|05/04/19||Seminario||16:30||17:30||1101 D'Antoni||Paolo Di Tella ||Technische Universitat Dresden||On The Weak Representation Property in Progressively Enlarged Filtrations
with an Application in Exponential Utility Maximization
In this paper we show that the weak representation property of a
semimartingale X with respect to a filtration F is preserved in the
progressive enlargement G by a random time τ avoiding F-stopping times and
such that F is immersed in G. As an application of this, we can solve an
exponential utility maximization problem in the enlarged filtration G
following the dynamical approach, based on suitable BSDEs, both over the
fixed-time horizon [0, T ], T > 0, and over the random-time horizon [0, T ∧ τ].
|01/04/19||Seminario||14:30||15:30||1201 Dal Passo||Dmitriy RUMYNIN||University of Warwick||Kac-Moody Groups: representations, localisation, duality
We will look at representation theory of a complete Kac-Moody group G over a finite field. G is a locally compact totally disconnected group, similar, yet slightly different to the group of points of a reductive group scheme over a local field. After defining the group we will prove that the category of smooth representations has finite homological dimension. At the end we discuss localisation and homological duality for this category.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
|27/03/19||Seminario||14:00||17:00||1101 D'Antoni||Espen Sande||University of Oslo||Optimal spline spaces for L2 n-width problems:III|
|26/03/19||Seminario||14:30||15:30||1201 Dal Passo||Alessandro Fortunati||University of Bristol (UK)||Arnold’s diffusion and variational methods: a constructive proof.|
The talk is focused on the well known phenomenon of topological instability that can occour in a class of quasi-integrable systems, as pointed out by V.I. Arnold in 1964.
Right after the publication of the comprehensive work by Chierchia and Gallavotti in 1994 (based on geometric methods), a pioneering paper by U. Bessi proposed a variational formulation for the very same model studied in the original paper by Arnold. However, the constructivity of this approach is not as manifest as in techniques of geometric nature such as the Chierchia-Gallavotti or the Windows methods.
The work presented is based on a revisitation of the tools proposed by Bessi then developed by Berti, Biasco and Bolle, in order to obtain a rigorous and constructive proof in the case of the Arnold example. New tools are introduced in order to formulate the quantitative estimates necessary for a machine implementation apt to construct the diffusing trajectories.
|26/03/19||Seminario||13:00||16:00||1101 D'Antoni||Espen Sande||University of Oslo||Optimal spline spaces for L2 n-width problems: II|
|25/03/19||Seminario||14:30||15:30||1201 Dal Passo||Claudio PROCESI||"Sapienza" Università di Roma - Accademia dei Lincei||Perpetuants: a lost treasure
Perpetuant is one of the several concepts invented (in 1882) by J. J. Sylvester in his investigations of covariants for binary forms. It appears in one of the first issues of the American Journal of Mathematics which he had founded a few years before. It is a name which will hardly appear in a mathematical paper of the last 70 years, due to the complex history of invariant theory which was at some time declared dead only to resurrect several decades later. I learned of this word from Gian-Carlo Rota who pronounced it with an enigmatic smile.
In this talk I want to explain the concept, a Theorem of Stroh, and some new explicit description.
|25/03/19||Seminario||14:00||17:00||1101 D'Antoni||Espen Sande||University of Oslo||Optimal spline spaces for L2 n-width problems: I|
This short course addresses the theory of Kolmogorov n-widths in the setting of Hilbert spaces. Starting from Kolmogorov's original paper we cover the main results up until the present day. The application of this theory to spline approximation and the modern field of Isogeometric Analysis will be explained
|20/03/19||Seminario||16:00||17:00||1201 Dal Passo||Valerio Proietti|| East China Normal University||On the K-theoretic approach to density of states in quasi-crystals|
One approach to generalizing Bloch theory to non-periodic materials makes use of the standard tools of noncommutative topology, such as crossed product operator algebras, dual traces, and K-theory. With this language, I will describe a model based on independent electron approximation, where the main properties of the motion of delocalized electrons are studied through the electronic band structure and the associated values of the integrated density of states (roughly, the number of available energy levels per unit volume). We will discuss the mathematical problems around this framework and some techniques for their solution.
|19/03/19||Seminario||16:00||17:00||1101 D'Antoni||Adriano Tomassini||Universita' di Parma||PROPRIETA' COOMOLOGICHE DI VARIETA' SIMPLETTICHE SPECIALI|
Sia (M,?) una varieta' simplettica di dimensione 2n. Una struttura complessa J su M si dice ?-simmetrica se, dato comunque x ? M, risulta
?(u, Jv) = ?(v, Ju),
per ogni coppia di vettori tangenti u,v ? TxM.
Si discuteranno alcuni risultati ottenuti recentemente in collaborazione con X. Wang, relativi alla coomologia di varieta' simplettiche compatte dotate di una struttura complessa ?-simmetrica.
 A. Tomassini, X. Wang, Some results on Hard Lefschetz Condition, Inter-nat. J. Math. 29, n. 13, (2018).
 A. Tomassini, X. Wang, in preparazione.
|19/03/19||Seminario||14:30||15:30||1201 Dal Passo||Marcello Lucia||The City University of New York||Some results related to Schiffer problem|
Motivated by some earlier work by Schiffer, we consider an
overdetermined semilinear problem in a two dimensional bounded domain
where the Dirichlet data and Neumann boundary conditions are prescribed.
In this talk I will provide some conditions that ensure the domain to
be a disc. This is a joint work with B. Kawohl.