Pagina 23

20/05/22Seminario16:0017:001201 Dal Passo
University of Edinburgh
Algebra & Representation Theory Seminar (ARTS)
"Gaudin algebras, RSK and Calogero-Moser cells in type A"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  A few years ago, Bonnafé-Rouquier defined 'Calogero-Moser cells' through the representation theory of rational Cherednik algebras. These cells partition the elements of a complex reflection group G, but are currently difficult to calculate except in small rank examples. In the special case when G is a finite Coxeter group, the cells are conjectured to be the same as Kazhdan-Lusztig cells. In other words, conjecturally 'Calogero-Moser cells' generalise Kazhdan-Lusztig cell theory from Coxeter groups to complex reflection groups. I will discuss a confirmation of this conjecture for G being the symmetric group. The proof uses ideas from integrable systems (Gaudin algebras), algebraic geometry (moduli of points on genus zero curves), and combinatorics (crystals).
  This is joint work with A.Brochier and N.White.
  N.B.: please click HERE to attend the talk in streaming.
20/05/22Seminario14:3015:301201 Dal Passo
Università di Roma "Tor Vergata"
Algebra & Representation Theory Seminar (ARTS)
"Multiparameter quantum groups: a unifying approach"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )

  The original quantum groups - in particular, quantized universal enveloping algebras, in short QUEA's - have been introduced as depending on just one "continuous" parameter. Later on, multiparameter quantum groups - in particular, multiparameter QUEA's - have been introduced in differente ways, with the new, "discrete" parameters either affecting the coalgebra structure or the algebra structure (while leaving the dual structure unchanged). Both cases can be realized as special type deformations - namely, either by twist, or by 2-cocycle deformation - of Drinfeld's celebrated QUEA Uh(g). In this talk I will introduce a new, far-reaching family of multiparameter QUEA's that encompasses and generalizes the previous ones, while also being stable with respect to both deformation by twists and deformations by cocycles. Taking semiclassical limits, these new multiparameter QUEA's give rise to a new family of multiparameter Lie bialgebras, that in turn is stable under both by twist and deformations by 2-cocycles (in the Lie bialgebraic sense).
  This is a joint work with Gastón Andrés García - cf. arXiv:2203.11023 (2022).
  N.B.: please click HERE to attend the talk in streaming.
18/05/22Seminario14:0015:002001Tom LycheUniversity of OsloA C1 simplex spline basis for the Alfeld split

Piecewise polynomials over triangles and tetrahedrons have applications in several branches ranging from finite element analysis, surfaces in computer aided design... The smoothness on tetrahedrons is obtained either by high degrees of polynomials or using smaller degrees when splitting the tetraehedron into smaller pieces. Here we consider the Alfeld split which generalizes the Clough-Tocher split of a triangle. Simplex splines with arbitrary knots are the natural generalization of univariate B-splines to several variables. We consider degrees d = 2s-1 in dimension s and construct a partition of unity basis for the space S12s-1;s on the Alfeld split, consisting of simplex-splines. We also show a Marsden like identity for s ≤ 5. Joint work with Jean-Louis Merrien. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
17/05/22Seminario16:0017:001201 Dal PassoChaona ZhuChinese Academy of Sciences and Roma "Tor Vergata"Prescribing scalar curvatures: the negative case
( MS Teams Link for the streaming )

The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant, Rauzy (Trans. Amer. Math. Soc. 1995) showed solvability, if the function to be prescribed is not too positive, as quantified by Aubin-Bismuth (J. Funct. Anal. 1997) later on. In this talk we will review these results variationally and shed some light on the case, when Rauzy’s conditions fail. This talk is joint work with Martin Mayer.  
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
13/05/22Colloquium15:0016:001201 Dal PassoMichela ProcesiUniversità di Roma Tre
May12: Celebrating Women in Maths
     Order and chaos and wave dynamics
(Opening address by Gabriella Tarantello)  
     (MS Teams link for the streaming at the end of the abstract)  

Many physical phenomena are well described as the propagation of waves: the motion of the sea, the transmission of sound, electromagnetic waves (light, radio waves). Their mathematical description is often extremely complicated, and characterized by the coexistence of stable and chaotic behaviors. I will discuss some models of wave propagation by nonlinear Partial Differential Equations illustrating briefly the main difficulties as well as some mathematical methods used to study them.

A small refreshment will be served at the end of the colloquium.

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
10/05/22Seminario16:0017:001201 Dal PassoFilippo GazzolaPolitecnico di MilanoLong-time behavior of partially damped systems modeling degenerate plates with piers
( MS Teams Link for the streaming )

We consider a partially damped nonlinear beam-wave system of evolution PDE's modeling the dynamics of a degenerate plate. The plate can move both vertically and torsionally and, consequently, the solution has two components. We show that the component from the damped beam equation always vanishes asymptotically while the component from the (undamped) wave equation does not. In case of small energies we show that the first component vanishes at exponential rate. Our results highlight that partial damping is not enough to steer the whole solution to rest and that the partially damped system can be less stable than the undamped system. Hence, the model and the behavior of the solution enter in the framework of the so-called "indirect damping" and "destabilization paradox". These phenomena are valorized by a physical interpretation leading to possible new explanations of the Tacoma Narrows Bridge collapse. Joint work with Abdelaziz Soufyane (University of Sharjah, UAE)
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
10/05/22Colloquium14:3015:301201 Dal PassoSlava RychkovIHES, Bures sur Yvette, Paris
“Bootstrap” method in physics and mathematics

In the last 10-15 years, “bootstrap” was applied to problems as disparate as critical exponents of second-order phase transitions, scattering of elementary particles, chaotic dynamical systems, and Laplacian spectra on hyperbolic manifolds. This produced many new computer-assisted bounds on various quantities of interest. I will explain common features of these problems, and what is this bootstrap method which applies to all of them.
09/05/22Colloquium15:0016:001201 Dal PassoLorenzo RosascoUniversity of GenovaA guided tour of machine learning (theory)

In this talk, we will provide a basic introduction to some of the fundamental ideas and results in machine learning, with emphasis on mathematical aspects. We will begin contrasting the modern data driven approach to modeling to classic mechanistic approaches. Then, we will discuss basic elements of machine learning theory connected to approximation theory, probability and optimization. Finally, we will discuss the need of new theoretical advances at the light of recent empirical observations while using deep neural networks.
06/05/22Seminario14:3015:301201 Dal Passo
Friedrich-Alexander-Universität Erlangen-Nürnberg
Algebra & Representation Theory Seminar (ARTS)
"Tilting modules and torsion phenomena"
- in live & streaming mode -
( click HERE to attend the talk in streaming )
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

  Given a root system and a prime number p we introduce a category X of “graded spaces with Lefschetz operators” over a ring A. Then we show that under a base change morphism from A to a field K this category specialises to representations of the hyperalgebra of a reductive group, if K is a field of positive characteristic, and of a quantum group at pl-th root of unity, if K is the pl-th cyclotomic field. In this category we then study torsion phenomena (over the ring A) and construct for any highest weight a family of universal objects with certain torsion vanishing condi-tions. By varying these conditions, we can interpolate between the Weyl modules (maximal torsion) and the tilting objects (no torsion). This construction might shed some light on the character generations philosophy of Lusztig and Lusztig-Williamson.
  N.B.: please click HERE to attend the talk in streaming.
04/05/22Seminario14:0015:002001Marjeta KnezUniversity of LjubljanaA super-smooth C1 spline space over planar mixed triangle and quadrilateral meshes

In the talk a C1 spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEM-based or isogeometric analysis, will be introduced. The mesh is considered to be a partition of a planar polygonal domain into triangles and/or quadrilaterals. The proposed space combines the Argyris triangle element with the C1 quadrilateral element for polynomial degrees d ≥ 5. The spline space is assumed to be C2 at all vertices and C1 across edges, and the splines are uniquely determined by C2-data at the vertices, values and normal derivatives at chosen points on the edges, and values at some additional points in the interior of the elements. The motivation for combining the Argyris triangle element with a recent C1 quadrilateral construction, inspired by isogeometric analysis, is two-fold: on one hand, the ability to connect triangle and quadrilateral finite elements in a C1 fashion is non-trivial and of theoretical interest. On the other hand, the construction facilitates the meshing process by allowing more flexibility while remaining C1 everywhere. This is for instance relevant when trimming of tensor-product B-splines is performed. As it will be demonstrated by numerical examples the presented spline space can be employed to various applications like interpolation and least square approximation of a given function or to solve the biharmonic equation via its weak form and Galerkin discretization. This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.

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