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 )
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
Let A be an abelian variety over a number field K, with A(K) Zariskidense 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 Krational points of A
that do not lift to X(K) is still Zariskidense in A, and that in fact it even contains a finiteindex 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 )
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
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 nonexisting) 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 pmultiplicativity. 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
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

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
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 ndimensional 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 McKeanVlasov
dynamics
(MS Teams link for the streaming at the end of the 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 McKeanVlasov dynamics, also known as mean field control. We establish an algebraic rate of convergence of the value functions of Nparticle stochastic control problems towards the value function of the corresponding McKeanVlasov 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 McKeanVlasov problem need not be smooth. Our approach relies crucially on Lipschitz and semiconcavity estimates, uniform in N, for the Nparticle 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 ParisSaclay  Geometry Seminar
Lagrangian fibrations on hyperKähler fourfolds
[click here to attend the talk in streaming (MS Teams)]
We will present joint work with Olivier Debarre, Daniel Huybrechts and
Claire Voisin on the SYZ hyperKähler conjecture for fourfolds under
certain topological assumptions.
As application, this proves a conjecture by O'Grady that a
hyperKähler fourfold whose cohomology ring is isomorphic to the one
of the Hilbert square of a K3 surface is a deformation of a Hilbert
square. 
25/02/22  Seminario  16:00  17:00  1201 Dal Passo  Eugenio GIANNELLI  Università di Firenze 
Algebra & Representation Theory Seminar (ARTS)
"On Sylow Branching Coefficients"
 in live & streaming mode 
( please click HERE to attend the talk in streaming )
In this talk we will discuss the nature of the relationship between the representations of a finite group G and those of a Sylow subgroup P of G.
We will introduce Sylow Branching Coefficients (SBCs) and we will show how the study of these numbers led us to prove a conjecture proposed by Malle and Navarro in 2012. We will conclude by presenting new results on SBCs in the case where G is the symmetric group.
The talk is based on joint works with Law, Long, Navarro, Vallejo and Volpato.
N.B.: please click HERE to attend the talk in streaming.
