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16/12/21Seminario15:1516:1521Enrico BozzoUniversità degli Studi di UdineOrdinamento attento al tempo e problema del consenso

Si esamina l'integrazione in alcuni noti metodi di ordinamento proposti in ambito sportivo dell'informazione relativa al momento in cui avvengono gli incontri. I metodi ottenuti, definibili attenti al tempo, sono descritti da ricorrenze a coefficienti variabili in cui appaiono delle matrici stocastiche. Nell'ambito della teoria dei sistemi lo studio della convergenza di queste ricorrenze viene definito problema del consenso. Malgrado sul problema del consenso esita una vasta letteratura ci sono meno risultati sulla velocità di convergenza che ha importanti ricadute pratiche. È una ricerca in collaborazione con Paolo Vidoni e Massimo Franceschet dell'Università di Udine. Questo seminario è parte dell'attività del Progetto MIUR Dipartimento d'Eccellenza CUP E83C18000100006.
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14/12/21Seminario14:3015:301201 Dal PassoSara Torelli
Lebniz University Hannover
Geometry Seminar
Holomorphic one forms on moduli of curves

In the talk I will prove that the moduli spaces Mg,n of n-marked curves of any genus g > 4 do not admit holomorphic 1-forms. The main difficulty is to prove the result for Mg, then one concludes the other cases by an inductive argument. This sheds new light on the question of how far Mg,n is from being projective. The work is joint with F.F. Favale and G.P.Pirola.
Università di Bologna
Algebra & Representation Theory Seminar (ARTS)
"Temperley-Lieb algebra and fully commutative elements in affine type C"
- 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 CUP E83C18000100006

  The Temperley-Lieb algebra is a well studied finite dimensional associative algebra: it can be realized as a diagram algebra and it has a basis indexed by the fully commutative elements in the Coxeter group of type A. A few years ago, Dana Ernst introduced an elegant generalization of such diagrammatic representation for the generalized Temperley-Lieb algebra of affine type C. The proof that such representation is faithful is quite involved and the same author wonders if an easier proof exists.
  In this talk, we present a new combinatorial way to describe Ernst's algebra homomorphism, from which injectivity and subjectivity follow more easily. Our results are based on a classification of fully commutative elements of affine type C in terms of heaps of pieces, and on certain operations that we define on such heaps.
  This talk is based on a joint work with Giuliana Fatabbi and Gabriele Calussi.
  N.B.: please click HERE to attend the talk in streaming
10/12/21Seminario14:3015:301201 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 Z-subalgebra 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 Z-subalgebra has been studied by Garland (in the untwisted case) and by Mitzman and by Fisher-Vasta (in the twisted case). Anyhow, the case when ĝ is of type A2n2 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
07/12/21Seminario16:0017:001201 Dal PassoTien Khai NguyenNorth Carolina State UniversityDifferential 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 risk-neutral lenders. Here, the yearly income of the borrower is governed by a stochastic process and bankruptcy instantly occurs when the debt-to-income ratio reaches a threshold. Since the borrower may go bankrupt in finite time, the risk-neutral 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
03/12/21Seminario15:0016:001201 Dal PassoLuca GiorgettiTor 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 2-categorical 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 Q-system. These results are both originally due to Longo in the subfactor case.

Based on

Supported by EU MSCA-IF 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

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30/11/21Seminario16:0017:301201 Dal PassoJoost HulshofVrije Universiteit AmsterdamAdvancing front solutions in a degenerate reaction-diffusion system
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We are interested in planar travelling wave solutions of the system $$ u_t=varepsilon, ablacdot u abla u+uv,quad v_t= ablacdot abla u-uv, $$ 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 $u_t=(uu_x)_x+u(1-u)$ (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
30/11/21Seminario14:3015:301201 Dal PassoFederico Pintore
Università di Bari
Geometry Seminar
Collisions in isogeny graphs, and the security of the SIDH-based identification protocol

The digital signature schemes that have been proposed so far in the setting of the Supersingular Isogeny Diffie-Hellman scheme (SIDH) were obtained by turning an interactive identification protocol by De Feo, Jao and Plût into non-interactive 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 above-mentioned SIDH-based identification protocol. The existence of some special cycles in supersingular isogeny graphs make such previous proofs fail.
26/11/21Seminario16:0017:001201 Dal Passo
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 Yetter-Drinfel'd contramodules and anti Yetter-Drinfel'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
26/11/21Seminario14:3015:301201 Dal Passo
"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 symmetric-symplectic 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

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