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The 35th Annual Workshop in Geometric Topology

Academics / Departments & Programs / Mathematics & Statistics / Events / Past Workshops / 2018 Workshop

Workshop Outcomes

Overview

The Workshop was held as scheduled on June 14-16, 2018 at Calvin College. The workshop began at 9:00 a.m. on Thursday, June 14, and ended at noon on Saturday, June 16. Each day there was a one-hour lecture by the principal speaker as well as contributed talks by participants. The featured speaker was Professor András Stipsicz of the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. He gave a series of three one-hour lectures on Invariants of Knots and Links. The program was designed so that there was ample time for informal networking among participants.

Abstracts of the Main Lectures

Lecture 1: Invariants of knots and links:
We planned to review definitions of the Alexander polynomial using Kauffman states and grid diagrams. These approaches then led to knot Floer homology; we sketched the definition of these groups.

Lecture 2: Knot Floer homology:
We defined knot Floer groups through grid diagrams, verified their main properties and applied these tools in solving some geometric problems, including the Milnor conjecture for torus knots.

Lecture 3: The Upsilon function of knots:
Applying the appropriate version of knot Floer homology and some ideas from homological algebra, a function-valued knot invariant can be derived. This function can be conveniently used in the study of the smooth concordance group. We showed some illustrative examples of such results.

Support and Funding

Financial support, provided by a grant from the National Science Foundation, was available to cover partial travel and living expenses of participants who do not have other funding for their research.

Organizers

Fredric Ancel, University of Wisconsin-Milwaukee
Greg Friedman, Texas Christian University
Craig Guilbault, University of Wisconsin-Milwaukee
Molly Moran, Colorado College
Eric Swenson, Brigham Young University
Frederick Tinsley, Colorado College
Nathan Sunukjian, Calvin University
Gerard Venema, Calvin University

Local Contacts

Contact Gerard Venema or Nathan Sunukjian if you have questions about the workshop or comments on this web site.

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