Seminars

Speakers:
Romain Aimino
Date: Friday, 15 June, 2018 - 14:30
Abstract:

Although one could naively expect that random Lorentz gases are easier to investigate than deterministic periodic ones, this seems not to be the case as essentially no results are available in the non periodic case. In this talk, I will present some general ideas towards studying random Lorentz gases and I will show how to apply them for a class of deterministic walks in random environments wit hone-dimensional uniformly expanding local dynamics. This is a joint work with Carlangelo Liverani.

 

Speakers:
Sylvain Lavau
Date: Monday, 11 June, 2018 - 10:00
Abstract:

The modular class is a generalization of the divergence of vector fields to other geometric structures such as Poisson manifolds and Lie algebroids. The modular class of a regular foliation involves a volume form on the conormal bundle and the associated Bott connection. It is a closed one form along the leaves. The vanishing of this modular class implies that there exists a volume form which is invariant along the leaves.  In the singular case, the above definition can not be summoned since the conormal bundle may not be even well defined.

Speakers:
Miguel Abreu
Date: Friday, 8 June, 2018 - 15:30
Abstract:

Links of Gorenstein toric isolated singularities are good toric contact 
manifolds with zero first Chern class. In this talk I will present some 
results relating contact and singularity invariants in this particular 
toric context. Namely, 
(i) I will explain why the contact mean Euler characteristic is equal 
to the Euler characteristic of any crepant toric smooth resolution of 
the singularity (joint work with Leonardo Macarini). 
(ii) I will discuss applications of contact invariants of Lens spaces 

Speakers:
Pin Liu
Date: Wednesday, 23 May, 2018 - 14:00
Abstract:

At the beginning of this century, Fomin and Zelevinsky invented a new class of algebras called cluster algebras motivated by total positivity in algebraic groups and canonical bases in quantum groups. Since their introduction, cluster algebras have found application in a diverse variety of settings which include Poisson geometry, Teichmüller theory, tropical geometry, algebraic combinatorics and last not least the representation theory of quivers and finite dimensional algebras.

Speakers:
Jeff Weeks
Date: Friday, 11 May, 2018 - 11:00
Abstract:

This talk will introduce a method for learning to visualize 4‑dimensional space, give participants a chance to work on some 4D visualization exercises in small groups, and then present a few solutions using interactive 4D graphics software.  The exercises range from elementary to advanced, so everyone from first-year undergraduates to experienced geometers should find something they like.

Speakers:
Lucas Branco
Date: Thursday, 10 May, 2018 - 10:00
Abstract:

Given a complex reductive group G, the moduli space M(G) of G-Higgs bundles on a curve has a natural hyperkähler structure and it comes equipped with an algebraically completely integrable system through the Hitchin fibration. These moduli spaces have played an important role in mirror symmetry and in the geometric Langlands program and thus it has become of particular interest the study of certain decorated special subvarieties (branes) of M(G).

Speakers:
Liliana Garrido da Silva
Date: Friday, 4 May, 2018 - 14:30
Abstract:

The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are one-dimensional and contained in flow-invariant spaces of equal dimension. These heteroclinic cycles exist both in symmetric and non-symmetric contexts. We make one assumption on the dynamics along the connections to ensure that the transition matrices have a convenient form.

Speakers:
Hector Barge
Date: Friday, 27 April, 2018 - 11:30
Abstract:

In this seminar we shall introduce the Conley index of an isolated invarant set of a flow on a locally compact metric space. The Conley index is a homotopical tool which encapsulates dynamical information near the isolated invariant set. The definition of this invariant involves the use of some external objects, namely isolating blocks (or, more generally, index pairs). We will give a way to compute this index in "intrinsic terms" for flows defined on surfaces. To do this we will deepen into the structure of the unstable manifold of an isolated invariant set.

Speakers:
Filipa Soares de Almeida
Date: Thursday, 26 April, 2018 - 14:30
Abstract:

In this talk, we explore a notion that sits between the concept of locally finite variety and that of periodic variety, using the inescapable Green's relations. Namely, a variety is said to be K-finite, where K stands for any of the Green's relations, if every finitely generated semigroup in this variety has but finitely many K-classes. Our characterization uses the language of "forbidden objects".

Speakers:
António Girão
Date: Friday, 20 April, 2018 - 15:30
Abstract:

In 1975, Sheehan conjectured that every d-regular Hamiltonian graph contains a second Hamiltonian cycle. This conjecture has been verified for all d greater than 22. In the light of Sheehan’s conjecture, it is natural to ask if regularity is genuinely necessary to force the existence of a second Hamiltonian cycle, or if a minimum degree condition is enough.