### Winter 2019

Thursday Jan 10, 2:10-3:00, Skye Building 277

Nur Saglam (UCR) 🔗

Title: Constructions of Lefschetz fibrations using cyclic group actions.

Abstract: We construct families of Lefschetz fibrations over S2 using finite order cyclic group actions on product manifolds Σgg for g > 0. We also obtain more families of Lefschetz fibrations by applying rational blow-down operation to these Lefschetz fibrations. This is joint work with Anar Akhmedov.

Thursday Jan 17, 2:10-3:00, Skye Building 277

Dmitri Gekhtman (Caltech) 🔗

Title: Holomorphic retracts of Teichmüller space.

Abstract: The Teichmüller space of a closed surface carries a natural complex structure, whose analytic properties reflect the topology and geometry of the surface. In this talk, we discuss the problem of classifying the holomorphic retracts of Teichmüller space. Our approach hinges on the analysis of two dynamical flows - one in the moduli space of half-translation surfaces, and the other in the space of bounded holomorphic functions on the polydisk.

Thursday Jan 24, 2:10-3:00, Skye Building 277

Stefano Vidussi (UCR)

Title: Some Smooth Surfaces with Several Symplectic Structures.

Abstract: Not sure. But the title alliterates beautifully.

Thursday Jan 31, 2:10-3:00, Skye Building 277

Matt Gibson (UCI)

Title: Symplectic Structures on an Open 4-Manifold with Non-Isomorphic Primitive Cohomology.

Abstract: In this talk we investigate applications of the primitive cohomology on a symplectic manifold, studied by Tseng, Tsai, and Yau. We begin by introducing the necessary background to study these groups and then turn to a famous example of a link complement worked on by McMullen, Taubes, and Vidussi. From this complement, one can construct a symplectic 4-fold fibering over the torus. We show that the dimension of the corresponding primitive cohomology groups can distinguish different fibration structures on this 4-fold, depending on the choice of symplectic form. Time permitting, we briefly introduce the $A_\infty$-structure on the underlying co-chain complex of the primitive cohomology groups and its possible role in the examples discussed. This talk is based on joint work with Li-Sheng Tseng and Stefano Vidussi.

Thursday Feb 7, 2:10-3:00, Skye Building 277

Lei Chen (Caltech) 🔗

Title: Methods in 2d dynamics and Nielsen realization problem.

Abstract: In this talk, I will discuss several methods in 2-dimensional dynamics including shadowing lemma, Ahlfors trick (describing rigidity of finite order homeomorphisms), Carathéodory's prime end theory, Thurston's stability theorem and Nielsen-Thurston classification theory etc. I will focus on discussing how to use dynamical method to solve different versions of the Nielsen realization problem about realizing subgroups of mapping class groups as a subgroup of homeomorphism groups.

Thursday Feb 14, 2:10-3:00, Skye Building 277

Jonathan Alcaraz (UCR)

Title: An Introduction to Surfaces, Fiber Bundles, and Other Words.

Abstract: A first-year graduate student sitting in on a research-level topology seminar will inevitably hear a lot of words they don't understand. If such a graduate student is taking a first-year course in topology, however, some of those words are very approachable. In this talk, I intend to develop intuition for some of this vocabulary using definitions, discussion, examples and exercises.

Thursday Feb 21, 2:10-3:00, Skye Building 277

Jonathan Alcaraz (UCR)

Title: The Mapping Class Groups of Some Surfaces

Abstract: In this talk I will define and compute some fun mapping class groups as done in Chapter 2 of "A Primer on Mapping Class Groups" by Benson Farb and Dan Margalit.

Thursday Feb 28, 2:10-3:00, Skye Building 277

Ben Russell (UCR)

Title: Foliations and the Godbillon-Vey Class

Abstract: A foliation is a decomposition of a manifold into injectively immersed submanifolds in a way that is locally modeled on the decomposition of R^n by (n-q)-planes. As such foliations reside in the intersection of geometric topology and dynamical systems. In this talk we introduce the basic definitions and machinery of foliations with an eye towards constructing the so-called Godbillon-Vey class of transversely orientable foliation of codimension 1, which Thurston described as measuring the "helical wobble" of the foliation.

Thursday Mar 7, 2:10-3:00, Skye Building 277

Wee Liang Gan (UCR)

Title: TBA

Abstract: TBA

Thursday Mar 14, 2:10-3:00, Skye Building 277

TBA

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### Spring 2019

Thursday Apr 4, 2:10-3:00, Skye Building 277

Francis Bonahon (USC) 🔗

Title: TBA

Abstract: TBA

Thursday April 11, 2:10-3:00, Skye Building 277

Alvaro Pelayo (UCSD) 🔗

Title: TBA

Abstract: TBA

Thursday April 18, 2:10-3:00, Skye Building 277

Marco Marengon (UCLA) 🔗

Title: TBA

Abstract: TBA

Thursday April 25, 2:10-3:00, Skye Building 277

TBA

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Thursday May 2, 2:10-3:00, Skye Building 277

TBA

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Thursday May 9, 2:10-3:00, Skye Building 277

TBA

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Thursday May 16, 2:10-3:00, Skye Building 277

TBA

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Abstract: TBA

Thursday May 23, 2:10-3:00, Skye Building 277

TBA

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Thursday May 30, 2:10-3:00, Skye Building 277

Caglar Uyanik (Yale) 🔗

Title: TBA

Abstract: TBA

Thursday June 6, 2:10-3:00, Skye Building 277

TBA

Title: TBA

Abstract: TBA