Settimana 15/01/2024 - 19/01/2024

 

• Seminari

• Eventi

• Archivio Bollettini

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Seminari

 

Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 

Geometry Seminar

Date: 16 January 2024

Schedule: 14:30 - Rome Time

Where: Conference Room 1101 "C. D'Antoni"

Title: " On towers of isogeny graphs with full level structure "

Speaker: Katharina Müller - Universität der Bundeswehr München

Abstract: Let k be a finite field of chracteristic q. Let p,l be primes corpime to q and let N be a positive integer coprime to pql. In this talk we will define graphs X_l^q(Np^n) whose vertices are tuples (E,P,Q), where E/k is an elliptic curves and P,Q is a basis for E[Np^n]. The edges are given by degree l isogenies. We will discuss when X_l^q(Np^n)/X_l^q(Np^{n-1}) is Galois and will describe the structure of these graphs as volcanos.
This is joint work with Antonio Lei.

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry

Organizing Committee:
Giulio Codogni (mail to contact) Guido Maria Lido (mail to contact)

Further Info: Click here for Geometry Page

Streaming Link (MS Teams): This seminar will be held in person

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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 

RoMaDS - Rome Centre on Mathematics for Modelling and Data ScienceS.

Date: 18 January 2024

Schedule: 15:45 - Rome Time

Where: Conference Room "R. Dal Passo"

Title: "The Minority Dynamics and the Power of Synchronicity"

Speaker: Andrea Clementi (Università di Roma Tor Vergata)

Abstract: We study the minority-opinion dynamics over a fully-connected network of n nodes with binary opinions. Upon activation, a node receives a sample of opinions from a limited number of neighbors chosen uniformly at random. Each activated node then adopts the opinion that is least common within the received sample. Unlike all other known consensus dynamics, we prove that this elementary protocol behaves in dramatically different ways, depending on whether activations occur sequentially or in parallel. Specifically, we show that its expected consensus time is exponential in n under asynchronous models, such as asynchronous GOSSIP. On the other hand, despite its chaotic nature, we show that it converges within O(log^2 n) rounds with high probability under synchronous models, such as synchronous GOSSIP. Finally, our results shed light on the bit-dissemination problem, that was previously introduced to model the spread of information in biological scenarios. Specifically, our analysis implies that the minority-opinion dynamics is the first stateless solution to this problem, in the parallel passive-communication setting, achieving convergence within a polylogarithmic number of rounds. This, together with a known lower bound for sequential stateless dynamics, implies a parallel-vs-sequential gap for this problem that is nearly quadratic in the number n of nodes. This is in contrast to all known results for problems in this area, which exhibit a linear gap between the parallel and the sequential setting.
Joint work with: L. Becchetti, F. Pasquale, L. Trevisan, R. Vacus, and I. Ziccardi The results will be presented at: ACM-SIAM Symposium on Discrete Algorithms (SODA24) Full version of the paper is available here: Click Here)

Nota: Questo seminario fa parte delle attività finanziate dal progetto M.I.U.R. Dipartimento d'eccellenza MATH@TOV CUP E83C18000100006

Organizing Committee:
Michele Salvi ( Mail to contact)
Stefano Vigogna (Mail to contact)

Further Info and Program: Click here for RoMaDS event Page

Streaming Link (MS Teams): TEAMS link for streamingThis seminar will be held in mix mode: in person and streaming web

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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 

Algebra and Representation Theory Seminar

Date: Friday 19 January 2024

Schedule: 14:30 Rome Time

Where: Conference Room 1201 “Roberta Dal Passo”

Speaker: Riccardo ARAGONA (Università de L'Aquila)

Title: "Normalizer chain, modular idealizer chain and partitions"

Abstract:

In recent joint works with Civino, Gavioli and Scoppola, we studied the conjugacy classes of an elementary Abelian regular subgroup T of the symmetric group on 2n elements. In particular we computed, via GAP software package, a chain of normalizers in a Sylow 2-subgroup of this symmetric group defined iteratively, starting from T. We noticed that the logarithm of the indice of the (i-1)-th normalizer in the i-th normalizer of our chain is equal to the i-th partial sum of the sequence of the numbers of partitions of an integer in at least two distinct parts. In this talk we present some techniques developed in order to prove this result, including the notion of a special family of elements of a Sylow 2-subgroup, called rigid commutators. Finally, some generalizations to Lie algebras are given, considering similar results for an idealizer chain.

Organizing Committee: Fabio Gavarini (mail to)
Niels Kowalzig (mail to)
Martina Lanini (mail to)

Further Info: Click here for webpage

Streaming Link (MS Teams): This seminar will be held in person

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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 

Algebra and Representation Theory Seminar

Date: Friday Friday 19 January 2024

Schedule: 16:00 - Rome Time

Where: Conference Room 1201 “Roberta Dal Passo”

Speaker: Tommaso Rossi Università degli Studi di Roma "Tor Vergata"

Title: " Homology operations for gravity algebras "

Abstract:

In the early nineties Getzler discovered a nice algebraic structure on the equivariant homology of a topological conformal field theory. He called this algebraic structure a "gravity algebra" and he showed that it is governed by an operad which is closely related to the homology of M0,n+1, the moduli space of genus zero Riemann surfaces with n+1 marked points. A gravity algebra can be thought as a generalization of a (dg) Lie algebra, in the sense that other than the Lie bracket we also have higher arity operations which satisfies a "generalized Jacobi identity". In this talk we will first give an introduction to gravity algebras, providing many interesting examples from both algebra (cyclic cohomology of a Frobenius algebra) and topology (S1-equivariant homology of the free loop space on a manifold). Then I will briefly explain that any class in the S1-equivariant homology of the (unordered) configuration spaces of points in the plane H*S1(Cn(R);Fp) (with coefficients in a field Fp of p elements) gives rise to an homology operation for gravity algebras. After that we will see how to compute this equivariant homology and if time permits we will see some applications.

Organizing Committee:
Fabio Gavarini (mail to)
Martina Lanini (mail to)

Further Info: Click here for webpage

Streaming Link (MS Teams): This seminar will be held in person

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Eventi