| 30/05/23 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Eleonora Cinti | Università 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 |
| 26/05/23 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Gleb NENASHEV | 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.
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| 26/05/23 | Seminario | 14:30 | 15:30 | 1201 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.
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| 25/05/23 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Mark Demers | Fairfield | Projective 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. |
| 23/05/23 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Piotr Oprocha | AGH University of Krakow | On 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. |
| 19/05/23 | Colloquium | 15:00 | 16:30 | 1201 Dal Passo | Eleonora Di Nezza | IMJ-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.
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| 17/05/23 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Sakshi Jain | Tor Vergata | Discrete 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]. |
| 16/05/23 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Roberta Bianchini | IAC - CNR | Seminario di Equazioni Differenziali
Mathematical analysis of stably stratified fluids
We will be interested in the analysis of a system of PDEs modeling continuously stratified fluids under the influence of gravity.
The system is obtained by a linearization of the equations of incompressible non-homogeneous fluids (non-homogeneous Euler equations) around a background density profile that increases with depth (spectrally stable density profile).
I will present some mathematical problems related to (asymptotic) stability and long-time dynamics.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |
| 12/05/23 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Emanuele LATINI | Università di Bologna |
Algebra & Representation Theory Seminar (ARTS)
"Higher conformal Yang-Mills equation"
On a pseudo Riemannian manifold consider a 2-form taking value in the adjoint representation of some (semisimple) Lie algebra. It is well known that the corresponding Yang-Mills functional is conformally invariant just in four dimensions. A natural question is whether there are natural replacements of the Yang-Mills functional that are conformally invariant.
In the first part of the talk we will describe the main tools needed to answer this question, namely conformal defining densities for conformally compact manifolds and the (adjoint) tractor bundle; then we will show how to set up and to formally solve the Yang-Mills boundary problem on conformally compact manifolds. In general, smooth solutions are obstructed by an invariant of boundary connections. Specializing to Poincaré-Einstein manifolds with even boundary dimension parity, this obstruction is a conformal invariant of boundary Yang-Mills connections. This yields conformally invariant, higher order generalizations of the Yang-Mills equations and their corresponding energy functionals.
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| 12/05/23 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Thomas WEBER | Università di Torino |
Algebra & Representation Theory Seminar (ARTS)
"Noncommutative differential geometry with Hopf algebra symmetry"
While in classical differential geometry one is given a unique differential structure, the de Rham calculus, such a canonical choice does not exist in noncommutative geometry. Moreover, while the de Rham differential is equivariant with respect to a given Lie group action, a noncommutative calculus might not be compatible with a corresponding Hopf algebra symmetry.
We give a gentle introduction to noncommutative differential geometry, reviewing seminal work of Woronowicz (covariant calculi on Hopf algebras) and Hermisson (covariant calculi on quantum homogeneous spaces). The latter invokes the notion of faithful flatness and Takeuchi/Schneider equivalence. Afterwards we discuss an original construction of a canonical equivariant calculus for algebras in symmetric monoidal categories, with main examples including algebras with (co)triangular Hopf algebra symmetry, particularly Drinfel’d twisted (star product) algebras. The approach relies on and is essentially dual to the concept of ‘braided derivations’ and we show that the corresponding braided Gerstenhaber algebra of multi-vector fields combines with the noncommutative calculus, forming a braided Cartan calculus. If time permits we illustrate how to formulate Riemannian geometry in this framework, proving that for every equivariant braided metric there is a unique quantum Levi-Civita connection. The second half of the talk is based on the thesis of the speaker.
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