Seminari/Colloquia
Pagina 26
Date | Type | Start | End | Room | Speaker | From | Title |
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01/03/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Pierre Cardaliaguet | Université Paris Dauphine | On the convergence rate for the optimal control of McKean-Vlasov dynamics (MS Teams link for the streaming at the end of the abstract)
In this talk I will report on a joint work with S. Daudin (Paris Dauphine), Joe Jackson (U. Texas) and P. Souganidis (U. Chicago). We are interested in the convergence problem for the optimal control of McKean-Vlasov dynamics, also known as mean field control. We establish an algebraic rate of convergence of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem. This convergence rate is established in the presence of both idiosyncratic and common noise, and in a setting where the value function for the McKean-Vlasov problem need not be smooth. Our approach relies crucially on Lipschitz and semi-concavity estimates, uniform in N, for the N-particle value functions, as well as a certain concentration inequality.
MS Teams Link for the streaming Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |
01/03/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Emanuele Macrì |
We will present joint work with Olivier Debarre, Daniel Huybrechts and
Claire Voisin on the SYZ hyper-Kähler conjecture for fourfolds under
certain topological assumptions.
As application, this proves a conjecture by O'Grady that a
hyper-Kähler fourfold whose cohomology ring is isomorphic to the one
of the Hilbert square of a K3 surface is a deformation of a Hilbert
square.
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25/02/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | "On Sylow Branching Coefficients" - in live & streaming mode - ( please click HERE to attend the talk in streaming )
In this talk we will discuss the nature of the relationship between the representations of a finite group G and those of a Sylow subgroup P of G.
We will introduce Sylow Branching Coefficients (SBCs) and we will show how the study of these numbers led us to prove a conjecture proposed by Malle and Navarro in 2012. We will conclude by presenting new results on SBCs in the case where G is the symmetric group. The talk is based on joint works with Law, Long, Navarro, Vallejo and Volpato. N.B.: please click HERE to attend the talk in streaming. | ||
25/02/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | "Fully commutative elements and spherical nilpotent orbits" - in live & streaming mode - ( please click HERE to attend the talk in streaming )
Let g be a simple Lie algebra, with a fixed Borel subalgebra b = t+n , and let W be the associated Weyl group. The Steinberg map associates to any element of W a nilpotent orbit in g, which is defined by the corresponding set of inversions. Extending on previous work of Fan and Stembridge, in this talk I will compare two different notions of "smallness", one available in the Weyl group and the other one for nilpotent orbits.
N.B.: please click HERE to attend the talk in streaming. | ||
22/02/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Cristian Mendico | Università di Roma | Asymptotic behavior of solutions to Hamilton-Jacobi-Bellmann equations (MS Teams link for the streaming at the end of the abstract)
The analysis of the ergodic behavior of solutions to Hamilton-Jacobi-Bellmann equations has a long history going back to the seminal paper by [Lions, P.-L., Papanicolaou, G. and Varadhan, S.R.S]. Since this work, the subject has grown very fast and when the Hamiltonian is of Tonelli type a large number of results have been proved. A full characterization of the ergodic behavior of solutions to Tonelli Hamilton-Jacobi equations can be found in the celebrated weak KAM theory and Aubry-Mather theory. However, few results are available if the Hamiltonian fails to be Tonelli, i.e.,
the Hamiltonian is neither strictly convex nor coercive with respect to the momentum variable. In particular, such results cover only some specific structure and so, the general problem is still open. In this talk, I will present some recent results obtained in collaboration with Piermarco Cannarsa and Pierre Cardaliaguet concerning the long time-average behavior of solutions to Hamilton-Jacobi-Bellman equations. We will look, first, to the case of control of acceleration and, then, to sub-Riemannian control systems. Finally, we conclude
this talk showing how the previous analysis applies to mean field game systems.
MS Teams Link for the streaming Note: This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |
22/02/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Roberto Fringuelli |
Let G be a complex (connected) reductive group and C be a complex smooth projective curve of genus at least four. It is known that the moduli space of semistable G-bundles over C is a projective variety. The automorphism group of this variety contains the so-called tautological automorphisms: they are induced by the automorphisms of the curve C, outer automorphisms of G and tensorization by Z-torsors, where Z is the center of G. It is a natural question to ask if they generate the entire automorphism group. Kouvidakis and Pantev gave a positive answer when G=SL(n). An alternative proof has been given by Hwang and Ramanan. Later, Biswas, Gomez and Muñoz, after simplifying the proof for G=SL(n), extended the result to the symplectic group Sp(2n). All the proofs rely on the study of the singular fibers of the Hitchin fibration. In this talk, we present a recent work where, by adapting the Biswas-Gomez-Muñoz strategy, we describe the automorphism group of the connected components of the moduli space of semistable G-bundles over C, for any almost-simple group G.
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15/02/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Nicolas Augier | CNRS-LAAS, Toulouse | On the use of quasi-static controls and duplication of controls for quantum systems
( MS Teams Link for the streaming )
In a first part of the talk, I will present some geometric techniques allowing to control quantum systems using slowly-varying controls, in the so-called adiabatic regime. The latter provides strong control results only when the system is driven by at least two controls, which is a strong requirement in practice. The second part of the talk will be dedicated to an averaging approximation (Rotating Wave Approximation) which allows to duplicate controls in this setting.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
15/02/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Luca De Feo |
Le isogenie sono morfismi di varietà abeliane. La loro teoria algoritmica è sviluppata da oltre 30 anni, motivata in parte dall'algoritmo di Schoof-Elkies-Atkin per il conteggio di punti, algoritmo fondamentale in crittografia ellittica. I progressi algoritmici hanno portato negli ultimi 20 anni allo sviluppo di una nuova branca della crittografia, detta a base d'isogenie. L'oggetto centrale di questa disciplina non è più una curva ellittica isolata, bensì un grafo di curve ellittiche legate da isogenie. I grafi d'isogenie esibiscono diverse strutture combinatorie interessanti (foreste, grafi di Cayeley, grafi espansori), e offrono dei problemi computazionalmente difficili come la ricerca di cammini. Su queste basi, siamo oggi in misura di costruire un vasto spettro di primitive crittografiche: cifratura e firma digitale resistenti agli attacchi quantistici, crittografia a orologeria, sistemi a soglia, ecc. In questo talk, darò un'introduzione alla teoria delle isogenie di curve ellittiche su corpi finiti, e spiegherò come la crittografia è costruita a partire da esse.
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11/02/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | “Sapienza” Università di Roma | "Paving Springer fibers" - in live & streaming mode - ( please click HERE to attend the talk in streaming )
In the paper [De Concini C., Lusztig G., Homology of the zero-set of a nilpotent vector field on a flag manifold, J. Amer. Math. Soc. 1 (1988), no. 1, 15-34] it was proven that the so called Springer fiber B_{n} for any nilpotent element n in a complex simple Lie algebra g has homological properties that suggest that B_{n} should have a paving by affine spaces.
This last statement was proved to hold in the case in which g is classical, but remained open for exceptional groups in types E_{7} and E_{8}. In a joint project with Maffei we are trying to fill the gap. At this point our efforts have been successful in type E_{7} and "almost" in type E_{8}, where one is reduced to show it only in one case. The goal of the talk is to survey the problem and give an idea on how to show our new results. N.B.: please click HERE to attend the talk in streaming. | |
11/02/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | "Brackets and products from centres in extension categories" - in live & streaming mode - ( please click HERE to attend the talk in streaming )
Building on Retakh's approach to Ext groups through categories of extensions, Schwede reobtained the well-known Gerstenhaber algebra structure on Ext groups over bimodules of associative algebras both from splicing extensions (leading to the cup product) and from a suitable loop in the categories of extensions (leading to the Lie bracket). We show how Schwede's construction admits a vast generalisation to general monoidal categories with coefficients of the Ext groups taken in (weak) left and right monoidal (or Drinfel'd) centres. In case of the category of left modules over bialgebroids and coefficients given by commuting pairs of braided (co)commutative (co)monoids in these categorical centres, we provide an explicit description of the algebraic structure obtained this way, and a complete proof that this leads to a Gerstenhaber algebra is then obtained from an operadic approach. This, in particular, considerably generalises the classical construction given by Gerstenhaber himself. Conjecturally, the algebraic structure we describe should produce a Gerstenhaber algebra for an arbitrary monoidal category enriched over abelian groups, but even the bilinearity of the cup product and of the Lie-type bracket defined by the abstract construction in terms of extension categories remain elusive in this general setting.
This is a joint work with Niels Kowalzig, cf. arXiv:2112.11552. N.B.: please click HERE to attend the talk in streaming. |
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