Pagina 6

Date | Type | Start | End | Room | Speaker | From | Title |
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02/04/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Donato Scarcella | UPC Barcelona | Seminario di Equazioni Differenziali Asymptotically quasiperiodic solutions for time-dependent Hamiltonians with a view to celestial mechanics
Dynamical systems subject to perturbations that decay over time are relevant in the description of many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, as well as in celestial mechanics. For this reason, in the present talk, we consider a time-dependent perturbation of a Hamiltonian dynamical system having an invariant torus supporting quasiperiodic solutions. Assuming the perturbation decays polynomially fast as time tends to infinity, we prove the existence of orbits converging in time to the quasiperiodic solutions associated with the unperturbed system. This result generalizes the work of Canadell and de la Llave, where exponential decay in time was considered, and the one of Fortunati and Wiggins, where arithmetic, non-degeneracy conditions, and exponential decay in time are assumed.
We apply this result to the example of the planar three-body problem perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit (modeled as a time-dependent perturbation).
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) |

27/03/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Yasuyuki Kawahigashi | The University of Tokyo | Operator Algebras Seminar
Quantum 6j-symbols and braiding
Alpha-induction is a tensor functor producing a new fusion
category from a modular tensor category and a Q-system. This can be
formulated in terms of quantum 6j-symbols and braiding and gives
alpha-induced bi-unitary connections. Last year, we showed that locality of
the Q-system implies flatness of the alpha-induced connections. We now
prove that the converse also holds.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0 |

26/03/24 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Luca Schaffler | Roma Tre University | An explicit wall crossing for the moduli space of hyperplane arrangements Given the moduli space of hyperplanes in projective space, V. Alexeev constructed a family of compactifications parametrizing stable hyperplane arrangements with respect to given weights. In particular, there is a toric compactification that generalizes the Losev–Manin compactification for the moduli of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. In particular, we prove that in dimensions two the wall crossing corresponds to blowing up at the identity of the generalized Losev–Manin space. As an application, we show that any Q-factorialization of this blow-up is not a Mori dream space for a sufficiently high number of lines. This is joint work in progress with Patricio Gallardo. |

25/03/24 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Hartmut Prautzsch | Karlsruhe Institute of Technology | The many aspects of de Casteljau's algorithm - A historical review Paul de Faget de Casteljau (1930-2022) was a highly gifted mathematician who worked in industry and made fundamental mathematical contributions. In this talk, I will focus on one central contribution that de Casteljau developed soon after he started working for Citroen in 1958. It is the algorithm of de Casteljau, a simple construction of polynomial curves from control points by iterated linear interpolation. This algorithm is not only very simple, very useful, and very well known, but it also has a great number of properties and generalizations that make it a fundamental and unifying theoretical tool for Geometric Design. As a tribute to an outstanding pioneer in CAGD, I will recall widely and little known generalizations and properties of this algorithm to remind us of its beauty, versatility and importance as THE algorithm and backbone of Computer Aided Geometric Design (CAGD). |

20/03/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Jacopo Bassi | Università di Roma Tor Vergata | Operator Algebras Seminar
How far is SL(3,Z) from being hyperbolic?
Motivated by the problem of determining whether biexactness, the (AO)-property and von Neumann solidity are equivalent properties for a discrete countable group, I will discuss few recent results regarding analytic properties of SL(3,Z), related to hyperbolicity. I will focus on the role of measurable dynamics and proximality arguments in this context. Partly based on joint works with F. Radulescu and T. Amrutam.
Some references: https://arxiv.org/abs/2305.16277 https://arxiv.org/abs/2111.13885 https://arxiv.org/abs/2403.05948 |

19/03/24 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Leo Herr | University of Utah | The rhizomic topology and tropical abelian varieties The log etale topology is a natural analogue of the etale topology for log schemes. Unfortunately, very few things satisfy log etale descent -- not even vector bundles or the structure sheaf. We introduce a new rhizomic topology that sits in between the usual and log etale topologies and show most things do satisfy rhizomic descent! As a case study, we look at tropical abelian varieties and give some exotic examples. |

15/03/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Université du Quebec à Montréal | Algebra & Representation Theory Seminar (ARTS) "Shi arrangements in Coxeter groups"
this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) N.B.: Given an arbitrary Coxeter system ( W,S) and a nonnegative integer m, the m-Shi arrangement of (W,S) is a subarrangement of the Coxeter hyperplane arrangement of (W,S). The classical Shi arrangement (m=0) was introduced in the case of affine Weyl groups by Shi to study Kazhdan-Lusztig cells for W. As two key results, Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in W and that the union of their inverses form a convex subset of the Coxeter complex. The set of m-low elements in W was introduced to study the word problem of the corresponding Artin-Tits (braid) group and they turn out to produce automata to study the combinatorics of reduced words in W. In this talk, I will discuss how to Shi's results extend to any Coxeter system and show that the minimal elements in each Shi region are in fact the m-low elements. This talk is based on joint work with Matthew Dyer, Susanna Fishel and Alice Mark. | |

15/03/24 | Seminario | 14:30 | 15:30 | Universität Magdeburg | Algebra & Representation Theory Seminar (ARTS) "Folded galleries - a museum tour through 192 years of math history"
this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006) N.B.: Folded galleries, as introduced by Peter Littelmann in the 1990s, are combinatorial objects related to certain (subsets of) elements of Coxeter groups. They have shown to have versatile applications in algebra and geometry, making them an object of interest for current research. In this talk we will retrace the roots of their invention 192 years back in history, contemplate colorful illustrations of examples, and discover open questions for future applications. the talk will be colloquium-style and aimed at a wide audience: no prerequisite of deep algebraic nor group theoretic knowledge is required.
N.B.: | ||

13/03/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Boris Bolvig Kjær | University of Copenhagen | Operator Algebras Seminar
The double semion model in infinite volume
According to physics literature, topologically ordered gapped ground states of 2-dimensional spin systems can be described by a topological quantum field theory. Many examples arise from microscopic models with local commuting projector Hamiltonians, namely Levin-Wen models.
In this talk, I will describe the general framework for classifying infinite volume gapped ground states (by Naaijkens, Ogata, et.al.) in the simple context of abelian Levin-Wen models. This framework is heavily inspired by the DHR analysis in relativistic quantum field theory. It applies to the doubled semion model whose anyon theory is a braided fusion category equivalent to the representation category of the twisted Drinfeld double of Z_2. Based on joint work with Alex Bols and Alvin Moon, https://arxiv.org/abs/2306.13762. Seminar schedule here: https://sites.google.com/view/oastorvergata/home-page. |

12/03/24 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Shuang Chen | Central China Normal University | Invariant manifolds theory for fast-slow systems and applictions Dynamical systems with multiple time scales appear in a range of problems from applications. Invariant manifolds theory forms the foundation of qualitative analysis for their dynamics. In this talk, we will show our recent results on invariant manifolds theory for two classes of fast-slow systems, i.e., normally hyperbolic invariant manifolds for fast-slow high-dimensional systems and invariant structures for neutral differential equations with small delays. |

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