| 16/06/21 | Seminario | 14:30 | 15:30 | | Stefano Galatolo | Pisa | Self consistent transfer operators in a weak coupling regime. Invariant measures, convergence to equilibrium, linear response and control of the statistical properties.
MS Teams link
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence and uniqueness of invariant measures, speed of convergence to equilibrium, statistical stability and linear response in a "weak coupling" or weak nonlinearity regime. We apply the general statements to examples of different nature: coupled expanding maps, coupled systems with additive noise, systems made of different maps coupled by a mean field interaction and other examples of self consistent transfer operators not coming from coupled maps. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way. |
| 11/06/21 | Seminario | 15:00 | 16:00 | | Lucien HENNECART | Université Paris Saclay |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Perverse sheaves with nilpotent singular support for curves and quivers"
- in streaming mode -
(see the instructions in the abstract)
Perverse sheaves on the representation stacks of quivers are fundamental in the categorification of quantum groups. I will explain how to prove that semisimple perverse sheaves with nilpotent singular support on the stack of representations of an affine quiver form Lusztig category and how to extend this question to quivers with loops. The analogous question for curves is to determine perverse sheaves on the stack of coherent sheaves whose singular support is a union of irreducible components of the global nilpotent cone. We solve this problem for elliptic curves, for which we also show that the characteristic cycle map induces a bijection between simple Eisenstein spherical perverse sheaves and irreducible components of the global nilpotent cone. This constitutes a step towards the understanding of the degree zero part of the cohomological Hall algebra of a curve.
N.B.: please click HERE to attend the talk in streaming
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| 11/06/21 | Seminario | 14:00 | 15:00 | 1201 Dal Passo | Roberto Fringuelli | Tor Vergata | The Picard group of the universal moduli stack of principal bundles over smooth projective curves
Geometry seminar in live mode!!! Up to 15 seat available (write to codogni@mat.uniroma2.it to book your seat). At the end of the abstract the link for streaming, if you are not coming in person.
Abstract: The Wess-Zumino-Witten model is a type of two-dimensional conformal field theory, which associates to the data of a smooth (projective) complex curve C, n points in C and n irreducible representations of a fixed complex Lie algebra, a finite-dimensional vector space satisfying certain axioms. The same construction can be done for families of marked curves. In this way, we get the sheaf of conformal blocks over the moduli space of marked smooth curves. This sheaf has a geometric interpretation as the sheaf of generalized theta functions, which is the push-forward of a certain line bundle from the universal moduli stack of principal bundles (with some extra-structure) over marked smooth curves to the moduli stack of marked smooth curves. The above application to conformal field theory leads naturally to the study of the Picard group of these universal moduli stacks. In this talk, we present a complete description of the Picard group of the universal moduli stack of G-bundles over n-marked smooth k-curves of genus g, for any reductive group G over an algebraically closed field k. As a consequence, we compute the divisor class group of the associated universal moduli space of semistable G-bundles. It is a joint work with Filippo Viviani.
Link for the streaming (via Teams):
https://teams.microsoft.com/l/meetup-join/19%3a0NlJ6uoaQVwRPyZ_hsMzkr18r_fRackRhBjBZVmmcsM1%40thread.tacv2/1622714552681?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22c4733e0c-f6c1-43fc-9f2a-e36dbb12a33f%22%7d
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| 10/06/21 | Seminario | 14:00 | 15:00 | | Francesco Palmurella | ETH Zürich | The parametric approach to the Willmore flow
( MS Teams Link for the streaming )
We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. In this first work we restrict to a small-energy regime and prove that, for small-energy weak immersions, the Cauchy problem in this class admits a unique solution. Joint work with T. Rivière.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 09/06/21 | Seminario | 16:00 | 17:00 | | Laszlo Zsido | Università Tor Vergata |
On the equality and inequality of weights and operator valued weights
- in streaming mode -
MS Teams link
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
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| 04/06/21 | Seminario | 16:00 | 17:00 | | Matteo Tanzi | New York University (USA) |
DinAmicI: Another Internet Seminar (DAI Seminar)
”Random-like properties of chaotic forcing”
- in streaming mode -
(see the instructions in the abstract)
We prove that skew systems with a sufficiently expanding base have “approximate” statistical properties similar to random ergodic Markov chains. For example, they exhibit approximate exponential decay of correlations, meaning that the exponential rate is observed modulo a controlled error. The fiber maps are only assumed to be Lipschitz regular and to depend on the base in a way that guarantees diffusive behaviour on the vertical component. The assumptions do not imply an hyperbolic picture and one cannot rely on the spectral properties of the transfer operators involved. The approximate nature of the result is the inevitable price one pays for having so mild assumptions on the dynamics on the vertical component. The error in the approximation is shown to go to zero when the expansion of the base tends to infinity.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 04/06/21 | Seminario | 15:00 | 16:00 | | Abel LACABANNE | Université Catholique de Louvain (Belgium) |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"An asymptotic cellular category for G(e,e,n)"
- in streaming mode -
(see the instructions in the abstract)
Given a Coxeter group W, one may consider its Hecke algebra, which is a deformation of the group algebra of W. Kazhdan and Lusztig have constructed the celebrated Kazhdan-Lusztig basis, which has many interesting properties. This basis can be used to construct a partition of W into Kazhdan-Lusztig cells, a partition of the irreducible complex representations of W into families and also a partition of the "unipotent characters" of W into families. There exist categorical counterparts of these objects, and the goal of this talk is to explain a tentative towards a partial generalization for the complex reflection group G( e, e, n).
First, I will describe the situation of a Coxeter group and then explain briefly what can be extended to (some) complex reflection groups. Finally, I will turn to an description of the asymptotic category, which is constructed from representations of quantum sln at a 2 e-th root of unity, and try to justify the term "asymptotic cellular category".
N.B.: please click HERE to attend the talk in streaming
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| 03/06/21 | Seminario | 16:30 | 17:30 | | Detlev Buchholz | Mathematisches Institut, Universitaet Goettingen |
Resolvent algebras and Bose-Einstein-condensation
- in streaming mode -
instructions in the abstract
The treatment of non-relativistic interacting bosonic systems,
exhibiting condensation in the limit of large particle numbers, is
commonly based on studies of single particle density matrices, determined
from the microscopic equilibrium states. In order to exhibit more detailed
properties of these states, such as correlations between observables, one
needs an algebra that is stable under the underlying dynamics and remains
meaningful in the limit. In the present talk it is shown that the
resolvent algebra of canonical quantum systems provides such a framework.
The popular mean field, dilute gas and Gross-Pitaevskii approximations of
the interactions lead to C*-dynamical systems based on the resolvent
algebra. This fact implies that the limits of equilibrium states are still
in equilibrium, satisfying the KMS condition. Moreover, the resolvent
algebra contains all observables needed to study the condensates and their
thermal background. If time permits, these results are illustrated by
examples.
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
Send an email to v.morinelli@gmail.com to get the link to the seminar. |
| 03/06/21 | Seminario | 14:00 | 15:00 | | Francesca Carlotta Chittaro | Université de Toulon (France) | Seminario di Equazioni Differenziali
Hamiltonian approach to sufficient optimality conditions
(MS Teams link for the streaming at the end of the abstract)
The celebrated Pontryagin Maximum Principle (PMP) provides a (first order) necessary condition for the optimality of trajectories of optimal control problems. In most cases, however, a trajectory satisfying PMP is not optimal. For these reasons, additional optimality conditions are required.
In this context, Hamiltonian methods are quite effective in establishing sufficient optimality conditions. In this talk, after a brief review of the main ideas of the general method, we will focus on optimal control problems associated with control-affine dynamics and costs of the form
$$
int_0^T |u(t)| |varphi( X(t))| dt
$$
Costs of these form are very common in problems modeling neurobiology, mechanics and fuel-consumption.
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
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| 28/05/21 | Seminario | 15:00 | 16:00 | 1201 Dal Passo | Alessio CIPRIANI | Università di Roma "Tor Vergata" |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Perverse Sheaves, Finite Dimensional Algebras and Quivers"
- in live mode: the speaker is there, and you can physically attend the talk! (up to 20 seats available) -
- in streaming mode -
(see the instructions in the abstract)
In this talk I will introduce the category of perverse sheaves on a topologically stratified space X and give some examples. Then, I will show that when X has finitely many strata, each with finite fundamental group, such category is equivalent to a category of modules over a finite dimensional algebra A. Finally, I will discuss some algebraic approaches one can use in order to describe the algebra A.
This talk is based on joint work with Jon Woolf.
N.B.: please click HERE to attend the talk in streaming
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