Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
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)
28/02/25	Seminario	16:00	17:00	1201 Dal Passo	Damien SIMON	Université Paris-Saclay	Algebra & Representation Theory Seminar (ARTS) "Chiral differential operators on a reductive group and representation theory" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Vertex algebras of chiral differential operators on a complex reductive group G are "Kac-Moody" versions of the usual algebra of differential operators on G. Their categories of modules are especially interesting because they are related to the theory of D-modules on the loop group of G. That allows one to reformulate some conjectures of the (quantum) geometric Langlands program in the language of vertex algebras. For instance, in view of the geometric Satake equivalence, one may expect the appearance of the category of representations of the Langlands dual group of G. In this talk I will define this family of vertex algebras and we will see that they are classified by a certain parameter called level. Then, for generic levels, we will see that "to find" the Langlands dual group, it is necessary to perform a quantum Hamiltonian reduction. Finally I will build simple modules on the closely related equivariant W-algebra that match the combinatorics of the Langlands dual group. N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
28/02/25	Seminario	14:30	15:30	1201 Dal Passo	Andrea Pizzi	Università di Roma "Tor Vergata"	Joint Topology & Algebra and Representation Theory Seminar (T-ARTS) (Multi-)Simplicial methods for Configuration Space Recognition Abstract The goal of this talk is to algebraically model the S_r-equivariant homotopy type of the configuration space of r labeled and distinct points in d-dimensional Euclidean space. I will present and compare two models: the Barratt-Eccles simplicial set and the multisimplicial set of 'surjections'. I will introduce multisimplicial sets and discuss their connection to more well-known simplicial sets. Multisimplicial sets can model homotopy types using fewer cells, making them a highly useful tool. Following this, we will explore in detail how to recognize configuration spaces in the aforementioned models by playing with a graph poset. An explicit relationship between the models will also be presented. This is a joint work with Anibal M. Medina-Mardones and Paolo Salvatore.
26/02/25	Seminario	16:00	17:00	1201 Dal Passo	Valerio Proietti	University of Oslo	Operator Algebras Seminar From aperiodic materials to rigidity of foliations C-algebras* Abstract Inspired by the C-algebra of observables for a conduction electron in an aperiodic material, we study dynamical systems associated to solvable Lie groups and their associated foliated spaces. We establish a relation between the homotopy type of the foliated space and the -isomorphism class of the foliation C-algebra which is naturally attached to it. This result can be viewed as a simple noncommutative analogue of the famous Borel conjecture in topology. We make use of the classification result for nuclear C-algebras in terms of the Elliott invariant. In cases of C*-algebras of physical origin, the tracial part of such invariant can be interpreted as the integrated density of states of the system. This is joint work with H. Wang and H. Guo.
25/02/25	Seminario	14:30	15:30	1201 Dal Passo	Dimitri Mugnai	Università della Tuscia	Seminario di Equazioni Differenziali Mixed operators in peridynamics Abstract We present some recent results concerning elliptic and evolution problems driven by mixed operators, which are the sum of local and nonlocal ones under a peridynamical approach, as introduced by Silling few years ago. NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
25/02/25	Seminario	14:30	16:00	1101 D'Antoni	Pim Spelier	Utrecht University	Geometry Seminar Gluing tropical curves and logarithmic curves, and logarithmic Gromov-Witten invariants Abstract The gluing maps on the moduli space of curves are integral to much of the enumerative geometry of curves. For example, Gromov-Witten invariants satisfy recursive relations with respect to the gluing maps. For log Gromov-Witten invariants, counting curves with tangency conditions, this fails at the very first step as logarithmic curves cannot be glued, by a simple tropical obstruction. I will describe a certain logarithmic enhancement of (M_{g,n}) from joint work with David Holmes that does admit gluing maps. With this enhancement, we can geometrically see a recursive structure appearing in log Gromov-Witten invariants. I will present how this leads to a pullback formula for the log double ramification cycle (roughly a log Gromov-Witten invariant of P^1). Time permitting, I will sketch how this extends to general log Gromov-Witten invariants (joint work with Leo Herr and David Holmes). This story tropicalises by replacing log curves with tropical curves (metrised dual graphs) and algebraic geometry by polyhedral geometry. In this language both the logarithmic enhancement and the recursive structure admit a simpler formulation. I will keep this tropical story central throughout. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
18/02/25	Seminario	14:30	15:30		Pierpaolo Esposito	Università Roma3	Seminario di Equazioni Differenziali Exponential PDEs in high dimensions Abstract For a quasilinear equation involving the n-Laplacian and an exponential nonlinearity, I will discuss quantization issues for blow-up masses in the non-compact situation, where the exponential nonlinearity concentrates as a sum of Dirac measures. A fundamental tool is provided here by some Harnack inequality of sup + inf type, a question of independent interest that we prove in the quasilinear context through a new and simple blow-up approach. If time permits, we will also discuss some recent progress concerning sharp sup+inf inequalities. Joint work with Marcello Lucia. NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
18/02/25	Seminario	14:30	16:00	1101 D'Antoni	Dario Weissmann	IMPAN, Warsaw	Geometry Seminar Distinguishing algebraic spaces from schemes Abstract We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. In the setting of a stack admitting a separated (good) moduli space this also yields a criterion for when the moduli space is a scheme. As an application we identify all separated good moduli spaces of vector bundles over a smooth projective curve which are schemes. This is joint work with Andres Fernandez Herrero and Xucheng Zhang. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
14/02/25	Seminario	16:00	17:00	1201 Dal Passo	Andrea GUIDOLIN	University of Southampton	Joint Topology & Algebra and Representation Theory Seminar (T-ARTS) "Algebraic Wasserstein distances and stable homological invariants of data" N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) Abstract Persistent homology, a popular method in Topological Data Analysis, encodes geometric information of data into algebraic objects called persistence modules. Invoking a decomposition theorem, these algebraic objects are usually represented as multisets of points in the plane, called persistence diagrams, which can be fruitfully used in data analysis in combination with statistical or machine learning methods. Wasserstein distances between persistence diagrams are a common way to compare the outputs of the persistent homology pipeline. In this talk, I will explain how a notion of p-norm for persistence modules leads to an algebraic version of Wasserstein distances which fit into a general framework for producing distances between persistence modules. I will then present stable invariants of persistence modules which depend on Wasserstein distances and can be computed efficiently. The use of these invariants in a supervised learning context will be illustrated with some examples. N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)