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Geometry-Topology Seminar

Friday, March 31, 2023 - 9:30am

Patrick Naylor and Dan Ketover

Princeton and Rutgers


University of Pennsylvania

DRL A5 morning / DRL A8 afternoon

This all-day Geometry-Topology Seminar is sponsored jointly with Temple, Bryn Mawr, Haverford and Swarthmore. The speakers will be Patrick Naylor from Princeton and Dan Ketover from Rutgers. They will give warmup talks in the morning directed at grad students, and regular research talks in the afternoon.


Here's the schedule, and after that, titles and abstracts. 


9:30 - 10:30     Patrick Naylor in DRL A5 

11 - 12             Dan Ketover in DRL A5 

12 - 2               Catered Lunch in DRL 4E17 

2 - 3                 Patrick Naylor in DRL A8 

3:30 - 4:30       Dan Ketover in DRL A8 

4:30 - 5:30       Wine reception in DRL 4E17 



Patrick Naylor 


Title: Doubles of Gluck twists 


Abstract: The Gluck twist of an embedded 2-sphere in the 4-sphere is a 4-manifold that is homeomorphic, but not obviously diffeomorphic to the 4-sphere. Despite considerable study, these homotopy spheres have resisted standardization except in special cases. In this talk, I will discuss some conditions that imply the double of a Gluck twist is standard, i.e., is diffeomorphic to the 4-sphere. This is based on joint work with Dave Gabai and Hannah Schwartz. 


In the morning, I’ll give a background talk to introduce some of the main ideas, along with some basic constructions of knotted 2-spheres. 



Dan Ketover 


Title: Stabilizations of Heegaard splittings and minimal surfaces

Abstract: In the 1930s, Reidemeister and Singer showed that any two Heegaard surfaces in a three-manifold become isotopic after adding sufficiently many trivial handles. I will show how this topological result gives rise to minimal surfaces of Morse index 2 in many ambient geometries.  In particular, applied to most lens spaces we obtain genus 2 minimal surfaces.  I’ll show using this that the number of distinct genus g minimal surfaces in the round sphere tends to infinity as g does (previously the lower bound for all large genera was two).