23/02/18  Seminario  14:00  15:00  1101 D'Antoni  Domenico FIORENZA  "Sapienza"Università di Roma  Tduality in rational homothopy theory
Sullivan models from rational homotopy theory can be used to describe a duality in string theory. Namely, what in string theory is known as topological Tduality between K^{0}cocycles in type IIA string theory and K^{1}cocycles in type IIB string theory, or as Hori's formula, can be recognized as a FourierMukai transform between twisted cohomologies when looked through the lenses of rational homotopy theory. This is an example of topological Tduality in rational homotopy theory, which can be completely formulated in terms of morphisms of Linfinity algebras. Based on joint work with Hisham Sati and Urs Schreiber (arXiv:1712.00758). 
21/02/18  Seminario  16:00  17:00  1201 Dal Passo  Matthias Schötz  University of Würzburg  From nonformal, nonC* deformation quantization in arbitrary dimensions to abstract O*algebras
Starting with any hilbertisable locally convex space V (i.e. locally convex space whose topology can be described by inner products), one can construct its usual deformations by means of exponential star products (like Moyal and Wick star product) on the commutative *algebra of polynomial functions over V, and finds that there is a unique coarsest topology on the deformed *algebras making all deformed products, all evaluating functionals and the *involution continuous. While this resulting deformed *algebra has some more nice properties, e.g. it allows to incorporate elements Q,P having canonical commutation relations [Q,P] = i and to exponentiate these elements in the completion of the algebra, its topology is far from being C*, yet not even submultiplicative. So the question arises, which of the properties that make C*algebras attractive as candidates for observable algebras in physics carry over to our construction (or to similar ones that have been examined recently on the hyperbolic disc or for the Gutt star product). The notion of an abstract O*algebra might provide a suitable framework to examine these problems: The idea is to focus more on the properties of the ordering on a *algebra coming from a suitable set of positive linear functionals, which e.g. allows to study properties of pure states in detail, and could eventually lead to a spectral theorem for *algebras of unbounded operators by applying the Freudenthal spectral theorem for lattice ordered vector spaces. 
20/02/18  Seminario  16:00  17:00  1101 D'Antoni  Xavier Buff  University of Toulouse  Families of rational maps and dynamics
Given integers $dgeq 2$ and $2leq kleq 2d2$, the family of
rational maps of degree $d$ having $k$ distinct critical points is a smooth
quasiprojective variety. We shall present results and open questions
regarding subvarieties where some of the critical points are periodic.
Are those subvarieties smooth, do they intersect transverally, how many
connected components do they have, how do they distribute as the period
tend to infinity ? 
20/02/18  Seminario  14:30  15:30  1201 Dal Passo  Paolo Albano  Universita' di Bologna  On the analytic regularity for operators sums of squares of vector fields
We describe the problem of the analytic and Gevrey regularity for operators sums of squares of realanalytic vector fields satisfying the Hoermander bracket generating condition. 
13/02/18  Seminario  14:30  15:30  1201 Dal Passo  Esther CabezasRivas  GoetheUniversitaet Frankfurt  Ricci flow beyond nonnegative curvature conditions
We generalize most of the known Ricci flow invariant nonnegative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time.
As an illustration of the contents of the talk, we prove that metrics whose curvature operator has eigenvalues greater than 1 can be evolved by the Ricci flow for some uniform time such that the eigenvalues of the curvature operator remain greater than C. Here the time of existence and the constant C only depend on the dimension and the degree of noncollapsedness. We obtain similar generalizations for other invariant curvature conditions, including positive biholomorphic curvature in the Kaehler case. We also get a local version of the main theorem.
As an application of our almost preservation results we deduce a variety of gap and smoothing results of independent interest, including a classification for noncollapsed manifolds with almost nonnegative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds. We also obtain a shorttime existence result for the Ricci flow on open manifolds with almost nonnegative curvature (without requiring upper curvature bounds).
This is a joint work with Richard Bamler (Berkeley) and Burkhard Wilking (Muenster). 
30/01/18  Seminario  16:00  17:00  1101 D'Antoni  Lorenzo Guerini  University of Amsterdam  Random local dynamics
The study of the dynamics of an holomorphic map near a fixed
point is a central subject in complex dynamics. In this talk we will
consider the corresponding random setting: given a probability measure
$mu$ with compact support on the space of germs of holomorphic maps
fixing the origin, we study the iterates $f_ncirccdotscirc f_1$,
where each $f_i$ is chosen with probability $mu$. We will see, as in
the nonrandom case, that the stability of the family of the random
iterates can be studied by looking at the linear part of the germs in
the support of the measure and, in particular, at some quantities
commonly known as Lyapunov indexes. A particularly interesting case
occurs when all Lyapunov indexes vanish. When this happens stability is
equivalent to simultaneous linearizability of all germs in $supp(mu)$. 
25/01/18  Colloquium  15:30  16:30  1201 Dal Passo  M. Iannelli  Università di Trento  2018, the year of Biomathematics: an overview for the centennial, along the trail of Volterra and Lotka
The European Society for Mathematical and Theoretical Biology celebrates 2018 as the year of Biomathematics, since one hundred years ago, in 1917, D'Arcy Thompson published his "On Growth and Form” where biological morphology was approached, based on physical analogy and mathematical transformations.
One century after we have to register such various and widespread developments concerning the interplay of Mathematics and Biology, that it is hard to say what Mathematical Biology is today.
In fact, the recent decades have seen an explosion in the use of mathematical methods in all areas of biology, from the use of advanced statistical methods in the analysis of medical trials, or in the alignment of DNA segments, to sophisticated pattern recognition methods in the analysis the signals from electroencephalogram data or the inference of vegetation structure from remotesensing data. This explosion may correspond to the joint high developments of specific mathematical methodologies and powerful implementation on computers, that contribute to make the field full of aspects difficult to follow and to understand in a unified view.
Thus this talk follows a preferred path, namely the trail started by Vito Volterra and Alfred Lotka in the field of Population Dynamics, trying to show how rich were their initial intuitions and how Mathematics and Biology have positively interacted gaining reciprocal advantage.
During a century, Mathematical Population Dynamics, initially restricted to Demography, has shaped fields such as Ecology, Epidemiology, cell growth, Immunology. Today, mathematical modeling is the common ground where the joint effort of mathematicians and biologists has produced a new perspective. 
23/01/18  Seminario  16:00  17:00  1101 D'Antoni  Anna Miriam Benini  Universitat de Barcelona  Singular values and nonrepelling cycles for entire transcendental maps
Let f be a map with bounded set of singular values for which
periodic dynamic rays exist and land. We prove that each nonrepelling cycle
is associated to a singular orbit which cannot accumulate on any other
nonrepelling cycle. When f has finitely many singular values this implies a
refinement of the FatouShishikura inequality. Our approach is combinatorial
in the spirit of the approach used by [Ki00], [BCL+16] for polynomials. 
23/01/18  Seminario  14:30  15:30  1201 Dal Passo  Emanuele Haus  Università degli Studi di Napoli Federico II  Time quasiperiodic gravity water waves in finite depth
We prove the existence and the linear stability of Cantor families of small amplitude time quasiperiodic standing water wave solutions  i.e. periodic and even in the space variable x  of a bidimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasilinear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. To overcome these problems, we first reduce the linearized operators obtained at each approximate quasiperiodic solution along the NashMoser iteration to constant coefficients up to smoothing operators, using pseudodifferential changes of variables that are quasiperiodic in time. Then we apply a KAM reducibility scheme that requires very weak Melnikov nonresonance conditions (which lose derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. This is a joint work with P. Baldi, M. Berti and R. Montalto.

16/01/18  Seminario  14:30  15:30  1201 Dal Passo  Sylvain Ervedoza  Institut de Mathématiques de Toulouse & CNRS  Minimal time issues for the observability of Grushin like equations
The goal of this talk is to discuss the observability properties of degenerate parabolic equations. Namely, when considering a Grushin operator of the form $partial_t  partial_{xx}  x^2 partial_{yy}$, there is a whole line of degeneracy at $x = 0$, which is known from recent works to strongly modify the observability properties of this operator. In particular, while the usual heat equation is observable from any open set in any small time (we will recall the precise definition of observability we are dealing with), the Grushin operator may require some strictly positive minimal time to be observable, depending on the observation set. The question thus is to give explicit estimates on this minimal time and to link it with the geometry under consideration. We shall present several results in this direction, in which we are able to characterize completely the minimal time required for observability.
In order to do this, we will use Carleman estimates to estimate precisely the cost of observability of the family of $1$d heat equations whose operators are $partial_t  partial_{xx} + n^2 x^2$ in the asymptotics $n o infty$.
This is a joint work with Karine Beauchard (ENS Rennes) and Jérémi Dardé (Institut de Mathématiques de Toulouse)
