo	Shuang Chen	Central China Normal University	Invariant manifolds theory for fast-slow systems and applictions Abstract Dynamical systems with multiple time scales appear in a range of problems from applications. Invariant manifolds theory forms the foundation of qualitative analysis for their dynamics. In this talk, we will show our recent results on invariant manifolds theory for two classes of fast-slow systems, i.e., normally hyperbolic invariant manifolds for fast-slow high-dimensional systems and invariant structures for neutral differential equations with small delays.
12/03/24	Seminario	14:30	15:30	1201 Dal Passo	Alessandro Scagliotti	TU Munchen	Seminario di Equazioni Differenziali Control-theoretic approach for the approximation of the optimal transport map Abstract In this presentation, we tackle the problem of reconstructing the optimal transport map $T$ between two absolutely continuous measures $mu, u in mathcal{P}(mathbb{R}^n)$, and for this approximation we employ flows generated by linear-control systems in $mathbb{R}^n$. We first show that, under suitable assumptions on the measures $mu, u$ and on the controlled vector fields, the optimal transport map is contained in the $C^0_c$-closure of the flows generable by the system. In the case that discrete approximations $mu_N, u_N$ of the measures $mu, u$ are available, we use a discrete optimal transport plan to set up an optimal control problem. With a $Gamma$-convergence argument, we prove that its solutions corresponds to flows that provide approximations of the optimal transport map $T$. Finally, in virtue of the Pontryagin Maximum Principle, we propose an iterative numerical scheme for the resolution of the optimal control problem, resulting in an algorithm for the practical computation of approximations of the optimal transport map. This approach can be interpreted as the construction of a ''Normalizing Flow'' by means of a Residual Neural Network (ResNet). Based on a joint work with Sara Farinelli. [1] A. Scagliotti, S. Farinelli. Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs. arXiv preprint, 2023. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
12/03/24	Seminario	14:30	16:00	1101 D'Antoni	Andrea Di Lorenzo	Humboldt University (Berlin)	The importance of being a weighted blow-up Abstract Blow-ups are fundamental tools in algebraic geometry, and there are several results (e.g the famous Castelnuovo's theorem) that can be used to determine when a variety is obtained as a blow-up of a smooth variety along a smooth center. Weighted blow-ups play a similar role for stacks. In this talk I will present a criterion for finding out if a smooth DM stack is a weighted blow-up. I will apply this result for showing that certain alternative compactifications of moduli of marked elliptic curves are obtained via weighted blow-ups (and blow-downs). This in turn will prove to be useful in order to compute certain invariants, like Chow rings or Brauer groups. First part of this talk is a joint work with Arena, Inchiostro, Mathur, Obinna and Pernice; the second part of this talk is a joint work with L. Battistella.
05/03/24	Seminario	14:30	16:01	1101 D'Antoni	Víctor González Alonso	Leibniz Universität Hannover	Embedded deformations of curves with maximal variation of Hodge structure Abstract Given a family of complex (smooth projective) manifolds, one can measure its non-triviality by looking at how much the Hodge structures of the fibres change. This leads to the notion of maximal (infinitesimal) variation of Hodge structure (IVHS). In the case of families of curves, results of Lee-Pirola and of myself with Torelli imply that a general deformation of any curve has maximal IVHS. This is however not so clear if one wants the deformation to keep some further structure, such as the gonality of the curve or an embedding into a given surface. For example, it was only recently proved by Favale and Pirola that every smooth plane curve admits a deformation as a plane curve with maximal IVHS, and the question remains open for deformations of curves inside any other surface. In this talk I will present a joint work in progress with Sara Torelli extending this result to curves in P^1 x P^1, which turns out to be way more involved than the plane case.
05/03/24	Seminario	14:30	15:30	1201 Dal Passo	Stefano Baranzini	Università di Torino	Seminario di Equazioni Differenziali Chaotic phenomena for singular systems on surfaces Abstract The main focus of the talk will be a class of 2d singular mechanical systems on a surface S with a potential V having a finite number of singularities C := {c_1,..., c_n} of the form V(q) ~ C_i d(c_i,q)^{-a_i} where C_i>0, a_i >= 1 and q in O(c_i). The first result I will present is an existence one: there are periodic solutions in (infinitely) many conjugacy classes of pi_1(S,C). Using this fact, I will construct an invariant set for the system which admits a semi-conjugation with a Bernoulli shift. The second result I will discuss aims at identifying some situation in which the semi-conjugation is actually a conjugation and the invariant set constructed displays a chaotic behaviour. This happens, for instance, under some negativity condition on the curvature of S and for large values of the energy. Much emphasis will be put on the interplay between geometry, topology and variational methods. This is a joint work with Gian Marco Canneori. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)