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Personal Profile of Eli Grigsby

Eli Grigsby
Home Page: https://www2.bc.edu/~grigsbyj/

• Talks

1. March 15, 2010 - March 19, 2010

   Workshop Research Workshop: Homology Theories of Knots and Links

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   Mar 19, 2010 Friday	11:00 AM - 12:00 PM   On sutured Khovanov homology and sutured Floer homology Eli Grigsby Location MSRI: Simons Auditorium Video Abstract -- Supplements -- Show Detail

2. March 05, 2010

   Seminar On Knot Homology Theories

3. January 25, 2010 - January 29, 2010

   Workshop Introductory Workshop: Homology Theories of Knots and Links

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   Jan 29, 2010 Friday	01:30 PM - 02:30 PM   A connection between Khovanov homology and Heegaard Floer homology Eli Grigsby Location MSRI: Simons Auditorium Video Abstract -- Supplements 13978.pdf 3.48 MB application/pdf Show Detail

4. January 21, 2010 - January 22, 2010

   Workshop Connections for Women: Homology Theories of Knots and Links

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   Jan 21, 2010 Thursday	09:00 AM - 10:30 AM   Introduction to knot homology theories and categorification Eli Grigsby Location MSRI: Simons Auditorium Video Abstract -- Supplements 13950.pdf 1.75 MB application/pdf Show Detail

5. October 08, 2008 - October 09, 2008

   Workshop Math Institutes Modern Mathematics Workshop

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   Oct 08, 2008 Wednesday

   03:00 PM - 04:00 PM   Knot homologies and applications to low-dimensional topology Eli Grigsby Location -- Video -- Abstract Roughly speaking, low dimensional topology is the study of 3-dimensional manifolds and the 4-dimensional cobordisms between them. Low dimensional topologists also like to study knots, i.e., smoothly imbedded circles in 3-manifolds (up to ambient isotopy), because of a classical theorem of Lickorish-Wallace: Every closed, connected, oriented (c.c.o.) 3-manifold can be obtained from the three-sphere (the simplest c.c.o. 3-maniofld) by doing surgery on a finite collection of knots. A corollary of the Lickorish-Wallace theorem is that any c.c.o. manifold is the boundary of some 4-manifold. Yet knots are remarkably tricky to study directly; it is difficult to tell, just by staring at pictures of two knots, whether they are the same or different. We confront this problem through the use of knot invariants, algebraic objects associated to knots that do not depend upon how the knots are drawn. I will discuss a couple of these: Khovanov homology and knot Floer homology, both inspired by ideas in physics. In the less than ten years since their introduction, they have generated a flurry of activity and a stunning array of applications. There are also intriguing connections between the two theories that have yet to be fully understood. Supplements -- Show Detail