# 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 .

# 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 WongCentre 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 WedrichMathematical 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 Helen Wong Claremont McKenna College Title: Abstract: Thursday Jan 31, 2019 12:00 pm 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 CottUniversity 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:

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