| 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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| 27/05/21 | Seminario | 14:00 | 15:00 | | Costante Bellettini | University College London (UK) | Seminario di Equazioni Differenziali
Existence of hypersurfaces with prescribed-mean-curvature
(MS Teams link for the streaming at the end of the abstract)
Let N be a compact Riemannian manifold of dimension 3 or higher, and g a Lipschitz non-negative (or non-positive) function on N. We prove that there exists a closed hypersurface M whose mean curvature attains the values prescribed by g (joint work with Neshan Wickramasekera, Cambridge). Except possibly for a small singular set (of codimension 7 or higher), the hypersurface M is C^2 immersed and two-sided (it admits a global unit normal); the scalar mean curvature at x is g(x) with respect to a global choice of unit normal. More precisely, the immersion is a quasi-embedding, namely the only non-embedded points are caused by tangential self-intersections: around such a non-embedded point, the local structure is given by two disks, lying on one side of each other, and intersecting tangentially (as in the case of two spherical caps touching at a point). A special case of PMC (prescribed-mean-curvature) hypersurfaces is obtained when g is a constant, in which the above result gives a CMC (constant-mean-curvature) hypersurface for any prescribed value of the mean curvature.
The construction of M is carried out largely by means of PDE principles: (i) a minmax for an Allen--Cahn (or Modica-Mortola) energy, involving a parameter that, when sent to 0, leads to an interface from which the desired PMC hypersurface is extracted; (ii) quasi-linear elliptic PDE and geometric-measure-theory arguments, to obtain regularity conclusions for said interface; (iii) parabolic semi-linear PDE (together with specific features of the Allen-Cahn framework), to tackle cancellation phenomena that can happen when sending to 0 the Allen-Cahn parameter.
Link
Note: Sponsored by the Grant MATH@TOV |
| 26/05/21 | Seminario | 16:00 | 17:00 | | Fabio Cipriani | (Politecnico Milano) |
Densities and their measurability in NCG
- online seminar - link to MS teams in the abstract
Abstract: The aim of the talk is to provide conditions ensuring Connes' measurability
of the canonical, $(1,infty)$-summable, spectral weight
$ho(D)$, we associate
to any self-adjoint operator $D$ with discrete spectrum and of its associated state $phi_D(T):={
m Tr,}_omega (T
ho(D))$. The framework allows to discuss measurability for discrete groups with sub-exponential growth and $ heta$-summable spectral triples. Examples also include 1. the volume density of Euclidean domains of infinite volume 2. densities on the C$^*$-algebra of pseudo-differential operators of 0-order on a compact Riemannian manifold 3. densities on Toeplitz extensions.
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
Link MS Teams
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| 21/05/21 | Seminario | 15:00 | 16:00 | | Sachin GAUTAM | Ohio State University |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"R-matrices and Yangians"
- in streaming mode -
(see the instructions in the abstract)
An R-matrix is a solution to the Yang-Baxter equation (YBE), a central object in Statistical Mechanics, discovered in 1970's. The R-matrix also features prominently in the theory of quantum groups formulated in the eighties. In recent years, many areas of mathematics and physics have found methods to construct R-matrices and solve the associated integrable system.
In this talk I will present one such method, which produces meromorphic solutions to (YBE) starting from the representation theory of a family of quantum groups called Yangians. Our techniques give (i) a constructive proof of the existence of the universal R-matrix of Yangians, which was obtained via cohomological methods by Drinfeld in 1983, and (ii) prove that Drinfeld's universal R-matrix is analytically well behaved.
This talk is based on joint works with Valerio Toledano Laredo and Curtis Wendlandt.
N.B.: please click HERE to attend the talk in streaming
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