|16/03/18||Seminario||15:30||16:30||1101 D'Antoni||Kirill ZAYNULLIN||University of Ottawa||TBA
|16/03/18||Seminario||14:00||15:00||1101 D'Antoni||Kirill ZAYNULLIN||University of Ottawa||TBA
|23/02/18||Seminario||15:30||16:30||1101 D'Antoni||Laura GEATTI||Università di Roma "Tor Vergata" ||The adapted hyper-Kähler structure on the tangent bundle of a Hermitian symmetric space II
The cotangent bundle of a compact Hermitian symmetric space X = G/K (a tubular neighbourhood of the zero section, in the non-compact case) carries a unique G-invariant hyper-Kähler structure compatible with the Kähler structure of X and the canonical complex symplectic form of T*X .
The tangent bundle TX, which is isomorphic to T*X, carries a canonical complex structure J, the so called "adapted complex structure", and admits a unique G-invariant hyper-Kähler structure compatible with the Kähler structure of X and the adapted complex structure J. The two hyper-Kähler structures are related by a G-equivariant fiber preserving diffeomorphism of TX, as already noticed by Dancer and Szöke.
The fact that the domain of existence of J in TX is biholomorphic to a
G-invariant domain in the complex homogeneous space GC/KC allows us to use Lie theoretical tools and moment map techniques to explicitly compute the various quantities of the "adapted hyper-Kähler structure".
This is part of a joint project with Andrea Iannuzzi, and this talk concludes his presentation of February 9.
|23/02/18||Seminario||14:00||15:00||1101 D'Antoni||Domenico FIORENZA||"Sapienza"Università di Roma||T-duality 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 T-duality between K0-cocycles in type IIA string theory and K1-cocycles in type IIB string theory, or as Hori's formula, can be recognized as a Fourier-Mukai transform between twisted cohomologies when looked through the lenses of rational homotopy theory. This is an example of topological T-duality in rational homotopy theory, which can be completely formulated in terms of morphisms of L-infinity 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 non-formal, non-C* 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 $2leq kleq 2d-2$, 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 real-analytic vector fields satisfying the Hoermander bracket generating condition.
|13/02/18||Seminario||14:30||15:30||1201 Dal Passo||Esther Cabezas-Rivas||Goethe-Universitaet Frankfurt||Ricci flow beyond non-negative curvature conditions|
We generalize most of the known Ricci flow invariant non-negative 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 non-collapsedness. 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 non-collapsed manifolds with almost non-negative curvature operator and a smoothing result for singular spaces coming from sequences of manifolds with lower curvature bounds. We also obtain a short-time existence result for the Ricci flow on open manifolds with almost non-negative 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 non-random 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 remote-sensing 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.