12/12/19  Seminario  16:30  17:30  1201 Dal Passo  Antonio Lerario  SISSA Trieste  Lowdegree approximation of real singularities
In this talk I will discuss some recent results that allow to approximate a real singularity given by polynomial equations of degree $d$ (e.g. the zero set of a polynomial, or the number of its critical points of a given Morse index) with a singularity which is diffeomorphic to the original one, but it is given by polynomials of degree $O(d^{1/2}log d)$. The approximation procedure is constructive (in the sense that one can read the approximating polynomial from a linear projection of the given one) and quantitative (in the sense that the approximating procedure will hold for a subset of the space of polynomials with measure increasing very quickly to full measure as the degree goes to infinity).
This is based on a combination of joint works with P. Breiding, D. N.
Diatta and H. Keneshlou. 
11/12/19  Seminario  16:00  17:00  1201 Dal Passo  Lorenzo Panebianco  Sapienza  A comment on the vacuum relative entropy for the Virasoro nets
Quantum information theoretic considerations in quantum field theory have attracted a lot of attention in recent years. In this context, relative entropy is one of the main studied objects and an explicit expression for it is a widely studied problem. In this talk we describe the structure of the Virasoro net and we illustrate our main result, that is a generalization of a recent work of S. Hollands. In particular, we verify the QNEC inequality for coherent states by calculating the second derivative of the vacuum relative entropy with respect to translations. 
10/12/19  Seminario  16:00  17:00  1101 D'Antoni  Eleonora di Nezza  Paris Sorbonne  Metric geometry of singularity types
(Quasi)Plurisubharmonic functions are a key notion in complex geometry.
The study of their singularity (in terms, for example, of integrability properties
or smoothing procedures) is conceived to develop analytic techniques in order to
solve problems in complex and algebraic geometry.
In this talk we study the space of all possible singularity types of
quasiplurisubharmonic functions and we introduce a natural (pseudo)distance on it.
As applications we present a stability result for complex MongeAmpe're equations with
prescribed singularity and a semicontinuity result for multiplier ideal sheaves
associated to singularity types. This is a joint work with T. Darvas and C. Lu. 
10/12/19  Seminario  14:30  15:30  1201 Dal Passo  Roberto Guglielmi  Fundação Getúlio Vargas, Rio de Janeiro, Brazil  Indirect stabilization of hyperbolic systems
We investigate stability properties of systems of hyperbolic equations, with coupling and damping terms acting either on the boundary of the domain or distributed in it.
We study systems where only one component is damped, while the other equation is indirectly stabilized through the coupling with the first component. We first show that uniform exponential stability cannot hold for the whole system, thus weaker decay rates should be sought for. Therefore, by means of energytype methods, we prove polynomial decay of the energy of solutions, linking the decay rate to the regularity of the initial conditions. 
06/12/19  Seminario  15:30  16:30  1101 D'Antoni  Federico Caucci  Sapienza Università di Roma  Derived invariants of irregular varieties
It is a natural and interesting problem to figure out how much of the geometry of a smooth complex projective variety is determined by its bounded derived category. We give a general result in this direction: the derived invariance of the cohomology ranks
of the pushforward under the Albanese map of the canonical line bundle. In the case of varieties of maximal Albanese dimension, this settles a conjecture of LombardiPopa and proves the derived invariance of the Hodge numbers h^{0, j}, for all j. This is a joint work with G. Pareschi. 
06/12/19  Seminario  14:30  15:30  1101 D'Antoni  Niels KOWALZIG  Università di Napoli "Federico II"  Cyclic GerstenhaberSchack cohomology
In this talk, we answer a longstanding question by explaining how the diagonal complex computing the GerstenhaberSchack cohomology of a bialgebra (that is, the cohomology theory governing bialgebra deformations) can be given the structure of an operad with
multiplication if the bialgebra is a (not necessarily finite dimensional) Hopf algebra with invertible antipode; if the antipode is involutive, the operad is even cyclic. Therefore, the GerstenhaberSchack cohomology of any such Hopf algebra carries a Gerstenhaber, resp. BatalinVilkovisky, algebra structure; in particular, one obtains a cup product and a cyclic boundary B that generate the Gerstenhaber bracket, and that allows to define cyclic GerstenhaberSchack cohomology. In case the Hopf algebra in question is finite dimensional, the Gerstenhaber bracket turns out to be zero in cohomology and hence the interesting structure is not given by this e2algebra structure, which is expressed in terms of the cup product and B. 
03/12/19  Seminario  14:30  15:30  1201 Dal Passo  Alberto Boscaggin  Università di Torino  Generalized periodic solutions to perturbed Kepler problems
For a perturbed Kepler problem (in dimension 2 or 3) we discuss the existence of periodic solutions, possibly interacting with the singular set. First, a suitable notion of generalized solution is introduced, based on the theory of regularization of collisions in Celestial Mechanics; second, existence and multiplicity results are provided, with suitable assumptions on the perturbation term, by the use of symplectic and variational methods. Joint works with W. Dambrosio (Torino), D. Papini (Udine), R. Ortega (Granada) and L. Zhao (Augsburg).
Note: This talk is part of the activity of the MIUR Department of Excellence Project CUP E83C18000100006 
29/11/19  Seminario  15:45  16:45  1101 D'Antoni  Giulio Codogni  Roma Tre  Positivity of the ChowMumford line bundle for families of Kstable Fano
varieties
The ChowMumford (CM) line bundle is a functorial line bundle defined on the
base of any families of Fano varieties. It is conjectured that it yields a
polarization on the moduli space of Kpolystable Fano varieties, whose
existence has been recently proven by C. Xu and coauthors, building on the
work of C. Birkar.
According to the YauTianDonaldson conjecture, Kpolystable Fano varieties are exactly the Fano varieties admitting a
KaehlerEinstein metric.
In this talk, after giving an overview about Kstability, I will present a result that I have recently obtained with Zs. Patakfalvi. We have shown that the CM line bundle is nef on the moduli space of Kpolystable Fano
varieties, and big on the components which intersect nontrivially the open
locus of uniformly Kstable Fano varieties.
This boils down to showing semipositivity/positivity statements about the CMline bundle for families with Kpolystable/uniformly Kstable fibers.

29/11/19  Seminario  14:30  15:30  1101 D'Antoni  Sean GRIFFIN  University of Washington  Ordered set partitions, Tanisaki ideals, and rank varieties
We introduce a family of ideals I_{n,λ} in Q[x_{1},...,x_{n}] for λ a partition of k≤n. This family contains both the Tanisaki ideals and the ideals I_{n,k} of HaglundRhoadesShimozono as special cases. We study the corresponding quotient rings R_{n,λ} as symmetric group modules. We give a monomial basis for R_{n,λ} in terms of (n,λ)staircases, unifying the monomial bases studied by GarsiaProcesi and HaglundRhoadesShimozono. Furthermore, we realize the S_{n}module structure of R_{n,λ} in terms of an action on (n,λ)ordered set partitions. We then prove that the graded Frobenius characteristic of R_{n,λ} has a positive expansion in terms of dual HallLittlewood functions. Finally, we use results of Weyman to connect the quotient rings R_{n,λ} to EisenbudSaltman rank varieties. This allows us to generalize results of De ConciniProcesi and Tanisaki on "nilpotent" diagonal matrices. 
27/11/19  Seminario  16:00  17:00  1201 Dal Passo  Tiziano Gaudio  Lancaster University  Constructing gradedlocal conformal nets from unitary vertex operator superalgebras
In the context of twodimensional chiral conformal field theory, Carpi, Kawahigashi, Longo and Weiner (CKLW) give a correspondence between unitary vertex operator algebras and local conformal nets. A natural question then arises: starting from the more general vertex operator superalgebra environment, is it possible to construct a gradedlocal conformal net under suitable requirements? In the present talk we will recall the main results of CKLW, deal with their gradedlocal generalisation, prove a number of interesting general statements and illustrate them with important models. The audience is not expected to be familiar with CKLW.
(j.w.w. S. Carpi and R. Hillier) 