10/12/21  Seminario  14:30  15:30  1201 Dal Passo  Margherita PAOLINI  Università de L'Aquila 
Algebra & Representation Theory Seminar (ARTS)
"Integral forms of affine Lie algebras"
 in live & streaming mode 
(see the instructions in the abstract)
Let be g a semisimple finite dimensional Lie algebra and U( g) its universal enveloping algebra. The theory of highest weight representations of g may passes through the description of an integral form of U( g), namely a suitable Zsubalgebra of U( g) generated by the divided powers of the Chevalley generators; for this reason it has been studied by several authors (e.g., Chevalley and Cartier).
If ĝ is an affine Lie algebra, in order to extend this approach, the analogous Zsubalgebra has been studied by Garland (in the untwisted case) and by Mitzman and by FisherVasta (in the twisted case). Anyhow, the case when ĝ is of type A_{2n}^{2} still remains obscure. In order to study the representation theory of this algebra we try to find more manageable techniques that will help to get a deeper understanding.
The aim of this talk is to present the structure of these integral forms and some related results.
N.B.: please click HERE to attend the talk in streaming

07/12/21  Seminario  16:00  17:00  1201 Dal Passo  Tien Khai Nguyen  North Carolina State University  Differential Game Models of Optimal Debt Management
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In this talk, I will present recent results on game theoretical formulation of optimal debt management problems in an infinite time horizon with exponential discount, modeled as a noncooperative interaction between a borrower and a pool of riskneutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debttoincome ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the riskneutral lenders will charge a higher interest rate in order to compensate for this possible loss of their investment. Thus, a "solution" must be understood as a Nash equilibrium, where the strategy implemented by the borrower represents the best reply to the strategy adopted by the lenders, and conversely. This leads to highly nonstandard optimization process
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
03/12/21  Seminario  15:00  16:00  1201 Dal Passo  Luca Giorgetti  Tor Vergata 
A planar algebraic description of conditional expectations
 in blended mode  Link in the abstract
Jones’ notion of index was introduced for II_1 subfactors and soon after
generalized to arbitrary inclusions of von Neumann algebras, not
necessarily tracial nor with trivial centers, in several ways. A unital
inclusion of von Neumann algebras N < M is said to have finite Jones
index if it admits at least one normal faithful conditional expectation
of M onto N with finite index. In the talk, I will report on a
representation formula for such finite index expectations and their dual
expectations (as defined by Haagerup and Kosaki) by means of the
solutions of the conjugate equations for the inclusion morphism of N
into M and its conjugate morphism. In particular, this provides a
2categorical formulation of the theory of index in this general
setting. Another consequence is that an arbitrary inclusion of von
Neumann algebras with a prescribed finite index expectation can be
described by a Qsystem. These results are both originally due to Longo
in the subfactor case.
Based on https://arxiv.org/abs/2111.04488
Supported by EU MSCAIF beyondRCFT grant n. 795151 and by MIUR
Excellence Department Project
awarded to the Department of Mathematics of the University of Rome Tor
Vergata, CUP E83C18000100006
Miscrisoft Teams Link

30/11/21  Seminario  16:00  17:30  1201 Dal Passo  Joost Hulshof  Vrije Universiteit Amsterdam  Advancing front solutions in a degenerate reactiondiffusion system
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We are interested in planar travelling wave solutions of the system
$$
u_t=varepsilon,
ablacdot u
abla u+uv,quad v_t=
ablacdot
abla uuv,
$$
with nonnegative profiles $U$ and $V$ that satisfy $U(infty)=V(+infty)=0$ and $U(infty)=V(infty)=1$.
The corresponding solutions have $u o1$ and $v o0$ as $t oinfty$.
Among these traveling wave profiles there's one with $Uequiv0$ on the left and $U>0$ on the right.
We discuss its existence and an approach towards its stability analysis, using a linearisation technigue
that we developed for the Porous Medium Fischer equation $u_t=(uu_x)_x+u(1u)$ (PMF).
This is part of an ongoing research project with Michiel Bertsch, Lorenzo Giacomelli and others, suggested to us by Mayan Mimura.
The ultimate goal is to show that for small $varepsilon>0$ the front solutions are stable in 1D but unstable in 2D.
For now it seems that the results for (PMF) are nontrivial and new.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

30/11/21  Seminario  14:30  15:30  1201 Dal Passo  Federico Pintore  Università di Bari  Geometry Seminar
Collisions in isogeny graphs, and the security of the SIDHbased identification protocol
The digital signature schemes that have been proposed so far in the setting of the Supersingular Isogeny DiffieHellman scheme (SIDH) were obtained by turning an interactive identification protocol by De Feo, Jao and Plût into noninteractive schemes. The security of the resulting schemes is therefore deduced from that of the base identification protocol. In this talk, we revisit the proofs that have appeared in the literature for the special soundness property of the abovementioned SIDHbased identification protocol. The existence of some special cycles in supersingular isogeny graphs make such previous proofs fail. 
26/11/21  Seminario  16:00  17:00  1201 Dal Passo  Niesl KOWALZIG  Università di Napoli "Federico II" 
Algebra & Representation Theory Seminar (ARTS)
"Centres, traces, and cyclic cohomology"
 in live & streaming mode 
(see the instructions in the abstract)
In this talk, we will discuss the biclosedness of the monoidal categories of modules and comodules over a (left or right) Hopf algebroid, along with the bimodule category centres of the respective opposite categories and a corresponding categorical equivalence to anti YetterDrinfel'd contramodules and anti YetterDrinfel'd modules, respectively. This is directly connected to the existence of a trace functor on the monoidal categories of modules and comodules in question, which in turn allows to recover (or define) cyclic operators enabling cyclic cohomology.
N.B.: please click HERE to attend the talk in streaming

26/11/21  Seminario  14:30  15:30  1201 Dal Passo  Marco TREVISIOL  "Sapienza" Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"Normality of closure of orthogonal nilpotent symmetric orbits"
 in live & streaming mode 
(see the instructions in the abstract)
Kraft and Procesi showed that the Zariski closure of the conjugacy classes of type A are all normal and, in type B, C and D, they have described which ones are normal. In their work the Lie group acts on its Lie algebra by the adjoint action. In types B, C, D, a similar question can be asked for the action of the Lie group on the odd part of the general linear Lie algebra; that is the orthogonal group acting on the symmetric matrices and the symplectic group acting on the symmetricsymplectic matrices. Ohta showed that in the latter case every orbit has normal closures while this conclusion is not valid in the former case. In this talk I will present the main result of my Ph.D. thesis which gives a combinatorial description of the orbit whose closures are normal in the orthogonal case.
N.B.: please click HERE to attend the talk in streaming

23/11/21  Seminario  16:00  17:00  1201 Dal Passo  Rafael SorianoLopez  Universidad Carlos III Madrid  Bound and ground states for an elliptic system with double criticality
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We will consider a nonlinear elliptic system in R^N. The interest of this problem is based on the presence of critical power nonlinearities and a nonlinear coupling, possibly critical, as well as Hardytype singular potentials. By means of variational methods, we will focus on the existence of solutions. More precisely, we shall derive new results on bound and ground states of the underlying energy functional. Finally, we extend our results to the special case of ''SchrödingerKortewegde Vries'' coupling type term.
This seminar is based on a couple of works in collaboration with Eduardo Colorado and Alejandro Ortega (UC3M).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
23/11/21  Seminario  14:30  15:30  1201 Dal Passo  Margherita Lelli Chiesa  Roma Tre  Geometry Seminar
Irreducibility of Severi varieties on K3 surfaces
Let (S,L) be a general K3 surface of genus g. I will prove that the closure in L of the Severi variety parametrizing curves in L of geometric genus h is connected for h>=1 and irreducible for h>=4, as predicted by a well known conjecture. This is joint work with Andrea Bruno. 
16/11/21  Seminario  14:00  15:00  1201 Dal Passo  Margarida Melo  Roma Tre  Geometry Seminar
On the top weight cohomology of the moduli space of abelian varieties
In the last few years, tropical methods have been applied quite successfully in understanding several aspects of the geometry of classical algebrogeometric moduli spaces. In particular, in several situations the combinatorics behind compactifications of moduli spaces have been given a tropical modular interpretation. Consequently, one can study different properties of these (compactified) spaces by studying their tropical counterparts.
In this talk, which is based in joint work with Madeleine Brandt, Juliette Bruce, Melody Chan, Gwyneth Moreland and Corey Wolfe, I will illustrate this phenomena for the moduli space Ag of abelian varities of dimension g. In particular, I will show how to apply the tropical understanding of the classical toroidal compactifications of Ag to compute, for small values of g, the top weight cohomology of Ag.
The techniques we use follow the breakthrough results and techniques recently developed by ChanGalatiusPayne in understanding the topology of the moduli space of curves via tropical geometry. 