|13/12/17||Seminario||15:00||16:00||1201 Dal Passo||Daniela Cadamuro||TUM -Munich||Direct construction of pointlike observables in the Ising model|
The construction of pointlike fields in quantum integrable
models was a central problem of the Form Factor Programme, which tried
to achieve this by constructing their n-point functions as a series of
“form factors”. However, convergence questions of the series remain
unresolved even in the simplest case of interacting QFT, namely the
massive Ising model. This model is of interest as its classical version
is related to magnetic spin chains. On the other hand, the C*-algebraic
approach to the construction considers semi-local bounded operators, but
yields local operators only in a very abstract way.
By combining these two approaches, we explicitly construct (all)
pointlike fields of the Ising model, not in the sense of the Wightman
axioms, but showing that smeared versions of the fields are closable
operators affiliated with the local algebras.
|12/12/17||Seminario||14:30||15:30||1201 Dal Passo||Gianmaria Verzini ||Politecnico di Milano||Spiraling asymptotic profiles of competition-diffusion systems
We describe the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction-diffusion systems with strongly competitive interactions of Lotka- Volterra type, when the matrix of the inter-specific competition coefficients is asymmetric and the competition parameter tends to infinity. Unlike the symmetric case, when it is known that the nodal set consists in a locally finite collection of curves meeting with equal angles at a locally finite number of singular points, the asymmetric case shows the emergence of spiraling nodal curves, still meeting at locally isolated points with finite vanishing order. This is a joint work with S. Terracini and A. Zilio.
|05/12/17||Seminario||14:30||15:30||1201 Dal Passo||Jessica Elisa Massetti||Universita' degli Studi "Roma Tre"||Almost-periodic tori for the nonlinear Schroedinger equation|
The problem of persistence of invariant tori in infinite dimension is a challenging problem in the study of PDEs. There is a rather well established literature on the persistence of n-dimensional invariant tori carrying a quasi-periodic Diophantine flow (for one-dimensional system) but very few on the persistence of infinite-dimensional ones.
Inspired by the classical "twisted conjugacy theorem" of M. Herman for perturbations of degenerate Hamiltonians possessing a Diophantine invariant torus, we intend to present a compact and unified frame in which recover the results of Bourgain and Poeschel on the existence of almost-periodic solutions for the Nonlinear Schroedinger equation. We shall discuss the main advantages of our approach as well as new perspectives. This is a joint work with L. Biasco and M. Procesi.
|04/12/17||Colloquium||14:30||15:30||1201 Dal Passo|| Jean-Pierre Eckmann||Universita' di Ginevra, Svizzera||A review of Heat Transport in Hamiltonian systems|
For the last few years, I have studied questions of heat transport in finite systems, made of N identical pieces. While none of the obvious physical ideas seem in reach of serious mathematics, some intriguing facts start to become clearer. Namely, that transport is hampered by metastable states. Over the years I have had pleasant collaborations with many people: Claude-Alain Pillet, Luc Rey-Bellet, Lai-Sang Young, Martin Hairer, Pierre Collet, Carlos Mejia- Monasterio, Noe Cuneo, and Gene Wayne.
|01/12/17||Seminario||15:30||16:30||1201 Dal Passo||Fabio GAVARINI||Università di Roma "Tor Vergata"||Supergroups vs. super Harish-Chandra pairs: a new equivalence
In the setup of supergeometry, "symmetries" are encoded as supergroups (algebraic or Lie ones), whose infinitesimal counterpart is given by Lie superalgebras. Moreover, every supergroup also bears a "classical (=non-super) content", in the form of a maximal classical subgroup. Thus every supergroup has an associated pair given by its tangent Lie superalgebra and its maximal classical
subgroup - what is called a "super Harish-Chandra pair" (or "sHCp" in short): overall, this yields a functor F from supergroups to sHCp's.
It is known that the functor F is an equivalence of categories: indeed, this was showed by providing an explicit quasi-inverse functor, say G, to F. Koszul first devised G for the real Lie case, then later on several other authors extended his recipe to more general cases.
In this talk I shall present a new functorial method to associate a Lie supergroup with a given sHCp: this gives a functor K from sHCp's to supergroups which happens to be a quasi-inverse to F, that is intrinsically different from G.
In spite of different technicalities, the spine of the method for constructing the functor K is the same regardless of the kind of supergeometry (i.e., algebraic, real differential or complex analytic one) we are dealing with, so I shall treat all cases at once.
|01/12/17||Seminario||14:00||15:00||1201 Dal Passo||Alessandro D'ANDREA||"Sapienza" Università di Roma||Dynamical systems on graphs and Hecke-Kiselman monoids
A Coxeter monoid is generated by idempotents satisfying the usual braid relations found in the presentation of Coxeter groups. Kiselman's semigroups are certain monoids, originally introduced in the context of convexity theory. Hecke-Kiselman monoids provide a generalization of both concepts. I will first address the finiteness problem for Hecke-Kiselman monoids, and then give a combinatorial description of Kiselman's semigroups - and possibly some of its quotients - by considering all possible evolutions of some special dynamical systems on a graph, called "update systems".
|30/11/17||Seminario||14:00||16:00||1201 Dal Passo||Gilberto Bini||Università degli Studi di Milano|| 0-cicli su varieta' di Calabi-Yau|
In questo seminario parleremo di un lavoro in collaborazione con Robert Laterveer e Gianluca Pacienza, in cui vengono presentati alcuni esempi di varieta' X di Calabi Yau (di dimensione al piu' 5) per le quali viene verificata una congettura di Voisin sugli 0-cicli del prodotto X x X.
|28/11/17||Seminario||14:30||15:30||1201 Dal Passo||Antonio Marigonda||Universita' di Verona||A comparison principle for viscosity solutions of an Hamilton-Jacobi Equation in Wasserstein spaces
In this talk we present recent results about the existence and uniqueness of the viscosity solution for a certain classes on Hamilton-Jacobi Equations in the Wasserstein space of probability measure, arising in problem of mean field control of multi-agent systems. We consider a multi-agent system subject to a centralized controller aiming to minimize a cost function. The microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation decribiing the macroscopical evlution of the system. We prove that the value function V of the problem solves a Hamilton-Jacobi equation in the Wasserstein space in a suitable viscosity sense, and prove a comparison principle for such an equation, thus characterizing V as the unique viscosity solution of the Hamilton-Jacobi equation associated to the problem.
|21/11/17||Seminario||15:00||16:00||1101 D'Antoni||Giulio Ciraolo||Universita' di Palermo||Stime quantitative per ipersuperifici a curvatura media quasi costante|
Discuteremo alcune versioni quantitative del Teorema di Alexandrov della bolla di sapone, che afferma che le sfere sono le sole ipersuperfici chiuse embedded a curvatura media costante. In particolare, considereremo ipersuperfici con curvatura media vicina ad una costante e descriveremo in maniera quantitativa la vicinanza ad una singola sfera o ad una collezione di sfere tangenti di raggio uguale in termini dell'oscillazione della curvatura media. Inoltre considereremo il problema analogo in ambito nonlocale, mostrando come l'effetto nonlocale implichi una maggiore rigidità del problema e prevenga la formazione di più bolle.
|17/11/17||Seminario||14:30||15:30||1201 Dal Passo||Michael Ehrig||University of Sydney||Functoriality of link homologies and higher representation theory
In this talk, we will discuss the notion of functoriality of link
homologies defined by Khovanov and Khovanov-Rozansky. These link
homologies are categorifications of the link invariants defined by
Reshetikhin-Turaev in case of the special linear group.
We will discuss why functoriality is an important notion and how to show
it. The latter will include the equivariant geometry of Grassmannians
and partial flag varieties as well as higher representation theory.