| 26/03/21 | Seminario | 15:00 | 16:00 | | Valerio TOLEDANO LAREDO | Northeastern University - Boston |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Stokes phenomena, Poisson-Lie groups and quantum groups"
- in streaming mode -
(see the instructions in the abstract)
Let G be a complex reductive group, G* its dual Poisson-Lie group, and g the Lie algebra of G. G-valued Stokes phenomena were exploited by P. Boalch to linearise the Poisson structure on G*. I will explain how U( g)-valued Stokes phenomena can be used to give a purely transcendental construction of the quantum group Uh( g), and show that the semiclassical limit of this construction recovers Boalch's. The latter result is joint work with Xiaomeng Xu.
N.B.: please click HERE to attend the talk in streaming |
| 25/03/21 | Seminario | 16:00 | 17:00 | | Álvaro del Pino Gómez | Utrecht University (The Netherlands) |
DinAmicI: Another Internet Seminar (DAI Seminar)
Billiards in subriemannian geometry
- in streaming mode -
(see the instructions in the abstract)
When one considers manifolds with boundary, billiard dynamics are the natural analogue of standard geodesic dynamics. Namely, instead of having geodesics escape at the boundary, we force them back into the manifold using the reflection law. In other dynamical settings, similar constructions are possible: In 2006, B. Khesin and S. Tabachnikov initiated the study of billiards in the semiriemannian setting, studying the integrability of various tables. In recent years we have also seen the appearance of several billiard setups of symplectic nature.
In this talk I will discuss recent work with L. Dahinden in which we look at billiards in subriemannian geometry. I will sketch how the reflection law arises naturally both from the control-theoretical and symplectic perspectives, how the reflection is problematic at tangency points between the distribution and the boundary of the table, and I will introduce some concrete examples. My ultimate goal will be to pose several intriguing open questions.
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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| 25/03/21 | Seminario | 14:00 | 15:00 | | Marco Caponigro | Università di Roma "Tor Vergata" | Geometric controllability of the bilinear Schrödinger equation
( MS Teams Link for the streaming )
We consider the bilinear Schrödinger equation with a discrete-spectrum free Hamiltonian and we present a general method for the approximate controllability based on Lie-algebraic control techniques applied to suitable finite dimensional approximation of the Galerkin-type. Under some regularity assumptions on the Hamiltonians and generic conditions on the controllability of the finite dimensional Galerkin approximations we show exact controllability in projection on an arbitrary given number of eigenstates.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 23/03/21 | Seminario | 14:30 | 15:30 | | Gilberto Bini | Università di Palermo | Geometria birazionale delle varietà algebriche e fibrati big
Lo studio dei morfismi birazionali e quindi dei vari modelli proiettivi di una varietà algebrica è uno dei problemi centrali in Geometria Algebrica.
Il caso dei fibrati lineari è classicamente più trattato, quindi più standard rispetto a quello dei fibrati vettoriali, che presentano invece
numerose questioni aperte.
Alcune di queste questioni, presentate come obiettivi di ricerca nel Progetto PRIN 2015 "Geometry of Algebraic Varieties"
(PE1 2015EYPTSB_011, Resp. Scientifico F. Flamini), sono state trattate in alcuni recenti risultati (già pubblicati od in progress) ottenuti, nell'ambito del progetto menzionato, in collaborazione con Flaminio Flamini (Università di Roma Tor Vergata),
Samuel Boissiére e Alessandra Sarti (Université de Poitiers) e che sono oggetto di questo seminario.
Per partecipare al seminario on-line su Zoom, scrivere all'oratore Gilberto Bini entro VENERDI' 19 MARZO 2021 all'indirizzo di posta elettronica gilberto.bini@unipa.it |
| 19/03/21 | Seminario | 15:00 | 16:00 | | Daniele VALERI | University of Glasgow |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Lax type operator for W-algebras"
- in streaming mode -
(see the instructions in the abstract)
In 1985 Zamolodchikov constructed a "non-linear" extension of the Virasoro algebra known as W3 algebra. This is one of the first appearances of a rich class of algebraic structures, known as W-algebras, which are intimately related to physical theories with symmetries and revealed many applications in mathematics. In the talk I will review some basic facts about the general theory of W-algebras and provide a description using Lax operators. This approach shows the deep connection of the theory of W-algebras with Yangians and integrable Hamiltonian hierarchies of Lax type equations.
This is a joint work with A. De Sole and V. G. Kac.
N.B.: please click HERE to attend the talk in streaming |
| 12/03/21 | Seminario | 15:00 | 16:00 | | Stephen GRIFFETH | Universidad de Talca |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Ideals of subspace arrangements and representation theory"
- in streaming mode
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I will discuss results linking the study of certain highly symmetric arrangements of linear subspaces in affine space to representation theory, describing how to obtain qualitative information (e.g., is the arrangement Cohen-Macaulay?) and quantitative information (e.g., what is the Hilbert series of the ideal of the arrangement?) using techniques from the representation theory of Cherednik algebras.
N.B.: please click HERE to attend the talk in streaming |
| 11/03/21 | Seminario | 17:00 | 18:00 | | Alessandro Della Corte | Università di Camerino |
DinAmicI: Another Internet Seminar (DAI Seminar)
The simplest erasing substitution
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The symbolic action of a substitution on the binary expansion generates naturally an interval map. In case of erasing substitutions, the map is typically Baire-1 and not Darboux. As a model case, we consider what is arguably the simplest erasing substitution, mapping 0s to the empty word and 1s to 0 or 1 depending on the parity. The corresponding interval map is shown to have fractal properties (bounds are given on the Hausdorff dimension of the fibers) and to display rich dynamical behavior, including Devaney chaos, uniform distributional chaos of type 1, infinite topological entropy as well as the presence of cycles attracting in a finite time every rational.
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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| 11/03/21 | Seminario | 14:00 | 15:00 | | Mohameden Ahmedou | Università di Gießen | New blow up phenomena for the Nirenberg's problem on half spheres
( MS Teams Link for the streaming )
In this talk I will report on a refined blow up analysis of finite energy approximated solutions to the Nirenberg's problem on half spheres. The later consists of prescribing under minimal boundary conditions the scalar curvature to be a given function. In particular we give a precise location of blow up points and blow up rates. Such an analysis shows that the blow up picture of the Nirenberg's problem on half spheres is far more complicated that in the case of closed spheres. Indeed besides the combination of interior and boundary blow ups, there are "non simples blow ups" for subcritical solutions having zero or nonzero weak limit. The formation of such non simple blow ups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics.
This is joint work with Mohamed Ben Ayed (Sfax University).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 05/03/21 | Seminario | 15:00 | 16:00 | | Olivier SCHIFFMANN | CNRS - Paris Saclay |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Cohomological Hall algebras associated to ADE surface singularities"
- in streaming mode
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To a (reasonable) CY category C of global dimension two one can attach an associative algebra - its cohomological Hall algebra (COHA) - which is an algebra structure on the Borel-Moore homology of the stack of objects in C. In examples related to quivers (i.e. when C is the category of representations of the preprojective algebra of a quiver Q) this yields (positive halves) of Kac-Moody Yangians. In ongoing joint work with Diaconescu, Sala and Vasserot, we consider the case of the category of coherent sheaves supported on the exceptional locus of a Kleinian surface singularity. This is related to the above quiver case by a '2d-COHA' version of Cramer's theorem relating the (usual) Hall algebras of two hereditary categories which are derived equivalent.
N.B.: please click HERE to attend the talk in streaming |
| 04/03/21 | Seminario | 14:00 | 15:00 | | Weiwei Ao | Wuhan University | Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality
( MS Teams Link for the streaming )
In this talk, I will discuss about a fractional version of the Caffarelli-Kohn-Nirenberg inequality.
We first study the existence and nonexistence of extremal solutions. We also show some results for the symmetry and symmetry breaking region for the minimizers. In order to get these result we reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in cylindrical variables. We also get the non-degeneracy and uniqueness of minimizers in the radial symmetry class. This is joint work with Azahara DelaTorre and Maria del Mar Gonzalez.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |