Seminari/Colloquia
Pagina 6
Date  Type  Start  End  Room  Speaker  From  Title 

09/04/24  Seminario  14:30  16:00  1101 D'Antoni  Ruijie Yang  HumboldtUniversität (Berlin)  Minimal exponent of a hypersurface
In this talk, I will go back to the origin of the minimal exponent and give a brief history on how it naturally arises in the context of integration over vanishing cycles (ArnoldVarchenko), counting integer solutions of congruence equations (Igusa) and Archimedean zeta functions (Atiyah, Bernstein, Loeser). Then I will talk about some joint work in progress with Dougal Davis (on birational formula of higher multiplier ideals via Beilinson’s formula from Jansen’s conjecture in geometry representation theory) and Ming Hao Quek (on birational characterization of minimal exponents via toric geometry and multi weighted blowups).

08/04/24  Colloquium  14:30  15:30  1201 Dal Passo  "Fractal, liftable and scale groups"
Scale groups are closed subgroups of the group of isometries of a regular tree that fixes an end of the tree and are vertextransitive. They play an important role in the study of locally compact totally disconnected groups as was recently observed by PE. Caprace and G. Willis. In the 80’s they were studied by A. FigaTalamanca and C. Nebbia in the context of abstract harmonic analysis and amenability. It is a miracle that they are closely related to fractal groups, a special subclass of selfsimilar groups.
In my talk I will discuss two ways of building scale groups. One is based on the use of scaleinvariant groups studied by V. Nekrashevych and G. Pete, and a second is based on the use of liftable fractal groups. The examples based on both approaches will be demonstrated using such groups as Basilica, Hanoi Tower Group, and a group of intermediate growth (between polynomial and exponential). Additionally, the group of isometries of the ring of padics and the group of dilations of the field of padics will be mentioned in relation with the discussed topics.  
03/04/24  Seminario  16:00  17:00  1201 Dal Passo  Florin Radulescu  Università di Roma Tor Vergata  Automorphic forms design of free group factors and quantum dynamics
The role of automorphic forms as intertwiners between various representations of free group factors was discovered a long time ago by Vaughan Jones, starting with a remarkable formula relating Peterson scalar product with the intrinsical trace. The intertwiner associated to an automorphic form is an eclectic object, not much can be computed, but the Muray von Neuman dimension can be used to get hints on its image. Vaughan Jones used that to settle the problem of finding analytic functions vanishing on the orbit under the modular group of a point in the upper half plane. In past work of the speaker, it was put in evidence that this is related to equivariant Berezin quantization.
This leads to a different representation of free group factors and to the existence of a quantum dynamics whose associated unbounded Hochschild 2 cocycle is related to the isomorphism problem. I will explain some concrete formulae and some new interpretation of the associated quantum dynamics

02/04/24  Seminario  16:00  17:00  1201 Dal Passo  Donato Scarcella  UPC Barcelona  Asymptotically quasiperiodic solutions for timedependent 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 timedependent 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, nondegeneracy conditions, and exponential decay in time are assumed.
We apply this result to the example of the planar threebody problem perturbed by a given comet coming from and going back to infinity asymptotically along a hyperbolic Keplerian orbit (modeled as a timedependent perturbation).
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
27/03/24  Seminario  16:00  17:00  1201 Dal Passo  Yasuyuki Kawahigashi  The University of Tokyo  Quantum 6jsymbols and braiding
Alphainduction is a tensor functor producing a new fusion
category from a modular tensor category and a Qsystem. This can be
formulated in terms of quantum 6jsymbols and braiding and gives
alphainduced biunitary connections. Last year, we showed that locality of
the Qsystem implies flatness of the alphainduced connections. We now
prove that the converse also holds.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?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 nontoric 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 Qfactorialization of this blowup 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 (19302022) 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  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  "Shi arrangements in Coxeter groups" N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Given an arbitrary Coxeter system (W,S) and a nonnegative integer m, the mShi 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 KazhdanLusztig 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 mlow elements in W was introduced to study the word problem of the corresponding ArtinTits (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 mlow elements. This talk is based on joint work with Matthew Dyer, Susanna Fishel and Alice Mark. 
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