Pagina 2

Date | Type | Start | End | Room | Speaker | From | Title |
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04/06/20 | Seminario | 17:00 | 18:00 | Sandro Vaienti | Centre de Physique Théorique, Marseille (France) | DinAmicI: Another Internet Seminar (DAI Seminar) "Thermodynamic formalism for random weighted covering systems"
- in streaming mode -
(see the instructions in the abstract)
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random covering condition.
Joint with J. Atnip, G. Froyland and C. Gonzalez-Tokman Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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29/05/20 | Seminario | 14:30 | 15:30 | The Hirzebruch-Riemann-Roch theorem in the fancy language of Spectra
- in streaming mode -
(see the instructions in the abstract)
The category of spectra indubitably is the best of possible worlds for cohomology theories. For instance in spectra one can start with a few basic morphisms, be confident that every natural diagram built from them will commute, and end up with a proof of the Hirzebruch-Riemann-Roch theorem. As in every good story we'll have a deus ex machina: Atiyah's identifi-cation of the Spanier-Whitehead dual of a manifold with the Thom spectrum of minus its tangent bundle. I will try to gently introduce all of this tools assuming basic notions of topology, geometry and algebra.
Based on a joint work with Domenico Fiorenza and Eugenio Landi. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the ARTS web-page and click on the link that you find there.Warning: | |||

28/05/20 | Seminario | 17:00 | 18:00 | Francesco Cellarosi | Queen's University (Canada) | DinAmicI: Another Internet Seminar (DAI Seminar) "Rational Horocycle lifts and the tails of Quadratic Weyl sums"
- in streaming mode -
(see the instructions in the abstract)
Equidistribution of horocycles on hyperbolic surfaces has been used to dynamically answer several probabilistic questions about number-theoretical objects. In this talk we focus on horocycle lifts, i.e. curves on higher-dimensional manifolds whose projection to the hyperbolic surface is a classical horocycle, and their behaviour under the action of the geodesic flow. It is known that when such horocycle lifts are 'generic’, then their push forward via the geodesic flow becomes equidistributed in the ambient manifold. We consider certain ‘non-generic’ (i.e. rational) horocycle lifts, in which case the equidistribution takes place on a sub-manifold. We then use this fact to study the tail distribution of quadratic Weyl sums when one of their arguments is random and the other is rational. In this case we obtain random variables with heavy tails, all of which only possess moments of order less than 4. Depending on the rational argument, we establish the exact tail decay, which can be described with the help of the Dedekind psi-function.
Joint work with Tariq Osman. Note: | |

27/05/20 | Colloquium | 15:00 | 16:00 | Lyapunov exponents
( in streaming, via
)
this link The concept of Lyapunov exponent goes back to Lyapunov's 1892 thesis on the stability of differential equations, and has numerous applications in various branches of mathematics and science. Starting from the 1960s, it found its proper mathematical framework in ergodic theory, where it has had a prominent role ever since. In this colloquium lecture I will review a few recent developments, especially about the way Lyapunov exponents depend on the underlying dynamical system. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
the Colloquium will be held in streaming, as a videoconference on-line, via Microsoft Teams; please Warning:use this link to join the videoconference. | |||

22/05/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Georg Schumacher | Philipps-Universität Marburg | |

22/05/20 | Seminario | 14:30 | 15:30 | Quantity vs. size in representation theory
- in streaming mode -
(see the instructions in the abstract)
Indecomposable modules over a finite-dimensional algebra R are largely thought of as the building blocks of the module category of R. A famous theorem of Auslander, Fuller-Reiten and Ringel-Tachikawa, states that a finite-dimensional algebra admits only finitely many indecom-posable modules up to isomorphism if and only if every indecomposable module is finite-dimen-sional. This establishes a correlation between quantity (of indecomposable finite-dimensional modules) and size (of indecomposable modules).
In this talk, we will take a macroscopic view of the module category and look at certain subcate-gories of modules rather than individual modules. Our focus will be on torsion pairs, which are orthogonal decompositions of the module category. We will show that a finite-dimensional algebra admits only finitely many torsion classes if and only if every torsion class is generated by a finite-dimensional module. Time permitting, I will also make a few comments on how this relation between quantity and size transfers to the derived category of a finite-dimensional algebra. This talk is based on joint works with Lidia Angeleri Hügel, Frederik Marks and David Pauksztello. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the ARTS web-page and click on the link that you find there.Warning: | |||

21/05/20 | Seminario | 17:00 | 18:00 | Martin Leguil | Université Paris-Sud 11 (France) | DinAmicI: Another Internet Seminar (DAI Seminar) "Some rigidity results for billiards and hyperbolic flows"
- in streaming mode -
(see the instructions in the abstract)
In a project with P. Bálint, J. De Simoi and V. Kaloshin, we have been studying the inverse problem for a class of open dispersing billiards obtained by removing from the plane a finite number of smooth strictly convex scatterers satisfying a non-eclipse condition. The dynamics of such billiards is hyperbolic (Axiom A), and there is a natural labeling of periodic orbits. We show that it is generically possible, in the analytic category and for billiard tables with two (partial) axial symmetries, to determine completely the geometry of those billiards from the purely dynamical data encoded in their Marked Length Spectrum (lengths of periodic orbits + marking). An important step is the obtention of asymptotic estimates for the Lyapunov exponents of certain periodic points accumulating a reference periodic point, which turn out to be useful in the study of other rigidity problems. In particular, I will explain the results obtained in a joint work with J. De Simoi, K. Vinhage and Y. Yang on the question of entropy rigidity for 3-dimensional Anosov flows and dispersing billiards.
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15/05/20 | Seminario | 15:15 | 16:15 | 1101 D'Antoni | Luca Tasin | Università di Milano | |

15/05/20 | Seminario | 14:30 | 15:30 | Continuum Kac-Moody algebras (and their quantizations)
- in streaming mode -
(see the instructions in the abstract)
In the present talk, I will define a family of infinite-dimensional Lie algebras associated with a "continuum" analog of Kac--Moody algebras. They depend on a "continuum" version of the notion of the quiver. These Lie algebras have some peculiar properties: for example, they do not have simple roots and in the description of them in terms of generators and relations, only quadratic (!) Serre type relations appear. If time permits, I will discuss their quantizations, called "continuum quantum groups". This is based on joint works with Andrea Appel and Olivier Schiffmann. Warning: the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the web-page
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14/05/20 | Seminario | 17:00 | 18:00 | Giulio Tiozzo | University of Toronto | DinAmicI: Another Internet Seminar (DAI Seminar) "Central limit theorems for counting measures in coarse negative curvature "
- in streaming mode -
(see the instructions in the abstract)
We establish general central limit theorems for an action of a group on a hyperbolic space with respect to counting for the word length in the group.
In 2013, Chas, Li, and Maskit produced numerical experiments on random closed geodesics on a hyperbolic pair of pants.
Namely, they drew uniformly at random conjugacy classes of a given word length, and considered the hyperbolic length of the
corresponding closed geodesic on the pair of pants. Their experiments lead to the conjecture that the length of these closed geodesics satisfies a central limit theorem, and we proved this conjecture in 2018.
In our new work, we remove the assumptions of properness and smoothness of the space, or cocompactness of the action, thus proving a general central limit theorem for group actions on hyperbolic spaces.
We will see how our techniques replace the classical thermodynamic formalism and allow us to provide new applications, including to lengths of geodesics in geometrically finite manifolds and to intersection numbers with submanifolds.
Joint work with I. Gekhtman and S. Taylor.
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