UCR Differential Geometry seminar

Friday 11am-12

Spring 2022 Schedule:

The current plan is to have most talks in person in Skye 268. This quarter, the seminar will be a mix of research talks by external speakers and expository talks whose aim is to understand a recent paper Uniformization of some weight 3 variations of Hodge structures, Anosov representations and Lyapunov exponents by Simion Filip. Depending on how this goes, we may continue this format in the fall quarter.

Title: An introduction to the paper.

Abstract: I will give an overview of what is done in the paper and why it is important. In future talks we will dive deeper into the background of the main objects. These objects include things at the intersection of geometric group theory, hyperbolic geometry, differential geometry, complex algebraic geometry, dynamics and Lie theory. Next week Patricio Gallardo will give another introduction to what is done in the paper but from the perspective of variations of Hodge structure.

Title: Certain Torelli theorem from Calabi Yau threefolds.

Abstract: We will define Hodge structures, VHS, and Torelli theorems. Then, we will visit related results from the article "Uniformization of some weight 3 variations of Hodge structures, Anosov representation, and Lyapunov exponents" by Simion Filip. Finally, we will discuss the context of such results within current research on moduli and Hodge theory.


  • April 22: No talk this week


Title: Minimal surfaces in products of R-trees

Abstract: Recently, Markovic proved that there exists a maximal representation into \prod_{i=1}^n PSL(2,R) such that the associated energy functional on Teichmueller space admits multiple critical points. In geometric terms, there is more than one minimal surface in the relevant homotopy class in the corresponding product of closed hyperbolic surfaces.

In some sense, high energy minimal surfaces in products of hyperbolic surfaces "converge" to equivariant minimal surfaces in products of R-trees. In this talk, we discuss energy minimizing properties for minimal maps into trees, and we give an application about the uniqueness of minimal diffeomorphisms of disks.


Title: Variations of Hodge structure and (G,X)-structures.

Abstract: We will define variations of Hodge structure and (G,X) structures. We will then specify to the spefic case considered in Filip's paper, define his Assumption A and state another one of the main theorems in the paper.


Title: Domains of discontinuity for Anosov representations

Abstract: The parameter spaces of Anosov representations can usually be seen as deformation spaces of parabolic geometric structures on some closed manifolds, this is due to Guichard-Wienhard and Kapovich-Leeb-Porti. A particularly interesting case is given by the Higher Teichmüller Spaces, spaces that generalize the classical Teichm\"uller spaces for higher rank Lie groups.

In this talk we will present a general structure theorem about the topology of such closed manifolds, and we will describe this topology explicitly in some interesting cases. This is based on a joint work with Colin Davalo and Qiongling Li, and a joint work with Sara Maloni, Nicolas Tholozan and Anna Wienhard.


Title: Certain Torelli theorem from Calabi Yau threefolds Part 2.

Abstract: Last time we defined Hodge structrures, this time we will define VHSs and Torelli theorems. Then, we will visit related results from the article "Uniformization of some weight 3 variations of Hodge structures, Anosov representation, and Lyapunov exponents" by Simion Filip. Finally, we will discuss the context of such results within current research on moduli and Hodge theory.


  • May 27: Zach Virgilio (UCR)

Title: TBA

Abstract: TBA



Fall 2021 Schedule

  • October 15: Claudio Meneses (Christian-Albrechts-Universität Kiel) Zoom talk

Title: Wall-crossing on moduli spaces of parabolic Higgs bundles in genus 0

Title: Introduction to Nonabelian Hodge part 1

Title: On volume of complements of geodesics random and non

Title: The wildest hyperbolic planes in Minkowski 3-space

Title: Introduction to Nonabelian Hodge part 2

Title: Characteristic numbers of elliptic fourfolds

  • December 3: Russel Phelan (UCR)

Title: Rational Ellipticity as an Obstruction to Non-Negative Curvature


Spring 2021 Schedule:

  • April 2, 2021 : Xian Dai (Heidelberg University)

Title: Correlation of Convex Projective Structures and Its Generalization

Title: Positively curved manifolds with discrete symmetry

Title: The energy functional of a Hitchin representation

Title: Plateau problem in psuedo-hyperbolic space

Title: Geometry of the Space of Sections of the Deligne--Hitchin Twistor Space

Title: Spectrum and Wave trace of Asymptotically Complex Hyperbolic Manifolds

Title: Degenerations and deformations of positive surface group representations

Title: Title: ALG Gravitational Instantons and Hitchin Moduli Spaces

Title: The co-tangent bundle to the moduli space of vector bundles and the GL_n character variety: a symplectomorphism