21/03/18  Seminario  16:00  17:00  1201 Dal Passo  Wojciech Dybalski  TUM Munich  Infravacuum representations and velocity superselection in nonrelativistic QED
It is well established that in QED planewave configurations of the electron corresponding to different velocities induce inequivalent representations of the algebra of the electromagnetic field. This phenomenon of velocity superselection is one of the standard features of the infraparticle picture of the electron, which
relies on mild fluctuations of the electromagnetic field at spacelike infinity. As these fluctuations are large in the complementary infravacuum description of the electron, it has long been conjectured that velocity superselection, and other aspects of the infraparticle problem, can be cured in this approach. We consider two implementations of the infravacuum picture in a PauliFierz model of QED. In the first one, which relies on a
decomposition of the electron into the bare electron and a cloud of soft photons, we prove the absence of velocity superselection. In the second one, which does not rely on such a decomposition, we show that velocity superselection persists, but can be eliminated by suitably inverting the representations. In the language of superselection theory,
we exhibit an unusual situation, where a family of distinct sectors has one and the same conjugate sector. (Joint work with Daniela Cadamuro). 
20/03/18  Seminario  14:30  15:30  1201 Dal Passo  Mikaela Iacobelli  Durham University  Recent results on quasineutral limit for VlasovPoisson via Wasserstein stability estimates
The VlasovPoisson system is a kinetic equation that models collisionless plasma. A plasma has a characteristic scale called the Debye length, which is typically much shorter than the scale of observation. In this case the plasma is called 'quasineutral'. This motivates studying the limit in which the ratio between the Debye length and the observation scale tends to zero. Under this scaling, the formal limit of the VlasovPoisson system is the Kinetic Isothermal Euler system.
The VlasovPoisson system itself can formally be derived as the limit of a system of ODEs describing the dynamics of a system of N interacting particles, as the number of particles approaches infinity. The rigorous justification of this mean field limit remains a fundamental open problem.
In this talk we present the rigorous justification of the quasineutral limit for very small but rough perturbations of analytic initial data for the VlasovPoisson equation in dimensions 1, 2, and 3. Also, we discuss a recent result in which we derive the Kinetic Isothermal Euler system from a regularised particle model. Our approach uses a combined mean field and quasineutral limit. 
16/03/18  Seminario  15:30  16:30  1101 D'Antoni  Kirill ZAYNULLIN  University of Ottawa  Equivariant motives and Sheaves on moment graphs
Goresky, Kottwitz and MacPherson showed that the equivariant
cohomology of varieties equipped with an action of a torus T can be
described using the so called moment graph, hence, translating computations in equivariant cohomology into a combinatorial problem. Braden and MacPherson proved that the information contained in this moment graph is sufficient to compute the equivariant intersection cohomology of the variety. In order to do this, they introduced the notion of a sheaf on moment graph whose space of sections (stalks) describes the (local) intersection cohomology. These results motivated
a series of paper by Fiebig, where he developed and axiomatized sheaves of moment graphs theory and exploited BradenMacPherson’s construction to attack representation theoretical problems.
In the talk we explain how to extend this theory of sheaves on moment
graphs to an arbitrary algebraic oriented equivariant cohomology h
in the sense of LevineMorel (e.g. to Ktheory or algebraic
cobordism). Moreover, we show that in the case of a total flag variety X the space of global sections of the respective hsheaf also describes an endomorphism ring of the equivariant hmotive of X.
This is a very recent joint work with Rostislav Devyatov and Martina Lanini. 
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. 