|13/12/18||Colloquium||14:30||15:30||1201 Dal Passo||Fulvio RICCI||SNS - Pisa||Aspetti dell'analisi sferica su spazi omogenei commutativi a crescita polinomiale
Uno spazio omogeneo M = G/K connesso di un gruppo di Lie G, con K sottogruppo compatto, si dice commutativo - si dice anche che (G,K) è una coppia di Gelfand - se l’algebra degli operatori differenziali G-invarianti su M è commutativa.
Nell’analisi di funzioni e di operatori G-invarianti su M, la trasformata sferica ha un ruolo analogo a quello svolto dalla trasformata di Fourier quando M = G = Rn.
Le analogie tra trasformata sferica e trasformata di Fourier classica diventano più forti utilizzando la rappresentazione, dovuta a F. Ferrari Ruffino, dello spettro di Gelfand come sottoinsieme chiuso di uno spazio euclideo.
In questo seminario presentiamo risultati recenti e problemi aperti sulla caratterizzazione delle trasformate sferiche di funzioni di Schwartz su M quando G ha crescita polinomiale.
|12/12/18||Seminario||17:30||18:30||1201 Dal Passo||Kei Hasegawa||University of Kyoto||Bass-Serre trees for amalgamated free products of C*-algebras and applications|
The Bass-Serre tree associated to an amalgamated free product of groups is a tree on which the group acts in a canonical way. This action is a powerful tool in various studies of the group itself.
In this talk, I will introduce its analogy for amalgamated free products of C*-algebras, and explain how ideas coming from geometric group theory can be used in the C*-algebra setting.
|12/12/18||Seminario||16:00||17:00||1201 Dal Passo||Yusuke Isono||RIMS Kyoto||Intertwining theory for general von Neumann algebras and applications|
We investigate Popa's intertwining condition, using Tomita-Takesaki's modular theory. In particular, we give a new characterization of Popa's condition in terms of their continuous cores.
In this talk, I will explain the idea and the difficulty of proving this
characterization, and also mention some applications.
|11/12/18||Seminario||14:30||15:30||1201 Dal Passo||Sunra Mosconi||Universita' di Catania||The Shrodinger-Poisson system with sign changing potential
The Shrodinger-Poisson system describes the motion of an electrically charged Bose-Einstein condensate subjected to potential field. We will consider the problem of existence of standing waves of arbitrary high energy. By solving the Poisson equation, this results in studying a stationary non-linear Shrodinger equation with a nonlocal sign-changing potential. Standard variational method apply when considering suitable nonlinearities, but fail for the simple yet paramount case of the Gross-Pitaevski equation. We will describe the physical model, discuss the variational formulation and related literature and propose a solution in the Gross-Pitaevski setting. This is a joint work with S. Liu, University of Xiamen
|10/12/18||Seminario||14:30||15:30||1201 Dal Passo||Gwyn BELLAMY||Glasgow University||
Resolutions of symplectic quotient singularities
In this talk I will explain how one can explicitly construct all crepant resolutions of the symplectic quotient singularities associated to wreath product groups. The resolutions are all given by Nakajima quiver varieties. In order to prove that all resolutions are obtained this way, one needs to describe what happens to the geometry as one crosses the walls inside the GIT parameter space for these quiver varieties. This is based on joint work with Alistair Craw.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
|04/12/18||Seminario||14:30||15:30||1201 Dal Passo||Benedetta Pellacci||Universita' della Campania||Asymptotic spherical shapes in some spectral optimization problems
We study the positive principal eigenvalue of a weighted problem associated with the Neumann Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to consider a shape optimization problem, which is known to admit spherical optimal shapes only in very specific cases. We investigate whether spherical shapes can be recovered in general situations, in some singular perturbation limit. We also consider a related problem, where the diffusion is triggered by a fractional
$s$-Laplacian, and the optimization is performed with respect to the fractional order $sin(0,1]$. These are joint works with Dario Mazzoleni and Gianmaria Verzini.
|03/12/18||Seminario||14:30||15:30||1201 Dal Passo||Spela SPENKO||Vrije Universiteit Brussel||Comparing commutative and noncommutative resolutions of singularities
Quotient singularities for reductive groups admit the canonical Kirwan (partial) resolution of singularities, and often also a noncommutative resolution. We will motivate the occurrence of noncommutative resolutions and compare them to their commutative counterparts (via derived categories in terms of the Bondal-Orlov conjecture). This is a joint work with Michel Van den Bergh.
|20/11/18||Colloquium||14:30||16:30||1201 Dal Passo||Masayasu Mimura||Musashino University/Meiji University||Transient Self-Organization: Closed Systems vs. Open systems of Reaction and Diffusion|
After Turing?s theoretical prediction on biological pattern formation, various types of patterns related to self-organization can be discovered in open systems due to the interaction of reaction with
diffusion. Turing said in his paper ?The model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of
greatest importance in the present state of knowledge?. Nevertheless, mathematical communities have been much influenced by his theory. We already recognize that open systems of reaction and diffusion have
generated enormous rich behaviors. On the other hand, closed systems have been gradually less interesting. However, I would like to emphasize that new biological pattern formation can be observed even in
closed systems as the consequence of transient self-organization, and that the theoretical understanding of such patterns is a very important subject in nonlinear mathematics.
|16/11/18||Seminario||17:15||18:15||1201 Dal Passo||Peter LITTELMANN||Cologne University||Standard Monomial Theory via Newton-Okounkov Theory|
Sequences of Schubert varieties, contained in each other and successively of codimension one, naturally lead to valuations on the field of rational functions of the flag variety. By taking the minimum over all these valuations, one gets a quasi valuation which leads to a flat semi-toric degeneration of the flag variety. This semi-toric degeneration is strongly related to the Standard Monomial Theory on flag varieties as originally initiated by Seshadri, Lakshmibai and Musili. This is work in progress jointly with Rocco Chirivi and Xin Fang.
|16/11/18||Seminario||15:45||16:45||1201 Dal Passo||Michèle VERGNE||Institut de Mathématiques de Jussieu / Académie de Sciences - Paris||Quiver Grassmannians, Q-intersection and Horn conditions
The abstract is available here