The seminar was previously organized by Universidad Católica del Norte (Antofagasta-Chile). This UCN-USP new edition of the seminar is organized in collaboration with Elizabeth Gasparim (UCN-Chile) and Francisco Rubilar (UCN-Chile). This is part of the research activities related to the project "Lefschetz fibrations, Lie groupoids and Noncommutative geometry" funded by Anid (Chile) and Fapesp (Brazil).

Taks will be held by zoom: https://reuna.zoom.us/j/82236847421

More information can be found here.

Next Talk (June 03 - 17:00 Sao Paulo; 16:00 Santiago Chile)

Speaker: James Pascaleff (University of Illinois at Urbana-Champaign)

Title: Structures in the Floer theory of Symplectic Groupoids

Abstract: A symplectic groupoid is a Lie groupoid with a multiplicative symplectic form. We take the perspective that such an

object is symplectic manifold with an extra categorical structure. Applying the machinery of Floer theory, the extra structure is expected to yield a monoidal structure on the Fukaya category. I will take an examples-based approach to working out what these structures are,  focusing on cases such as the cotangent bundle of a compact manifold.

Schedule

June 03: James Pascaleff (University of Illinois at Urbana-Champaign)

June 17: TBA 

July 01: Mark Colarusso (University of South Alabama)

Past Talks

May 20 (Thursday - 17:00 Sao Paulo; 16:00 Santiago Chile)

Speaker: Jorge Gamboa (University of Santiago - Chile)

Title: Corrections of the magnetic moment of the muon and possibilities of new physics.

Abstract: The seminar will explain the meaning of the recent measurements by FermiLab

and Brookhaven of the anomalous magnetic moment of the muon and the possibilities that 

these results have to understand Physics beyond the standard model.

May 06 (Thursday - 17:00 Sao Paulo; 16:00 Santiago Chile)

Speaker: João Nuno Mestre (University of Coimbra)

Title: Deformations of symplectic groupoids

Abstract: Symplectic groupoids are geometric objects that function as global counterparts to Poisson manifolds, in the same way that Lie groups are global counterparts to Lie algebras. In this talk I will first give an idea of what these objects are and of how that analogy works, and I will then present the construction of the deformation cohomology controlling deformations of symplectic groupoids.

I will then compute this cohomology in some examples, explain how to use it in a Moser path argument, and relate it to the deformation theory of the corresponding Poisson manifolds. The talk is based on joint work with Cristian Cárdenas (UFF) and Ivan Struchiner (USP).

April 22 (Thursday - 17:00 Sao Paulo; 16:00 Santiago Chile)

Speaker: Brent Pym (McGill University)

Title: A global Weinstein splitting theorem for holomorphic Poisson manifolds.

Abstract:  A foundational result in Poisson geometry, due to Weinstein, states that any Poisson bracket on a manifold can be written locally as the Poisson bracket of symplectic form in canonical coordinates, and a Poisson bracket that vanishes at a point.  A key consequence is that every Poisson manifold has a canonical foliation with symplectic leaves. I will give an introduction to these ideas, and then discuss the problem of globalizing Weinstein's decomposition, to split the manifold itself (or a covering thereof) as a product of a symplectic leaf and a transverse Poisson manifold.  While the existence of such a splitting is rare in the context of smooth manifolds, it turns out to be automatic for holomorphic Poisson structures on compact Kähler manifold admitting a simply-connected compact symplectic leaf.  This talk is based on joint work with Stéphane Druel, Jorge Vitório Pereira, and Frédéric Touzet, which in turn relies in an essential way on a notion of "subcalibations" in Poisson geometry introduced recently by Pedro Frejlich and Ioan Mărcuț.

April 08 (Thursday - 17:00 Sao Paulo, 16:00 Santiago Chile)

Speaker: Emilia Mazzetti (Universitá degli Studi di Trieste)

Title: Lefschetz properties, Laplace equations and Galois covering. 

Abstract: In an article in collaboration with Rosa M. Mirò-Roig and Giorgio Ottaviani (Canad. J. Math. 65, 2013), we established a relation, due to apolarity, between Artinian homogeneous ideals of a polynomial ring not satisfying the Weak Lefschetz Property - WLP - and projective varieties that verify a Laplace equation of a certain order s, i.e. such that all the s-osculating spaces have dimension less than expected. Thanks to this relation, it is possible to extend to various classes of toric varieties some classical results due to Eugenio Togliatti. In the seminar, I will introduce these notions and I will speak of some recent results in collaboration with Liena Colarte and Rosa M. Miro'-Roig, relating them to cyclic Galois coverings.