Claremont Topology Seminar

Founded 1989


The Claremont Topology Seminar meets on Thursday's from 12:00-1:30 pm in Roberts North 105 (RN 105), Claremont McKenna College. Lunch (12:00-12:30) will be provided for outside speakers--locals, please bring your lunch. Click here for a map of the Claremont McKenna Campus.

To reach Claremont McKenna College from the 10 freeway, exit at Indian Hill, go north, turn right (east) on 6th street and then turn left (north) on College Avenue. To reach Claremont McKenna College from the 210 freeway, if traveling East, exit at Towne Avenue, turn right (south) on Towne, turn left (east) on Foothill Blvd, and turn right (south) onto College Avenue. If traveling West on the 210 freeway, exit at Baseline/Padua, turn right (west) onto Baseline, turn left (south) onto Padua at the first light, turn right (west) onto Foothill Blvd at the third light, turn left (south) onto College Avenue.

Parking on College Avenue is free. Park near 8th street, then walk 1 block East on 8th street, continue East past Honnold Library on your left, and then past the Kravis Center (across the street from Honnold) to enter the CMC campus.

For more information about the Seminar, or to suggest speakers, contact Sam Nelson , Helen Wong, Vin de Silva, Jim Hoste , or Dave Bachman .


2018-19 Schedule


Fall, 2018

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Sept 4, 2018

12:00 pm

Organizational Meeting Meet at Hagelbarger's for organizational meeting.
Thursday

Sept 13, 2018

12:00 pm

Sam Nelson

Claremont McKenna College

Title: Virtual Tribrackets and Niebrzydowski Algebras

Abstract: Tribrackets are sets with ternary operations motivated by region colorings of Reidemeister moves. In this talk we will collect results from two recent projects, defining region coloring structures for oriented virtual knots and links and for Y-oriented trivalent spatial graphs and handlebody-links. This is joint work with undergrad students Shane Pico (Claremont McKenna College) and Paige Graves (University of La Verne) and PhD student Sherrilyn Tamagawa (University of California, Santa Barbara).

Thursday

Sept 20, 2018

12:00 pm

Dave Bachman

Pitzer College

Title: Visualizing lifts of the Figure eight knot fiber

Abstract: I will describe a sculpture recently made with Henry Segerman to visualize lifts of the spanning surface for the figure eight knot to its universal cover, the Poincare ball.

Thursday

Sept 27, 2018

12:00 pm

Stephen Bigelow

U.C. Santa Barbara

Title: The Temperley-Lieb algebra: words and pictures.

Abstract: The Temperley-Lieb algebra $TL_n(\delta)$ can be defined by generators and relations, or using a certain kind of pictures. I will describe my favorite proof that these two definitions give the same algebra, which perhaps deserves to be called "the fundamental theorem of Temperley-Lieb algebras". The two approaches to these algebras partly explain their wide range of applications in physics, representations theory, knot theory, and so on.

Thursday

Oct 4, 2018

12:00 pm

Jim Hoste

Pitzer College

Title: A partial order on knots.

Abstract: We may define a partial order on prime knots by declaring that J is greater than or equal to K if the fundamental group of the complement of J maps onto the fundamental group of the complement of K. When restricting to 2-bridge knots, one can determine if two knots are comparable or if they have an upper bound by comparing the continued fractions associated to each knot. We prove that if a 2-bridge knot J is strictly greater than m distinct nontrivial knots, then the crossing number of J is at least c(m), the smallest positive odd integer having at least m proper divisors. This answers a question of M. Suzuki. This is joint work with Joshua Ocana-Mercado, and Patrick D. Shanahan.

Thursday

Oct 11, 2018

12:00 pm

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Thursday

Oct 18, 2018

12:00 pm

Peter Samuelson

U.C. Riverside

Title: Algebras from Surfaces

Abstract: In the 80's, Goldman defined a Lie algebra associated to a surface using homotopy classes of loops, and he showed that it encoded his symplectic structure on the GL_n character varieties of the surface. Later, Turaev showed that this Lie algebra is "quantized" by the Homfly skein algebra of the surface. Morton and I gave an explicit description of the skein algebra of the torus, and showed that it is isomorphic to an algebra defined in terms of vector bundles over an elliptic curve over a finite field. My goal for the talk is to explain these statements "from scratch."

Thursday

Oct 25, 2018

12:00 pm

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Thursday

Nov 1, 2018

12:00 pm

Colleen Delaney

U.C. Santa Barbara

Title: Link invariants and anyon models

Abstract: When the spacetime trajectories of anyons in (2+1)D topological phases of matter trace out knots or links, the probability amplitudes of these physical processes is given by a knot or link invariant. These invariants can be computed from the algebraic theory of anyons, which is given by a unitary modular tensor category (UMTC). An interesting question is when a family of UMTCs can be distinguished by the invariants they produce for a finite set of knots and links. I will report on some recent progress in this direction based on joint work with Alan Tran, Parsa Bonderson, Cesar Galindo, Eric Rowell, and Zhenghan Wang.

Thursday

Nov 8, 2018

12:00 pm

Biji Wong

Centre interuniversitaire de recherches en géométrie et topologie, Montréal

Title: A Floer homology invariant for 3-orbifolds via bordered Floer theory

Abstract: Using bordered Floer theory, we construct an invariant for 3-orbifolds with singular set a knot that generalizes the hat flavor of Heegaard Floer homology. We show that for a large class of 3-orbifolds the orbifold invariant behaves like HF-hat in that the orbifold invariant, together with a relative Z_2-grading, categorifies the order of H_1^orb. When the 3-orbifold arises as Dehn surgery on an integer-framed knot in S^3, we use the {-1,0,1}-valued knot invariant epsilon to determine the relationship between the orbifold invariant and HF-hat of the 3-manifold underlying the 3-orbifold.

Thursday

Nov 15, 2018

12:00 pm

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Thursday

Nov 22, 2018

No Meeting Thanksgiving Break
Thursday

Nov 29, 2018

12:00 pm

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Thursday

Dec 6, 2018

12:00 pm

Paul Wedrich

Mathematical Sciences Institute

The Australian National University

Title: Knots and quivers, HOMFLY and DT

Abstract: I will describe a surprising connection between the colored HOMFLY-PT polynomials of knots and the motivic Donaldson-Thomas invariants of certain symmetric quivers, which was recently conjectured by Kucharski-Reineke-Stosic-Sulkowski. I will outline a proof of this correspondence for 2-bridge knots and then speculate about how much of the HOMFLY-PT skein theory might carry over to the realm of DT quiver invariants and what kind of geometric information about knots might be encoded in these quivers. This is joint work with Marko Stosic.

Thursday

Dec 13, 2018

12:00 pm

Jesse Levitt

USC

Title:

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Spring 2019 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract
Thursday

Jan 24, 2019

12:00 pm

Helen Wong

Claremont McKenna College

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Thursday

Jan 31, 2019

12:00 pm

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Thursday

Feb 7, 2019

12:00 pm

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Thursday

Fab 14, 2019

12:00 pm

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Thursday

Feb 21, 2019

12:00 pm

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Thursday

Feb 28, 2019

12:00 pm

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Thursday

Mar 7, 2019

12:00 pm

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Thursday

Mar 14, 2019

12:00 pm

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Thursday

Mar 21, 2019

No Meeting Spring Break
Thursday

Mar 28, 2019

12:00 pm

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Thursday

Apr 4, 2019

12:00 pm

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Thursday

Apr 11, 2019

12:00 pm

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Thursday

Apr 18, 2019

12:00 pm

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Thursday

Apr 25, 2019

12:00 pm

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Thursday

May 2, 2019

12:00 pm

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Thursday

May 9, 2019

12:00 pm

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Archived Schedules

2017-2018

2016-2017

2015-2016

2014-2015

2013-2014

2012-2013

2011-2012

2010-2011

2009-2010

2008-2009

2007-2008

2006-2007

2005-2006

2004-2005

2003-2004