Pagina 1

Date | Type | Start | End | Room | Speaker | From | Title |
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08/07/20 | Seminario | 17:00 | 18:00 | Françoise Pène | Université de Bretagne Occidentale (France) | DinAmicI: Another Internet Seminar (DAI Seminar) Invariance by induction of the asymptotic variance
- in streaming mode -
(see the instructions in the abstract)
It is well known that the integral of an observable is preserved by induction. We are interested here in extensions of this result to moments of order 2 and 3. We have two natural candidates for the second and third order moments: the classical asymptotic variance (given by the Green-Kubo formula) and an analogous quantity of the third order. This question arises from the proof of CLT. In some cases, the asymptotic variance in the CLT can be expressed on the one hand in terms of the classical Green-Kubo formula and on the other hand in terms of the Green-Kubo formula for the induced system. Under general assumptions (involving transfer operators), we prove that the asymptotic variance is preserved by induction and that the natural third order quantity is preserved up to an error term.
This is joint work with Damien Thomine. 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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01/07/20 | Seminario | 17:00 | 18:00 | Marta Maggioni | Universiteit Leiden (Netherlands) | DinAmicI: Another Internet Seminar (DAI Seminar) "Matching for random systems with an application to minimal weight expansions"
- in streaming mode -
(see the instructions in the abstract)
We consider families of skew-product maps, representing systems evolving in discrete time in which, at each time step, one of a number of transformations is chosen according to an i.i.d process and applied. We extend the notion of matching for such dynamical systems and we show that, for a certain family of piecewise affine random maps of the interval, the property of random matching implies that any invariant density is piecewise constant. We give an application by introducing a one-parameter family of random maps generating signed binary expansions of numbers. This family has random matching for Lebesgue almost every parameter, producing matching intervals that are related to the ones obtained for the Nakada continued fraction transformations. We use this property to study the expansions with minimal weight.
Joint with K. Dajani, and C. Kalle. Note: | |

01/07/20 | Colloquium | 15:00 | 16:00 | Nonautonomous and Random Dynamical Systems in the Climate Sciences
( in streaming, via
)
this linkN.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
H. Poincaré already raised doubts about the predictability of weather due to the divergence of orbits of dynamical systems associated more recently with chaos. Progress in the theory of nonlinear, deterministic dynamical systems (DDS theory) and the work of E. N. Lorenz justified Poincaré’s doubts. The theory of autonomous DDSs, with time-independent forcing and coefficients, provided a solid mathematical basis for the work on weather predictability over several decades. More recently, an interesting convergence occurred between studies of climate predictability and the development of the theory of nonautonomous and random dynamical systems (NDS and RDS). The diurnal and the seasonal cycle of insolation played a somewhat limited role in weather predictability for 10–15 days, but it became impossible to ignore the role of the seasonal cycle and of anthropogenic effects in climate predictability for years to decades. At the same time, the theory of purely deterministic, skew product flows, as well as that of RDSs, incorporated time-dependent forcing and coefficients and took huge mathematical strides, including the rigorous formulation and application of pullback attractors. A parallel development formulated and applied the concept of snapshot attractors. I will present some of the mathematical background and applications to the climate sciences, including: (i) the use of pullback and snapshot attractors for the proper understanding of the effects of time-dependent forcing upon intrinsic climate variability; (ii) the use of Wasserstein distance between time-dependent invariant measures to estimate these effects; (iii) the topological aspects of nonautonomous effects upon the intrinsic variability; and (iv) a “grand unification” between the nonlinear, deterministic and autonomous point of view and the linear, stochastically driven one. | |||

30/06/20 | Seminario | 14:30 | 15:30 | Tere Seara | UPC Barcelona | Mechanism of instability in Hamiltonian Systems: Skipping along a normally hyperbolic invariant manifold
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We describe a recent method to show instability in Hamiltonian systems. The mechanism works if some explicit and verifiable transversality conditions are satisfied. The hypothesis can be verified by just checking that some Melnikov type integrals have non-degenerate zeros. This holds for Baire generic sets of perturbations in the C^r topology.
The method uses these hypotheses to conclude the existence of orbits, in near integrable Hamiltonian Systems, which change the action coordinate by a quantity independent of the size of the perturbation. Note:
To attend the lecture, click on the following
Teams Link
This talk is part of the activity of the MIUR Department of Excellence Grant 2018-2022, CUP E83C18000100006. | |

24/06/20 | Seminario | 17:00 | 18:00 | Andreas Knauf | Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) | DinAmicI: Another Internet Seminar (DAI Seminar) Asymptotic velocity for scattering particles
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Partly with Jacques Fejoz, Richard Montgomery, Stefan Fleischer and Manuel Quaschner.
The past and future of scattering particle systems is partly determined by their asymptotic velocity, that is, the Cesàro limit of the velocity. That this exists for bounded interactions and all initial conditions, is part of a statement sometimes called ‘asymptotic completeness’. The same statement does not apply to individual initial conditions in celestial mechanics. However, at least for up to four particles, nonexistence of asymptotic velocity is a measure zero phenomenon. We explain some new ideas connected with the proof (Poincaré section techniques for wandering sets, non-deterministic particle systems, and walks on a poset of set partitions). Note: | |

19/06/20 | Seminario | 14:30 | 15:30 | Cluster algebras and generalized minors reloaded
- in streaming via this link: https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1591029204732?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d (see also the instructions in the abstract)
In a work with D. Rupel and H. Williams we showed that, given an acyclic finite or affine cluster algebra, its cluster monomials can be understood as generalized minors of the associated Kac-Moody group. The proof hinges upon a double recursion made possible by a technical tool, the double cambrian fan. In this talk I will explain how one can prove a slightly weaker, but at the same time much more general result in a cleaner way. This is a work in progress in collaboration also with A. Appel. the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the ARTS web-page - at
http://www.mat.uniroma2.it/~ricerca/algebr/page-AREA_files/page-AREA-2_files/talks-2.html#19/06/2020 - and click on the link that you find there.Warning: | |||

17/06/20 | Seminario | 17:00 | 18:00 | Sunrose Shrestha | Tufts University, USA | DinAmicI: Another Internet Seminar (DAI Seminar) The topology and geometry of random square-tiled surfaces
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Abstract
A square-tiled surface (STS) is a branched cover of the standard square torus with branching over exactly one point. They are concrete examples of translation surfaces which are an important class of singular flat metrics on 2-manifolds with applications in Teichmüller theory and polygonal billiards. In this talk we will consider a randomizing model for STSs based on permutation pairs and use it to compute the genus distribution. We also study holonomy vectors (Euclidean displacement vectors between cone points) on a random STS. Holonomy vectors of translation surfaces provide coordinates on the space of translation surfaces and their enumeration up to a fixed length has been studied by various authors such as Eskin and Masur. In this talk, we obtain finer information about the set of holonomy vectors, Hol(S), of a random STS. In particular, we will see how often Hol(S) contains the set of primitive integer vectors and find how often these sets are exactly equal. Note: | |

12/06/20 | Seminario | 14:30 | 15:30 | The Reeder’s Conjecture for Classical Lie Algebras
- in streaming via this link: https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1591028479219?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d (see also the instructions in the abstract)
A well known result of the first half of XX century asserts that the cohomology of a compact connected Lie group G is isomorphic as a graded vector space to the ring of G-invariants of the exterior algebra of g = Lie(G) . Finding Betti numbers of G then corresponds to identifying copies of the trivial representation in Λg . Reeder in '95 reduces this computation to the problem of finding copies of the trivial representation of the Weyl group of G in a suitable bi-graded algebra. As a generalization of this result, he conjectured that it is possible to compute the graded multiplicites in Λg of a special class of representations reducing to a similar “Weyl group representation”-problem. In the talk I will give a proof of the Reeder's Conjecture for the C case and present some new progress for type _{n}D.
the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the ARTS web-page - at
http://www.mat.uniroma2.it/~ricerca/algebr/page-AREA_files/page-AREA-2_files/talks-2.html#12/06/2020 - and click on the link that you find there.Warning: | |||

09/06/20 | Seminario | 15:00 | 17:00 | Lucia Caporaso | Università Roma Tre | May 12 - Online event:
"Varieties of varieties after Mirzakhani"
followed by the screening of the documentary: " Secrets of the surface: the mathematical vision of Maryam Mirzakhani" by George Csicsery
- in streaming mode -
(see the instructions in the abstract)
The event will be live-streamed on the youtube channel: https://www.youtube.com/channel/UCYj2TA5j363-eQK391WjqoA
For More information visit the web-page: http://www.mat.uniroma2.it/may12.php The event is sponsored by the MIUR Excellence Department Project CUP E83C18000100006 | |

05/06/20 | Seminario | 14:30 | 15:30 | TDA for medical data analysis, how can we help in the current pandemic?
- in streaming via this link -
(see also the instructions in the abstract)
Topological data analysis is a source of stable and explainable methods to analyze data. Those features are of the key importance in medical applications. In this talk I will review concepts of conventional and ball mapper. I will highlight how those tools have been used to analyze medical data, starting from work performed in Ayasdi, ending up in my work related to the current pandemic. I will finish by describing my work with Oxford Covid19 database (OxCDB).
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the ARTS web-page - at
http://www.mat.uniroma2.it/~ricerca/algebr/page-AREA_files/page-AREA-2_files/talks-2.html#05/06/2020 - and click on the link that you find there.Warning: |