| 09/04/21 | Seminario | 15:00 | 16:00 | | Giovanna CARNOVALE | Università di Padova |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Approximations of a Nichols algebra from a geometric point of view"
- in streaming mode -
(see the instructions in the abstract)
The talk is based on work in progress with Francesco Esposito and Lleonard Rubio y Degrassi.
Recently Kapranov and Schechtman have settled an equivalence between the category of graded connected co-connected bialgebras in a braided monoidal category W and the category of factorizable systems of perverse sheaves on all symmetric products Sym n( C) with values in W. The Nichols (shuffle) algebra associated with an object V corresponds to the system of intersection cohomology extensions of a precise local system on the open strata.
Motivated by the study of Fomin-Kirillov algebras and their relation with Nichols algebras, we describe the factorizable perverse sheaves counterpart of some algebraic constructions, including the n-th approximation of a graded bialgebra, and we translate into geometric statements when a Nichols algebra is quadratic.
N.B.: please click HERE to attend the talk in streaming
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| 08/04/21 | Seminario | 16:00 | 17:00 | | Eva Miranda & Daniel Peralta-Salas | UPC Barcelona & ICMAT Madrid |
DinAmicI: Another Internet Seminar (DAI Seminar)
Looking at Euler flows through a contact mirror: Universality and Turing completeness
- in streaming mode -
(see the instructions in the abstract)
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. Inspired by this proposal, we show that the stationary Euler equations exhibit several universality features, In the sense that, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension.
These results can be viewed as lending support to the intuition that solutions to the Euler equations can be extremely complicated in nature.
A key point in the proof is looking at the h-principle in contact geometry through a contact mirror, unveiled by Sullivan, Etnyre and Ghrist more than two decades ago.
We end up this talk addressing an apparently different question: What kind of physics might be non-computational? Using the former universality result, we can establish the Turing completeness of the steady Euler flows, i.e., there exist solutions that encode a universal Turing machine and, in particular, these solutions have undecidable trajectories..
This talk is based on joint work with Robert Cardona and Fran Presas.
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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| 01/04/21 | Seminario | 14:00 | 15:00 | | Louis Jeanjean | Università di Bourgogne Franche-Comté | Prescribed norm solutions of Schrödinger equations with mixed power nonlinearities.
( MS Teams Link for the streaming )
In this talk, I will present some recent results concerning the existence of prescribed norm solutions in problems where the associated nonlinearity is the sum of two powers, one which is mass-subcritical and one mass-supercritical. This leads to consider a constrained variational problem presenting a so-called convex-concave geometry. The issues of existence, multiplicity and orbital stability of solutions will be addressed with a special emphasize on the cases where the mass-supercritical power is Sobolev critical.
The content of this talk is based on some jointed work with J. Jendrej, T. T. Le and N. Visciglia. |
| 30/03/21 | Seminario | 15:00 | 16:00 | | Filippo AMBROSIO | EPFL Lausanne |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Birational sheets in linear algebraic groups"
- in streaming mode -
(see the instructions in the abstract)
The sheets of a variety X under the action of an algebraic group G are the irreducible components of subsets of elements of X with equidimensional G-orbits. For G complex connected reductive, the sheets for the adjoint action of G on its Lie algebra g were studied by Borho and Kraft in 1979. In 2016, Losev introduced finitely many subvarieties of g consisting of equidimensional orbits, called birational sheets: their definition is less immediate than the one of a sheet, but they enjoy better geometric and representation-theoretic properties and are central in Losev's suggestion of an Orbit method for semisimple Lie algebras.
In the opening part of the seminar we give a brief overview of sheets and recall some basics about Lusztig-Spaltenstein induction of conjugacy classes in terms of the so-called Springer generalized map and analyse its interplay with birationality. This will give the instruments to introduce Losev's birational sheets in g.
The main part is aimed at investigating analogues of birational sheets of conjugacy classes in G. To conclude, assuming that the derived subgroup of G is simply connected, we illustrate the main features of these varieties, comparing them with the objects defined by Losev.
Part of the talk is based on joint works with G. Carnovale and F. Esposito, and M. Costantini.
N.B.: please click HERE to attend the talk in streaming.
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| 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 -
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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
(see the instructions in the abstract)
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 |