| 28/01/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Andrea FERRAGUTI | SNS Pisa |
Algebra & Representation Theory Seminar (ARTS)
"Abelian dynamical Galois groups"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
Dynamical Galois groups are invariants associated to dynamical systems generated by the iteration of a self-rational map of P1. These are still very mysterious objects, and it is conjectured that abelian groups only appear in very special cases. We will show how the problem is deeply related to a dynamical property of these rational maps (namely that of being post-critically finite) and we will explain how to approach and prove certain non-trivial cases of the conjecture.
This is based on joint works with A. Ostafe, C. Pagano and U. Zannier.
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| 25/01/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Rafael Ruggiero | PUC Rio De Janeiro | Seminario di Equazioni Differenziali
On the graph property for totally irrational Lagrangian invariant tori
(MS Teams link for the streaming at the end of the abstract)
We show that every C2 Lagrangian invariant torus W of a Tonelli Hamiltonian defined in the n-torus
containing an orbit with totally irrational homology class is a graph of the canonical projection. This result extends the graph property obtained by Bangert and Bialy-Polterovich for Lagrangian minimizing tori without periodic orbits in the unit tangent bundle of a Riemannian metric in the two torus. Motivated by the famous Hedlund's examples of Riemannian metrics in the n-torus with n closed, homology independent, minimizing geodesics having minimizing tunnels, we also show the C1-generic nonexistence of Lagrangian invariant tori with "large" homology.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |
| 25/01/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Simone Diverio | La Sapienza | Geometry Seminar
Universal Gysin formulae and positivity of some characteristic
In the last years there have been a renewed interest for a conjecture by Griffiths stated in 1969. The conjecture characterises the positive characteristic forms for positive (in the sense of Griffiths) holomorphic Hermitian vector bundles: those should be the exactly the forms belonging to the positive cone spanned by Schur forms. After recalling the various definitions of positivity for holomorphic Hermitian vector bundles and (p,p)-forms, we shall explain a recent result, obtained in collaboration with my PhD student F. Fagioli, which partially confirms Griffiths' conjecture. The result is obtained as an application of a pointwise, differential-geometric version of a Gysin type formula for the push-forward of the curvature of tautological bundles over the flag bundle. |
| 18/01/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Eleonora di Nezza | Ecole Polytechnique de Paris | Geometry Seminar
Families of Kähler-Einstein metrics.
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. |
| 14/01/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Jens EBERHARDT | University of Bonn |
Algebra & Representation Theory Seminar (ARTS)
"Motivic Springer theory"
- 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
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.
N.B.: please click HERE to attend the talk in streaming.
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| 16/12/21 | Colloquium | 16:00 | 17:30 | 1201 Dal Passo | Nicola Gigli | SISSA Trieste | Differentiating in a non-differentiable environment
( MS Teams Link for the streaming )
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.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 16/12/21 | Seminario | 15:15 | 16:15 | 21 | Enrico Bozzo | Università degli Studi di Udine | Ordinamento 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.
MS Teams link for the streaming
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| 14/12/21 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Sara 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. |
| 10/12/21 | Seminario | 16:00 | 17:00 | | Riccardo BIAGIOLI | 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
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| 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 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
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