Seminário Simplético do Rio 

- Seminários de 2025: -

# Sex 5/Set, 14:30hs: 2 palestras
@IMPA, sala a confirmar

[14:30-15:30hs]
Revisiting cotangent bundles
Miquel Cueca (KU Leuven)

Abstract:  Cotangent bundles provide key examples of symplectic manifolds. On the other hand, one can think of Lie groupoids as generalizations of manifolds. In this context, Alan Weinstein constructed their cotangent bundles and proved that they are so-called symplectic groupoids. In this talk, I will recall this construction and explain what happens when one replaces a Lie groupoid with a Lie 2 (or n)-groupoid. If time permits, I will exhibit some of their main applications. This is joint work with Stefano Ronchi.

[16-17hs]
On barcode entropy and the variational principle
Rafael Fernandes (UCSC)

Abstract: In this seminar talk, we will explore a relatively new invariant associated with certain variational principles. For filtered homologies that arise from such principles, one can define an invariant using their barcode, called barcode entropy. Barcode entropy measures the growth rate of bars that are not too short in the barcode of the filtered homology. This invariant captures the complexity of cancellations that occur when passing from a chain complex to its homology. When the filtered homology is derived from an underlying dynamical system, barcode entropy is expected to reflect dynamical features such as topological or metric entropy. We will discuss the definition of barcode entropy, its motivations, and some examples that illustrate its relation to the complexity of the underlying dynamics.

# Sex 11/Abr, 14:30hs: 2 palestras
@IMPA, sala 236

[14:30-15:30hs]
Algebraic string topology operations and noncommutative Poisson geometry
Alex Takeda (Uppsala U.)

Abstract:  In this talk I will explain how to recover algebraic structures similar to those found in string topology, that is, the homology of loop spaces, from a certain type of noncommutative homotopy Poisson structure. This structure can be found, for instance, on the algebra of chains on the based loop space of an orientable manifold, recovering usual string topology operations, but also on examples coming from algebraic geometry and representation theory. Time allowing, I will explain the relation between this notion of nc homotopy Poisson structures and other similar definitions that have been made before. This talk is about joint work with Manuel Rivera and Zhengfang Wang.

[16-17hs]
On the integration of Manin triples and Courant algebroids over homogeneous spaces
Daniel Alvarez (IMPA)

Abstract: I will review the Lu-Weinstein construction of double symplectic groupoids. Then I will explain how to produce simple and explicit 2- shifted symplectic 2-groupoids over homogeneous spaces corresponding to action Courant algebroids with coisotropic stabilizers. This construction is related to generalized Kahler geometry and certain Manin triples over flag varieties. This is work in progress with Marco Gualtieri.