16/03/18  Seminario  14:00  15:00  1101 D'Antoni  Kirill ZAYNULLIN  University of Ottawa  Equivariant oriented cohomology and generalized Schubert calculus
This lecture can be viewed as an introduction to algebraic oriented cohomology theories (cohomology/Chow groups, Ktheory, (local) elliptic cohomology, algebraic cobordism, etc.) and their (mostly T)equivariant analogues. Our basic motivating example is the algebraic cobordism ? which was constructed by LevineMorel
around 05's.
This theory serves as an algebraic analogue of the usual complex
cobordism from algebraic topology of 60's (similarly, the Chow group serves as an algebraic version of the usual singular cohomology). We explain a general procedure which allows to compute such theories for generalized flag varieties G/P.
The talk is based on my joint results with Calmès, Petrov, Zhong and others. 
14/03/18  Seminario  16:00  17:00  1201 Dal Passo  Stefano Viaggiu  Roma Tor Vergata  A statistical description of black hole entropy, its corrections and the origin of the cosmological constant.
We present a new approach to describe the Black hole entropy in terms of trapped gravitons inside the event horizon. The discrete spectrum of the so trapped gravitons is obtained together with the thermodynamical quantities. Moreover, we obtain the log corrections to the black hole entropy by means of a (Planckian) mechanism converting radiation into a gamma linear equation of state. Finally, it is shown how with the help of this mechanism, a statistical description of the dark energy is indeed possible. 
13/03/18  Seminario  14:30  15:30  1201 Dal Passo  Tobias weth  Universita' di Francoforte, Germania  Serrin's overdetermined problem on the sphere
In this talk, I will discuss Serrin's overdetermined
boundary value problem
egin{equation*}
Delta_{S^N}, u=1 quad ext{ in $Omega$},qquad u=0, ; partial_eta u= extrm{const} quad ext{on $partial Omega$}
end{equation*}
in subdomains $Omega$ of the round unit sphere $S^N subset
{mathbb R}^{N+1}$, where $Delta_{S^N}$ denotes the LaplaceBeltrami
operator on $S^N$. We call a subdomain $Omega$ of $S^N$ a Serrin
domain if it admits a solution of this overdetermined problem. In
our main result, we construct Serrin domains in $S^N$, $N ge 2$
which bifurcate from symmetric straight tubular neighborhoods of the
equator. By this we complement recent rigidity results for Serrin domains on the sphere.\
This is joint work with M.M.Fall and I.A.Minlend (AIMS Senegal).

13/03/18  Seminario  14:00  15:30  1101 D'Antoni  Alice Garbagnati  Universita' di Milano  CalabiYau quotients of hyperkaehler manifolds.
Given a compact complex smooth hyperkaehler manifold (HK) X with an automorphism a, it is known that if a is symplectic and dim(X)>2, in general X/a does not admit a symplectic resolution. On the other hand, if the automorphism is non symplectic is still possible that it preserves the volume form and in this case one can ask if the quotient of X/a admits a crepant resolution. If it is so, one obtains a CalabiYau manifold (CY). In the talk we
discuss the properties required to the a in order to obtain a CY, and we observe that among the known explicit examples of pairs
(X,a), the unique possibility is that the dimension of X is 4 and the order of a is 2. In this case one is able to compute the Hodge numbers of the CalabiYau fourfold Y, desingularization of X/a, and to discuss several geometric properties if X is the Hilbert scheme of 2 points of a K3 surface S and a is an involution induced on X by an involution on S. Moreover, we relate
Y with another CY fourfold, the BorceaVoisin of S, and we discuss the problem of finding a mirror CY for Y. This is a joint work with Chiara Camere and Giovanni Mongardi.

02/03/18  Seminario  15:00  16:00  1101 D'Antoni  Eleonora Di Nezza  Institut des Hautes Études Scientifiques, Paris  The Calabi conjecture on compact Hermitian manifolds.
We present a paper of TosattiWeinkove on the resolution of the
hermitian version of the Calabi conjecture. More precisely, they prove that
each element in the first BottChern class can be represented as the first
Chern from of a Hermitian metric. The result is obtained as corollary of
uniform estimates for a complex MongeAmpére equation type on a compact
Hermitian manifold. We are going to show such estimates (especially the
C^0estimate) in detail. 
01/03/18  Colloquium  15:00  16:00  1201 Dal Passo  Eleonora Di Nezza  Institut des Hautes Études Scientifiques, Paris  Special metrics in Kähler geometry
A basic problem in geometry is to try to classify manifolds, the main object of study for geometers. The most well known example is the Uniformization Theorem that ensures that every orientable compact manifold of real dimension 2 admits a constant curvature metric.
There are several ways to try and generalize the Uniformization Theorem in higher dimension. In this concerns, an interesting option is to restrict our attention to Kähler manifolds. The problem is then to study canonical metrics in Kähler geometry. Among those, the notion of KählerEinstein metrics is very important.
In this talk we are going to introduce all these notions and we show how the study of special (=KählerEinstein) metrics gives insights into the classification of Kähler manifolds. 
23/02/18  Seminario  15:30  16:30  1101 D'Antoni  Laura GEATTI  Università di Roma "Tor Vergata"  The adapted hyperKähler 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 noncompact case) carries a unique Ginvariant hyperKähler 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 Ginvariant hyperKähler structure compatible with the Kähler structure of X and the adapted complex structure J. The two hyperKähler structures are related by a Gequivariant 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
Ginvariant domain in the complex homogeneous space G_{C}/K_{C} allows us to use Lie theoretical tools and moment map techniques to explicitly compute the various quantities of the "adapted hyperKähler 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  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 ? 