Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
25/03/22	Seminario	14:30	15:30	1201 Dal Passo	Andrea SANTI	UiT The Arctic University of Norway Università di Roma "Tor Vergata"	Algebra & Representation Theory Seminar (ARTS) "G(3) supergeometry and a supersymmetric extension of the Hilbert-Cartan equation" - in live & streaming mode - ( click HERE* to attend the talk in streaming )* Abstract I will report on the realization of the simple Lie superalgebra G(3) as symmetry superalgebra of various geometric structures - most importantly super-versions of the Hilbert-Cartan equation and Cartan's involutive system that exhibit G(2) symmetry - and compute, via Spencer cohomology groups, the Tanaka-Weisfeiler prolongation of the negatively graded Lie superalgebras associated with two particular choices of parabolics. I will then discuss non-holonomic superdistributions with growth vector (2\|4 , 1\|2 , 2\|0) obtained as super-deformations of rank 2 distributions in a 5-dimensional space, and show that the second Spencer cohomology group gives a binary quadric, thereby providing a "square-root" of Cartan's classical binary quartic invariant for (2,3,5)-distributions. This is a joint work with B. Kruglikov and D. The. N.B.: please click HERE to attend the talk in streaming.
22/03/22	Seminario	16:00	17:00	1201 Dal Passo	Piero Montecchiari	Università Politecnica Delle Marche	Nondegeneracy Conditions and Multiplicity of Solutions for Differential Equations ( MS Teams Link for the streaming ) Abstract We discuss some results about the existence and multiplicity problem of different kind of entire solutions for some systems of semilinear elliptic equations, including the Allen Cahn and the NLS type models, under weak global non degeneracy conditions. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
22/03/22	Seminario	14:30	15:30	1201 Dal Passo	Davide Lombardo	Università di Pisa	Geometry Seminar On the distribution of rational points on ramified covers of abelian varieties Abstract Let A be an abelian variety over a number field K, with A(K) Zariski-dense in A. In this talk I will show that for every irreducible ramified cover π : X → A the set A(K) \ π (X(K)) of K-rational points of A that do not lift to X(K) is still Zariski-dense in A, and that in fact it even contains a finite-index coset of A(K). This result is motivated by Lang's conjecture on the distribution of rational points on varieties of general type and confirms a conjecture of Corvaja and Zannier concerning the "weak Hilbert property" in the special case of abelian varieties.
15/03/22	Seminario	16:00	17:00	1201 Dal Passo	Anna Maria Candela	Universita' di Bari	Soliton solutions for quasilinear modified Schroedinger equations ( MS Teams Link for the streaming ) Abstract Link to the abstract NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
15/03/22	Seminario	14:30	15:30	1201 Dal Passo	Mark de Cataldo	Stony Brook	Geometry Seminar Some things I know and some I don't about moduli spaces of Higgs bundles Abstract I report on two joint works: with my current student Siqing Zhang, and with Davesh Maulik (MIT), Junliang Shen (Yale) and Siqing Zhang. The Dolbeault moduli space of Higgs bundles over a complex algebraic curve is one of the ingredients in the Nonabelian Hodge Theory of the curve. Much is known and much is not known about this theory. From my current point of view, I consider some of the structures on the cohomology ring of these moduli spaces. I will start by introducing the P=W conjecture in Nonabelian Hodge Theory, mostly as motivation for the two joint works. The first work provides a cohomological shadow of a (strictly speaking non-existing) Nonabelian Hodge Theory for curves over fields of positive characteristic, and it unearths a new pattern for moduli of Higgs bundles in positive characteristic, which we call p-multiplicativity. The second work applies the first over a finite field to provide indirect evidence for the P=W conjecture over the complex numbers.
11/03/22	Seminario	16:00	17:00	1201 Dal Passo	Rita FIORESI	Università di Bologna	Algebra & Representation Theory Seminar (ARTS) "Generalized Root Systems" - in live & streaming mode - ( please click HERE* to attend the talk in streaming )* N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 Abstract In Lie theory we define root systems in several contexts: Lie algebras, superalgebras, affine algebras, etc. There is even more: Kostant defines a more general notion of root systems, by taking roots with respect to a generic toral subalgebra (i.e. not necessarily maximal). All these notions of root systems do not behave well with respect to quotients: the quotient (or projection) of a root systems is not in general a root system. We present here a more general notion of root system, inspired by Kostant, which accomodates all of the above examples and behaves well with respect to quotients and projections. We give a classification theorem for rank 2 generalized root system: there are only 14 of them up to combinatorial equivalence, moreover they are all quotients of Lie algebra root systems. We also prove that root systems of contragredient Lie superalgebras are quotients of root systems of Lie algebras, up to combinatorial equivalence. In the end, we relate our construction with the problem of determining the conjugacy class of two Levi subgroups in a Lie (super)algebra. N.B.: please click HERE to attend the talk in streaming.
11/03/22	Seminario	14:30	15:30	1201 Dal Passo	Andrea BIANCHI	University of Copenhagen	Algebra & Representation Theory Seminar (ARTS) "Symmetric groups, Hurwitz spaces and moduli spaces of surfaces" - in live & streaming mode - ( please click HERE* to attend the talk in streaming )* N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 Abstract
08/03/22	Seminario	14:30	15:30	1201 Dal Passo	Matilde Manzaroli	University of Tübingen	Geometry Seminar Real fibered morphisms of real del Pezzo surfaces Abstract A morphism of smooth varieties of the same dimension is called real fibered if the inverse image of the real part of the target is the real part of the source. It goes back to Ahlfors that a real algebraic curve admits a real fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, in a joint work with Mario Kummer and Cédric Le Texier, we are interested in characterising real algebraic varieties of dimension n admitting real fibered morphisms to the n-dimensional projective space. We present a criterion to construct real fibered morphisms that arise as finite surjective linear projections from an embedded variety; this criterion relies on topological linking numbers. We address special attention to real algebraic surfaces. We classify all real fibered morphisms from real del Pezzo surfaces to the projective plane and determine when such morphisms arise as the composition of a projective embedding with a linear projection.
01/03/22	Seminario	16:00	17:00	1201 Dal Passo	Pierre Cardaliaguet	Université Paris Dauphine	Seminario di Equazioni Differenziali On the convergence rate for the optimal control of McKean-Vlasov dynamics (MS Teams link for the streaming at the end of the abstract) Abstract In this talk I will report on a joint work with S. Daudin (Paris Dauphine), Joe Jackson (U. Texas) and P. Souganidis (U. Chicago). We are interested in the convergence problem for the optimal control of McKean-Vlasov dynamics, also known as mean field control. We establish an algebraic rate of convergence of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem. This convergence rate is established in the presence of both idiosyncratic and common noise, and in a setting where the value function for the McKean-Vlasov problem need not be smooth. Our approach relies crucially on Lipschitz and semi-concavity estimates, uniform in N, for the N-particle value functions, as well as a certain concentration inequality. MS Teams Link for the streaming Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006
01/03/22	Seminario	14:30	15:30	1201 Dal Passo	Emanuele Macrì	Université Paris-Saclay	Geometry Seminar Lagrangian fibrations on hyper-Kähler fourfolds [click here to attend the talk in streaming (MS Teams)] Abstract We will present joint work with Olivier Debarre, Daniel Huybrechts and Claire Voisin on the SYZ hyper-Kähler conjecture for fourfolds under certain topological assumptions. As application, this proves a conjecture by O'Grady that a hyper-Kähler fourfold whose cohomology ring is isomorphic to the one of the Hilbert square of a K3 surface is a deformation of a Hilbert square.