15/10/19  Seminario  16:00  17:00  1101 D'Antoni  Gautam Bharali  Indian Institute of Science  Visibility spaces for the Kobayashi distance and applications
Given a metric space, there are several notions of it being negatively curved.
In this talk, we single out a weak notion of negative curvature (which, in fact, is a
consequence of negative curvature in the Riemannian category) that turns out to be very
useful in proving results about holomorphic maps. This property is a form of visibility,
the underlying metric spaces being bounded domains in $mathbb{C}^n$ equipped with the
Kobayashi distance. In this talk, we shall present a general quantitative condition for a
domain to be a visibility space in the sense alluded to above. A class of domains known
as Goldilocks domains  introduced in joint work with Andrew Zimmer in 2017  possess
this visibility property. Visibility domains form a broad class of domains that includes,
for instance, all pseudoconvex domains of finite type. Throughout the talk, we shall
refer to the WolffDenjoy theorem  which was previously known to hold true on certain
convex domains and on strongly pseudoconvex domains  as a framing device for the sort
of phenomena that extend to visibility domains. We shall also discuss methods for
determining when a domain is a visibility space and for constructing new examples with
rough boundaries. This is joint work with Andrew Zimmer and Anwoy Maitra. 
15/10/19  Seminario  14:30  15:30  1201 Dal Passo  Giuseppe Riey  Universita' della Calabria  Regularity results for anisotropic elliptic equations
We first prove local regularity estimates for positive weak solutions of
quasilinear anisotropic elliptic equations, defined on a smooth bounded
domain: a weighted integral hessian estimate and the integrability of the
inverse of the gradient.
Moreover, we also prove a Hopf type Lemma and, thanks to this result, the
local results are then extended to the whole domain.
sunto 
14/10/19  Seminario  14:30  15:30  1201 Dal Passo  Mark Andrea de Cataldo  Stony Brook University  I numeri di Hodge di O'Grady 10 via le stringhe di N^go
Discuto il preprint omonimo recente in collaborazione con A. Rapagnetta e G. Sacca' dove calcoliamo i numeri di Hodge della' varieta' olomorfica simplettica 10dimensional nota col nome di O'Grady 10.
Algebraic Geometry Seminar, in the framework of MIUR Excellence Project 20182022 Mat@Tov, CUPE83C18000100006 
08/10/19  Seminario  15:00  16:00  1101 D'Antoni  Finnur Larusson  Adelaide  Chaos in higherdimensional complex dynamics.
I will report on new and recent work with Leandro Arosio on chaos and other aspects of dynamics in certain highly symmetric complex manifolds. For example, we prove that for many linear algebraic groups G,
chaotic automorphisms are generic among volumepreserving holomorphic automorphisms of G.
I will start with some background on holomorphic dynamics in general, on chaos, and on the highly symmetric complex
manifolds to which our results apply.

08/10/19  Seminario  14:30  15:30  1201 Dal Passo  Liliane A. Maia  Universidade de Brasília  Semilinear Parabolic Equations with asymptotically linear growth
We present some recent work on the existence and behaviour of
solutions for a class of semilinear parabolic equation, defined on a bounded smooth domain and we assume that the nonlinearity is asymptotically linear at infinity.
We analyse the behavior of the solutions when the initial data varies in the phase space. We obtain global solutions which may be bounded or blowup in infinite time (growup). Our main tools are the comparison principle and variational methods.
Particular attention is paid to initial data at high energy level. We use the Nehari manifold to separate the phase space into regions of initial data where uniform boundedness or growup behavior of the semiflow may occur.
This is work in collaboration with Juliana Pimentel (UFRJ, Brazil).

04/10/19  Seminario  16:30  17:30  1201 Dal Passo  Fabio Antonelli  Università degli Studi dell'Aquila  Credit value adjustment in modelli a volatilità stocastica
Valutare correttamente il prezzo di prodotti finanziari soggetti a rischio di credito è diventato sempre più oggetto di interesse nell'ultima decade, sopratutto in condizioni di Wrong Way Risk, quando ad un deterioramento del credito corrisponde un aumento di valore del prodotto scambiato.
Partendo dai modelli di mercato a volatilità stocastica più diffusi, esprimiamo il WWR in termini della correlazione tra prezzo del sottostante ed evento di default. Sfruttando il cosiddetto intensity approach per l'evento di default e modellizzando l'intensità secondo un modello affine, siamo in grado di parametrizzare questa correlazione.
Con un'attenta applicazione della formula di Ito e delle caratteristiche affini del modello, proponiamo una formula approssimata del prezzo in termini di un polinomio di Taylor sviluppato intorno a correlazione 0.
II metodo sembra essere abbastanza generale ed i risultati numerici mostrano una buona performance in termini di velocità e precisione. 
04/10/19  Seminario  14:30  15:30  1101 D'Antoni  Gianluca MARZO  Università di Roma "Tor Vergata"  Functorial resolution of singularities
Resolution of singularities, already in the category of complex analytic spaces, cannot be achieved in a way that is both étale local and independent of the resolution process itself while blowing up in smooth centres. However, we will explain how this can be achieved in the 2category of DeligneMumford champ following a new method based on smoothed weighted blow up in regular centre. We construct an invariant, inv, of regular mdimensional characteristic zero local rings and their ideals, that makes the resolution process functorial and more widely applicable, rather than just complex spaces. The goal of the talk is to relate the construction of the invariant with a functorial definition of the Newton polyhedron of an ideal, and show how we get a very easy and fully functorial resolution of complex singularities.
This is based on joint work with M. McQuillan. 
01/10/19  Colloquium  14:30  15:30  1201 Dal Passo  Manuel Del Pino  University of Bath  Singularity formation and bubbling in nonlinear diffusions
A fundamental question in nonlinear evolution equations is the analysis
of solutions which develop singularities (blowup) in finite time or as
time goes to infinity. We review recent results on the construction of
solutions to nonlinear parabolic PDE which exhibit this kind of
behavior in the form of ”bubbling”. This means solutions that at
main order look like asymptotically singular timedependent scalings of
a fixed finite energy entire steady state. We mainly focus on the
classical twodimensional harmonic map flow into the sphere, and the
KellerSegel system of chemotaxis. 
26/09/19  Colloquium  14:30  15:30  1201 Dal Passo  Alexander Ioffe  Technion  Metric regularity theory: introduction and applications to analysis
It was discovered in the 70s that the classical regularity concept (derivative of a mapping is a linear operator onto the range space) can be expressed in purely metric terms. This led to creation of ''metric regularity theory" extending its classical predecessor to (even setvalued) mappings between metric spaces. Surprisingly, applications of the theory in fairly classical situations sometimes lead to new results and/or new and nontrivial interpretations of known facts, as well as to noticeably simpler proofs. Several such applications (e.g. to the theory of optimal control ) will be discussed in the talk after brief and nontechnical introduction into the theory. 
26/09/19  Seminario  12:00  13:00  1201 Dal Passo  Michael S. Floater  University of Oslo  Bivariate polynomial interpolation on interlacing rectangular grids
The question of whether polynomial interpolation in two variables is well defined, or unisolvent, depends not only on the number of points but on their positions. For polynomial degree n we need N = (n+2)(n+1)/2 points.
Two wellknown point configurations for which interpolation is unisolvent are the "principal lattice", which is a triangular grid, and the "natural lattice", which is the intersections of nonparallel lines.
In this talk I will discuss the "interlacing lattice", which is the union of two interlacing rectangular grids, one square, the other almost square. The Padua points are an example of such a lattice, with a specific spacing of the points. In this talk I will explain why the interlacing lattice is unisolvent for any spacing of the points.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. 