Seminars and Colloquia by Series

TBD

Series
Geometry Topology Seminar
Time
Monday, April 21, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Diana HubbardBrooklyn College, CUNY

TBD

Two-component L-space links, satellite and the tau-invariant

Series
Geometry Topology Seminar
Time
Monday, April 7, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daren ChenCalTech

A result by Ozsvath and Szabo states that the knot Floer complex of an L-space knot is a staircase. In this talk, we will discuss a similar result for two-component L-space links: the link Floer complex of such links can be thought of as an array of staircases. We will describe an algorithm to extract this array directly from the H-function of the link. As an application, we will discuss how to use this and the link surgery formula to compute the knot Floer complex and the tau-invariant of a certain class of satellite knots. This is joint work with Ian Zemke and Hugo Zhou.

TBD

Series
Geometry Topology Seminar
Time
Monday, March 31, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ryan DickmannVanderbilt

TBD

Vanishing cycles and almost toric fibrations by Jie Min

Series
Geometry Topology Seminar
Time
Monday, March 10, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jie MinUniversity of Massachusetts Amherst

Vanishing cycles of Lefschetz fibrations give examples of Lagrangian spheres in the fiber. A natural question, first raised by Donaldson, is whether all Lagrangian spheres arise this way. We focus on this problem for positive rational surfaces, which were shown to admit a geometric structure called almost toric fibrations. I will talk about a work-in-progress showing all Lagrangian spheres here are visible in an almost toric fibration and thus are vanishing cycles of a nodal degeneration.

2-torsion in instanton Floer homology

Series
Geometry Topology Seminar
Time
Monday, March 3, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhenkun LiUniversity of South Florida

Instanton Floer homology, introduced by Floer in the 1980s, has become a power tool in the study of 3-dimensional topology. Its application has led to significant achievements, such as the proof of the Property P conjecture. While instanton Floer homology with complex coefficients is widely studied and conjectured to be isomorphic to the hat version of Heegaard Floer homology, its counterpart with integral coefficients is less understood. In this talk, we will explore the abundance of 2-torsion in instanton Floer homology with integral coefficients and demonstrate how this 2-torsion encodes intriguing topological information about relevant 3-manifolds and knots. This is a joint work with Fan Ye.

 

Anosov representations of cubulated hyperbolic groups

Series
Geometry Topology Seminar
Time
Wednesday, February 26, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Theodore WeismanUniversity of Michigan

Please Note: Note the unusual date of a research seminar on Wednesday

An Anosov representation of a hyperbolic group $\Gamma$ is a representation which quasi-isometrically embeds $\Gamma$ into a semisimple Lie group - say, SL(d, R) - in a way which imitates and generalizes the behavior of a convex cocompact group acting on a hyperbolic metric space. It is unknown whether every linear hyperbolic group admits an Anosov representation. In this talk, I will discuss joint work with Sami Douba, Balthazar Flechelles, and Feng Zhu, which shows that every hyperbolic group that acts geometrically on a CAT(0) cube complex admits a 1-Anosov representation into SL(d, R) for some d. Mainly, the proof exploits the relationship between the combinatorial/CAT(0) geometry of right-angled Coxeter groups and the projective geometry of a convex domain in real projective space on which a Coxeter group acts by reflections.

Poincaré Algorithm for Non-compact Lie Groups

Series
Geometry Topology Seminar
Time
Monday, February 24, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yukun DuUniversity of Georgia

In this talk, I will present a geometric algorithm for determining whether a given set of elements in SO+(n,1) generates a discrete subgroup, as well as identifying the relators for the corresponding group presentation. The algorithm constructs certain hyperbolic manifolds that are always complete, a key condition for applying Poincaré Fundamental Polyhedron Theorem and ensuring the algorithm is valid. I will also introduce a generalization of this algorithm to the Lie group SL(n, R) and explore how the completeness condition extends to this broader setting.
 

Branched covers and SU(2)-representations

Series
Geometry Topology Seminar
Time
Monday, February 10, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Juanita Pinzon-CaicedoNotre Dame

The fundamental group is one of the most powerful invariants to distinguish closed three-manifolds, and the existence of non-trivial homomorphisms $\pi_1(M)\to SU(2)$ is a great way of measuring the non-triviality of a three-manifold $M$. It is known that if an integer homology 3-sphere is either Seifert fibered or toroidal, then irreducible representations do exist. In contrast, the existence of SU(2)-representations for hyperbolic homology spheres has not been completely established. With this as motivation, I will talk about partial progress made in the case of hyperbolic homology spheres realized as branched covers. This is joint work with Sudipta Ghosh and Zhenkun Li.

Pages