Monday, February 17, 2020

[DMANET] TOMORROW: Online Combinatorics Colloquium--Lou Kauffman

Please join us for our next online Virtual Combinatorics Colloquium (VCC).


*Date:* Tuesday, February 18, 3:00 Eastern Standard Time *[Note the new
time!]*

*Speaker:* Louis H. Kauffman

*Title:* Trivalent Graphs, Perfect Matchings and Virtual Knot Theory

*Zoom Link:* Meeting ID: 463-430-866, https://wpi.zoom.us/j/463430866

*Abstract: * (This talk is joint work with Scott Baldridge and William
Rushworth.) We review knot invariants such as the bracket state sum model
for the Jones polynomial and its relation to the Tutte polynomial. We
recall trivalent graphs immersed in the plane and the well-known Penrose
evaluation formula for them. We generalize the Penrose formula to a Penrose
polynomial that is defined on trivalent graphs with perfect matchings (G,
M) where M is a perfect matching on the trivalent graph G. Remarkably,
these perfect matching polynomials are directly related to the Jones
polynomial of virtual knots and links via a mapping K from trivalent
perfect matchings to virtual link diagrams. The talk discusses how the
mapping K induces structural correspondences between graph theory and knot
theory. These include the above relationship between the Penrose matching
polynomial and the Jones polynomial and new relationships with Khovanov
homology and other knot invariants. Reformulations of coloring problems
arise in this context and are intertwined with virtual knot theory.


Individuals and viewing party groups from around the world can "attend"
these online talks and interact with the speaker and other attendees
remotely via Zoom. It is very easy--Just click on the link below to join.
If you have not used Zoom before, there may be a very brief download, but
then you will be in the event. Here are quick instructions for joining a
Zoom meeting if you would like more details:
https://support.zoom.us/hc/en-us/articles/201362193-How-Do-I-Join-A-Meeting-

The talk will start at the stated time, but the Zoom invitation will open
20 minutes earlier so that participants may call in early if they wish to
get a sense of how the platform works (how to mute/unmute, share screens,
shared whiteboard, raise hand, chat, etc.).


*Jo*

Jo Ellis-Monaghan

Chair, Department of Mathematics and Statistics (on sabbatical 2019-2020)

Editor-in-Chief, PRIMUS

Saint Michael's College

One Winooski Park

Colchester, VT 05439

office: Jeanmarie 279

website: http://academics.smcvt.edu/jellis-monaghan/

phone: 802 654 2660

fax: 802 654 2960

e-mail: je <jellis-monaghan@smcvt.edu>llismonaghan@gmail.com

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