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.

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.

4-ended Tangles, Heegaard Floer Homology, and Norm Detection

Series
Geometry Topology Seminar
Time
Monday, February 16, 2026 - 16:30 for 1 hour (actually 50 minutes)
Location
Boyd 322, University of Georgia
Speaker
Fraser Binns – Princeton

Link Floer homology is a powerful invariant of links due to Ozsváth and Szabó. One of its most striking properties is that it detects each link's Thurston norm, a result also due to Ozsváth and Szabó. In this talk I will discuss generalizations of this result to the context of 4-ended tangles, as well as some tangle detection results. This is joint work in progress with Subhankar Dey and Claudius Zibrowius.

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