Seminars and Colloquia by Series

Real bordered Floer homology

Series
Geometry Topology Seminar
Time
Monday, April 13, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert Lipshitz – University of Oregon –

Real Heegaard Floer homology is a new invariant of branched double covers, introduced by Gary Guth and Ciprian Manolescu, and inspired by work of Jiakai Li and others in Seiberg-Witten theory. After sketching their construction, we will describe an extension of the "hat" variant to 3-manifolds with boundary, and the algorithm this gives to compute it when the fixed set is connected. We will end with some open questions.

Washington University of St. Louis

Series
Geometry Topology Seminar
Time
Monday, March 16, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki Mi – UGA

One of the fundamental problems in contact topology is to classify contact structures on a given 3-manifold. In particular, classifying contact structures on surgeries along a given knot has been very poorly studied. The only fully understood case so far is that of the unknot 
(lens spaces); for all other knots we have only partial results, or none at all. Several topological and algebraic tools have been developed to 
attack this problem. In this talk, we discuss recent developments and the strategy for classifying tight contact structures on surgeries along torus knots. This is joint work with John Etnyre, Bülent Tosun, and Konstantinos Varvarezos.

Geometrizing Surface Group Representations

Series
Geometry Topology Seminar
Time
Monday, March 9, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Parker Evans – Washington University of St. Louis

Abstract: The Teichmuller space T(S) of a closed surface S is a moduli space where each point represents a hyperbolic metric on the surface S. Interpreted appropriately, each of these hyperbolic metrics is encoded by a representation of the fundamental group of S to PSL(2,R), the group of isometries of the hyperbolic plane. This talk concerns a similar story with the Lie group PSL(2,R) replaced by the exceptional split real Lie group G2’ of type G2. That is, we shall “geometrize” surface group representations to G2’ as holonomies of some (explicitly constructed) locally homogenous (G,X)-manifolds. Along the way, we encounter pseudoholomorphic curves in a non-compact pseudosphere that carry a (T,N,B)-framing analogous to that of space curves in Euclidean 3-space. These curves play a key role in the construction. Time permitting, we discuss how this specific G_2’ recipe relates to a broader construction that unifies other approaches to geometrize representations in rank two. This talk concerns joint work with Colin Davalo.

Construction of Exotic 4-Manifolds Using Finite Order Cyclic Group Actions

Series
Geometry Topology Seminar
Time
Monday, March 2, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nur Saglam – University of Georgia –

In this talk, we will discuss the construction of exotic 4-manifolds using Lefschetz fibrations over S^2, which are obtained by finite order cyclic group actions on Σg. We will first apply various cyclic group actions on Σg for g>0, and then extend it diagonally to the product manifolds ΣgxΣg. These will give singular manifolds with cyclic quotient singularities. Then, by resolving the singularities, we will obtain families of Lefschetz fibrations over S^2. Following the resolution process, we will determine the configurations of the singular fibers and the monodromy of the total space. In some cases, deformations of the Lefschetz fibrations give rise to nice applications using the rational blow-down operation, which provides exotic examples. This is a joint work with A. Akhmedov and M. Bhupal.

Distinguishing Exotic R^4's With Heegaard Floer Homology

Series
Geometry Topology Seminar
Time
Monday, February 23, 2026 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Sean Eli – Georgia Tech

This is joint work with Jen Hom and Tye Lidman. Attaching a Casson handle to a slice disk complement gives a smooth manifold homeomorphic to R^4. In the 90's De Michelis and Freedman asked how these choices affect the smooth type of the resulting manifold. This problem has seen some progress since then but is still not well understood. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic R^4's made with the simplest Casson handle are distinct. This gives a countably infinite family of exotic R^4's made with different slice disk complements. We then produce exotic R^4's with various phenomena, and re-prove a theorem of Bizaca-Etnyre on smoothings of product manifolds Y x R. Our main tool is Gadgil's end Floer homology, which we show how to compute effectively by analyzing a certain cobordism map. Time permitting, I'll discuss an upcoming result on exotic planes in R^4 and branched covers, and plans to study more noncompact exotic phenomena.

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