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
Title:
Abstract:

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
Title:
Abstract:

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
Title:
Abstract:

Thursday
Nov 22, 2018
No Meeting Thanksgiving Break

Thursday
Nov 29, 2018

12:00 pm
Title:
Abstract:

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:
Abstract:

Spring 2019 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract

Thursday
Jan 24, 2019

12:00 pm
Title:
Abstract:

Thursday
Jan 31, 2019

12:00 pm
Helen Wong
Claremont McKenna College
Title:
Abstract:

Thursday
Feb 7, 2019

12:00 pm
Title:
Abstract:

Thursday
Fab 14, 2019

12:00 pm
Title:
Abstract:

Thursday
Feb 21, 2019

12:00 pm
Cornelia A. Van Cott
University of San Francisco
Title:
Abstract:

Thursday
Feb 28, 2019

12:00 pm
Title:
Abstract:

Thursday
Mar 7, 2019

12:00 pm
Title:
Abstract:

Thursday
Mar 14, 2019

12:00 pm
Title:
Abstract:

Thursday
Mar 21, 2019
No Meeting Spring Break

Thursday
Mar 28, 2019

12:00 pm
Title:
Abstract:

Thursday
Apr 4, 2019

12:00 pm
Title:
Abstract:

Thursday
Apr 11, 2019

12:00 pm
Title:
Abstract:

Thursday
Apr 18, 2019

12:00 pm
Title:
Abstract:

Thursday
Apr 25, 2019

12:00 pm
Title:
Abstract:

Thursday
May 2, 2019

12:00 pm
Title:
Abstract:

Thursday
May 9, 2019

12:00 pm
Title:
Abstract:

Archived Schedules

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		Title: Abstract:
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		Title: Abstract:
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		Title: Abstract:
Thursday Nov 22, 2018	No Meeting	Thanksgiving Break
Thursday Nov 29, 2018 12:00 pm		Title: Abstract:
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: Abstract: