Pagina 15

09/06/23Seminario16:0017:001201 Dal Passo
Alessandro ZAMPINI
Università di Napoli "Federico II"
Algebra & Representation Theory Seminar (ARTS)
"Derivation based differential calculus for a class of noncommutative spaces"

N.B.: partially supported by the MIUR Excellence Department Project MatMod@TOV awarded to the Department of Mathematics, University of Rome "Tor Vergata"

  After a general introduction on differential calculi on noncommutative spaces, we equip a family of algebras whose noncommutativity is of Lie type with a derivation based differential calculus obtained, upon suitably using both inner and outer derivations, as a reduction of a redundant calculus over the Moyal four dimensional space.
09/06/23Seminario14:3015:301201 Dal Passo
Rosanna LAKING
Università di Verona
Algebra & Representation Theory Seminar (ARTS)
"Cosilting complexes and asymptotic triangulations of the annulus"

N.B.: partially supported by the MIUR Excellence Department Project MatMod@TOV awarded to the Department of Mathematics, University of Rome "Tor Vergata"

  In 2014 Baur and Dupont introduced the notion of an asymptotic triangulation. This is a combinatorial object arising naturally from the combinatorics of cluster algebras of type Ã. They showed that the set of all asymptotic triangulations has an interesting combinatorial structure: it is a poset and the edges of the Hasse graph can be obtained by flipping the asymptotic arcs. In this talk I will explain how this set parametrises certain 2-term complexes in derived category of a finite-dimensional algebra called a cluster-tilted algebra of type à and that the flip operation corresponds to a mutation operation.
  This is joint work with L. Angeleri Hügel, K. Baur and F. Sentieri.
07/06/23Seminario16:0017:001201 Dal PassoClaudio DappiaggiUniverità di Pavia
Seminario di Algebre di Operatori
Stochastic Partial Differential Equations and Renormalization à la Epstein-Glaser

We present a novel framework for the study of a large class of nonlinear stochastic partial differential equations, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use specific techniques proper of microlocal analysis.These allow us to deal with renormalization using an Epstein-Glaser perspective, hence without resorting to any specific regularization scheme. As a concrete example we shall use this method to discuss the stochastic Phi^3_d model and we shall comment on its applicability to the stochastic nonlinear Schrödinger equation.
30/05/23Seminario14:3015:301201 Dal PassoEleonora CintiUniversità di Bologna
Seminario di Equazioni Differenziali
A regularity result for isoperimetric sets with density

In this talk, I will present a recent regularity result for isoperimetric sets with densities, under mild Holder regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to reach the regularity class C^{1,frac{alpha}{2-alpha}} in any dimension. This is a joint work with L. Beck and C. Seis.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
26/05/23Seminario16:0017:001201 Dal Passo
Brandeis University
Algebra & Representation Theory Seminar (ARTS)
"Schubert Calculus and bosonic operators"

  In this talk I will present a new point of view on Schubert polynomials via bosonic operators. In particular, we extend the definition of bosonic operators from the case of Schur polynomials to Schubert polynomials. More precisely, we work with back-stable Schubert polynomials and our operators act on the left weak Bruhat order. Furthermore, these operators with an extra condition give sufficiently enough linear equations for the structure of the cohomology ring of flag varieties.
26/05/23Seminario14:3015:301201 Dal Passo
Arun RAM
University of Melbourne
Algebra & Representation Theory Seminar (ARTS)
"Boson-Fermion correspondence for Macdonald polynomials"

N.B.: partially supported by the MIUR Excellence Department Project MatMod@TOV awarded to the Department of Mathematics, University of Rome "Tor Vergata"

  In its simplest form, this correspondence is the map from symmetric functions to skew-symmetric functions given by multiplication by the Weyl denominator (the Vandermonde determinant). A generalization produces the motivating shadow of “geometric Satake”, a diagram which contains the Satake isomorphism, the center of the affine Hecke algebra and the Casselman-Shalika formula. In a miracle that I wish I understood better, the whole diagram generalizes to the case of Macdonald polynomials and sends the bosonic Macdonald polynomial to the fermionic Macdonald polynomial. Does this suggest an “elliptic version" of geometric Langlands?
  This talk is based upon arXiv2212.03312, joint with Laura Colmenarejo.
25/05/23Seminario16:0017:001201 Dal PassoMark DemersFairfieldProjective cones for dispersing billiards

We describe the recent construction of Birkhoff cones which are contracted by the action of transfer operators corresponding to dispersing billiard maps. The explicit contraction provided by this construction permits the study of statistical properties of a variety of sequential and open billiards. We will discuss some applications of this technique to chaotic scattering and the random Lorentz gas. This is joint work with C. Liverani.
23/05/23Seminario14:3015:301201 Dal PassoPiotr Oprocha AGH University of KrakowOn invariant sets with vanishing derivative and Cantor set dynamics (joint work with Silvere Gangloff)

Combinatorial graphs can serve as a nice tool for description of dynamical systems on Cantor set. A classical example of this type are Bratelli- Vershik diagrams. Recently, Shimomura, motivated by works of Akin, Glasner and Weiss, developed an alternative approach, which helps to describe dynamical systems on Cantor set by employing inverse limit of graphs. This approach provides a useful tool for description of dynamical systems on Cantor set. As a particular application of the above approach we will present a method of construction of Cantor set $C$ with prescribed dynamics and its extension to interval maps with derivative zero on $C$. Starting motivation for this study is an old question whether invariant subset $Csubset [0,1]$ on which derivative of interval map $f$ vanishes must contain a periodic point.
19/05/23Colloquium15:0016:301201 Dal PassoEleonora Di NezzaIMJ-PRG, Sorbonne Université
Evento "May 12: Celebrating Women in Maths"
      Ricci-flat spaces: one of the building blocks of the Universe
(Opening address by Barbara Nelli, University of L'Aquila)

Webpage (con link per lo streaming)
Note: This event is part of the activity of the MIUR Department of Excellence Project MatMod@TOV.
17/05/23Seminario14:3015:301101 D'AntoniSakshi JainTor VergataDiscrete spectrum is independent of the Banach space

We recall and discuss the result of Baladi & Tsujii which tells that, under mild conditions, a linear operator considered acting on two different Banach spaces will have spectra which coincide outside of the essential spectrum. * [Lemma A.3 of "Dynamical zeta functions and dynamical determinants for hyperbolic maps" by Viviane Baladi].

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