12/01/18  Seminario  15:30  16:30  1101 D'Antoni  Ilaria DAMIANI  Università di Roma "Tor Vergata"  On the Drinfeld coproduct
In an unpublished note Drinfeld defined a new ''coproduct'' on the affine quantum algebras U_{q} (different from the DrinfeldJimbo one), which actually takes values in a completion of the tensor product of U_{q} x U_{q} . In the simply laced case it is not too hard to prove that the relations defining U_{q} are preserved by the Drinfeld coproduct (which is then a well defined algebra homomorphism); but in the other cases the expression of the Drinfeld coproduct applied to the Serre relations is very complicated, and till now the direct attempts to prove that it is zero failed. In this talk a different strategy is presented: the bracket by the Drinfeld generators is
deformed so to get a locally nilpotent derivation D on a suitable algebra V; the study of the exponential of D, which is an algebra automorphism of D, provides a proof that the Drinfeld coproduct is well defined.
This construction works for both the affine quantum algebras and the toroidal quantum algebras. 
12/01/18  Seminario  14:00  15:00  1101 D'Antoni  Alberto DE SOLE  "Sapienza" Università di Roma  Walgebre: dall'identità di Capelli generalizzata alle gerarchie KdV generalizzate
Descriverò la costruzione di un operatore di tipo Lax L(z) associato sia
alle Walgebre W(g,f) quantistiche finite, sia a quelle classiche affini. Per g = gl_{N} , tale operatore si costruisce, nel caso quantistico finito, tramite una formula che generalizza l'identità di Capelli. Nel caso classico affine, invece, l'operatore di Lax L(z) può essere utilizzato per costruire una gerarchia integrabile di equazioni alle derivate parziali che generalizza la gerarchia KdV.
I risultati presentati sono frutto di un lavoro in collaborazione con V. Kac e D. Valeri. 
19/12/17  Seminario  16:30  17:30  1201 Dal Passo  Emanuele Macri'  Northeastern University  The period map for polarized hyperkaehler manifolds
The aim of the talk is to study smooth projective hyperkaehler manifolds which are deformations of Hilbert schemes of points on K3 surfaces and are equipped with a polarization of fixed type. These are parametrized by a quasiprojective 20dimensional moduli space and Verbitsky Torelli theorem implies that their period map is an open embedding when restricted to each irreducible component. Our main result is that the complement of the image of the period map is a finite union of explicit Heegner divisors that we describe. The key technical ingredient is the description of the nef and movable cone for projective hyperkaehler manifolds (deformation equivalent to Hilbert schemes of points on K3 surfaces) by Bayer, Hassett, and Tschinkel. As an application we will present a new short proof (by Bayer and Mongardi) for the celebrated result by Laza and Looijenga on the image of the period map for cubic fourfolds. If time permits, as second application, we will show that infinitely many Heegner divisors in a given period space have the property that their general points correspond to projective hyperkaehler manifolds which are isomorphic to Hilbert schemes of points on K3 surfaces. This is joint work with Olivier Debarre. 
19/12/17  Seminario  15:15  16:15  1200 Biblioteca Storica  AnaMaria Castravet  Northeastern University  Derived categories of moduli spaces of stable rational curves
A question of Orlov is whether the derived category of the GrothendieckKnudsen moduli space M(0,n) of stable, rational curves with n markings admits a full, strong, exceptional collection that is invariant under the action of the symmetric group S_n. I will present several approaches towards answering this question. In particular, I will explain a construction of an invariant full exceptional collection on the LosevManin space. This is joint work with Jenia Tevelev. 
19/12/17  Seminario  14:30  15:30  1201 Dal Passo  Teresa Scarinci  Universita' di Vienna  On the regularity and the singular support of the minimum time function with Hormander vector fields
Let $Omega subset mathbb{R}^n$ be an open bounded set with smooth boundary, $Gamma$, and let
$X_1, dots, X_N$
be smooth real vector fields on an open set $Omega' supset Omega$.
We assume that they satisfy the H\"ormander bracket generating condition, i.e., $Lie lbrace X_1,dots,X_N
brace(x)= mathbb{R} ^n, ; forall xin Omega'$.
%end{equation}
%
Here, $Lie lbrace X_1,dots,X_N
brace(x)$ denotes the space of all values at $x$ of the vector fields of the Lie algebra generated by $lbrace X_1,dots,X_N
brace$. In this context we consider the following Dirichlet problem
egin{equation}label{eq1}
leftlbrace
egin{array}{ll}
sum_{j=1}^N ( X_j T )^2 (x)=1, & xinOmega, \
T(x)=0, & xin Gamma.
end{array}
ight.
end{equation}
Existence and uniqueness of the viscosity solution (
ef{eq1}) are wellknown. Moreover, this solution $T$ is the value function of the timeoptimal control problem with target $Gamma$ and state equation
egin{equation}
y'(t)=sum_{j=1}^N u_j(t)X_j(y(t)),;;; tgeq 0, quad
y(0)=x.
end{equation}
The controls $u=(u_1,dots,u_N)$ take values in the $n$dimensional closed ball of unit radius centered at the origin. The quadratic
form associated with the eikonal equation (
ef{eq1}) is not positive definite. Thus, emph{singular trajectories} may occur, destroying the smoothness of $T$.
In this talk, we investigate the regularity of $T$, the properties of its singular support, and the role played by the singular trajectories.
The results presented appear in the following works: P. Albano, P. Cannarsa, T. Scarinci, emph{Regularity results for the minimum time function with H\"ormander vector fields} (J. Differential Equations 2017), and by the same authors emph{On the partial regularity of the solution of the subelliptic eikonal equation} (Preprint, 2017). 
13/12/17  Seminario  16:15  17:15  1201 Dal Passo  Henning Bostelmann  University of York  Quantum backflow and scattering

13/12/17  Seminario  15:00  16:00  1201 Dal Passo  Daniela Cadamuro  TUM Munich  Direct construction of pointlike observables in the Ising model
The construction of pointlike fields in quantum integrable
models was a central problem of the Form Factor Programme, which tried
to achieve this by constructing their npoint functions as a series of
“form factors”. However, convergence questions of the series remain
unresolved even in the simplest case of interacting QFT, namely the
massive Ising model. This model is of interest as its classical version
is related to magnetic spin chains. On the other hand, the C*algebraic
approach to the construction considers semilocal bounded operators, but
yields local operators only in a very abstract way.
By combining these two approaches, we explicitly construct (all)
pointlike fields of the Ising model, not in the sense of the Wightman
axioms, but showing that smeared versions of the fields are closable
operators affiliated with the local algebras. 
12/12/17  Seminario  14:30  15:30  1201 Dal Passo  Gianmaria Verzini  Politecnico di Milano  Spiraling asymptotic profiles of competitiondiffusion systems
We describe the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reactiondiffusion systems with strongly competitive interactions of Lotka Volterra type, when the matrix of the interspecific competition coefficients is asymmetric and the competition parameter tends to infinity. Unlike the symmetric case, when it is known that the nodal set consists in a locally finite collection of curves meeting with equal angles at a locally finite number of singular points, the asymmetric case shows the emergence of spiraling nodal curves, still meeting at locally isolated points with finite vanishing order. This is a joint work with S. Terracini and A. Zilio.

05/12/17  Seminario  14:30  15:30  1201 Dal Passo  Jessica Elisa Massetti  Universita' degli Studi "Roma Tre"  Almostperiodic tori for the nonlinear Schroedinger equation
The problem of persistence of invariant tori in infinite dimension is a challenging problem in the study of PDEs. There is a rather well established literature on the persistence of ndimensional invariant tori carrying a quasiperiodic Diophantine flow (for onedimensional system) but very few on the persistence of infinitedimensional ones.
Inspired by the classical "twisted conjugacy theorem" of M. Herman for perturbations of degenerate Hamiltonians possessing a Diophantine invariant torus, we intend to present a compact and unified frame in which recover the results of Bourgain and Poeschel on the existence of almostperiodic solutions for the Nonlinear Schroedinger equation. We shall discuss the main advantages of our approach as well as new perspectives. This is a joint work with L. Biasco and M. Procesi. 
04/12/17  Colloquium  14:30  15:30  1201 Dal Passo  JeanPierre Eckmann  Universita' di Ginevra, Svizzera  A review of Heat Transport in Hamiltonian systems
For the last few years, I have studied questions of heat transport in finite systems, made of N identical pieces. While none of the obvious physical ideas seem in reach of serious mathematics, some intriguing facts start to become clearer. Namely, that transport is hampered by metastable states. Over the years I have had pleasant collaborations with many people: ClaudeAlain Pillet, Luc ReyBellet, LaiSang Young, Martin Hairer, Pierre Collet, Carlos Mejia Monasterio, Noe Cuneo, and Gene Wayne. 