In a lot of geometric situations we need to work with families of varieties. In this talk we focus on families of singular Kähler-Einstein metric. In particular we study the case of a family of Kähler varieties and we develop the first steps of pluripotential theory in family, which will allow us to have a control on the C^0 estimate when the complex structure varies. This type of result will be applied in different geometric contexts. This is a joint work with V. Guedj and H. Guenancia.

&nbsp; Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible repre-sentations of a Weyl group can be realised in terms of a convolution action on the vector spaces of irreducible components of Springer fibers. Similar situations yield the affine Hecke algebra, quiver Hecke algebra (KLR algebra), quiver Schur algebra or Soergel bimodules. <br> &nbsp; <strong>N.B.:</strong> please <a href="https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1614163430980?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d" target="Teams">click <strong>HERE</strong> to attend the talk</a> in streaming.

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. <br> <a href="https://teams.microsoft.com/l/meetup-join/19%3ad48916dee7364e0bbb08216ea621de47%40thread.tacv2/1638994200875?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22c2aef70f-5baf-4851-af7c-b0e3d343779b%22%7d"><strong>MS Teams link for the streaming</strong></a>

We all know what the differential of a smooth map from R to R is. By looking at coordinates and then at charts, we also know what it is the differential of a smooth map between differentiable manifolds. With a little bit of work, we can also define a (weak) differential for Sobolev/BV maps in this setting (but the case of manifold-valued maps presents challenges already at this level). In this talk I will discuss how it is possible to differentiate maps between spaces that have no underlying differentiable structure at all. The concepts of Sobolev/BV maps in this setting will also be discussed. <br> <b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>

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.

&nbsp; Let be <strong>g</strong> a semisimple finite dimensional Lie algebra and <em>U</em>(<strong>g</strong>) its universal enveloping algebra. The theory of highest weight representations of g may passes through the description of an integral form of <em>U</em>(<strong>g</strong>), namely a suitable <strong>Z</strong>-subalgebra of <em>U</em>(<strong>g</strong>) generated by the divided powers of the Chevalley generators; for this reason it has been studied by several authors (e.g., Chevalley and Cartier). <br> &nbsp; If <strong>&gcirc;</strong> is an affine Lie algebra, in order to extend this approach, the analogous <strong>Z</strong>-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 <strong>&gcirc;</strong> is of type <em>A</em>_2<em>n</em>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. <br> &nbsp; The aim of this talk is to present the structure of these integral forms and some related results. <br> &nbsp; <strong>N.B.:</strong> please <a href="https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1614163430980?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d" target="Teams">click <strong>HERE</strong> to attend the talk</a> in streaming

&nbsp; 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 <em>A</em>. A few years ago, Dana Ernst introduced an elegant generalization of such diagrammatic representation for the generalized Temperley-Lieb algebra of affine type <em>C</em>. The proof that such representation is faithful is quite involved and the same author wonders if an easier proof exists. <br> &nbsp; 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 <em>C</em> in terms of heaps of pieces, and on certain operations that we define on such heaps. <br> &nbsp; This talk is based on a joint work with Giuliana Fatabbi and Gabriele Calussi. <br> &nbsp; <strong>N.B.:</strong> please <a href="https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1614163430980?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d" target="Teams">click <strong>HERE</strong> to attend the talk</a> in streaming

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<br> <b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>

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. <br> <br> Based on https://arxiv.org/abs/2111.04488 <br> <br> 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 <br> <br> <a haref="https://teams.microsoft.com/l/meetup-join/19%3a428ea736adc6424c8ae37f187c91b51b%40thread.tacv2/1637749896212?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22e6325df7-3e74-4c88-ab0b-65ff8a758e69%22%7d"> Miscrisoft Teams Link</a>

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.