# Founded 1989

The Claremont Topology Seminar meets on Tuesday's from 3:00-4:00 pm in Millikan 2099, Pomona College. Millikan is located on the NE corner of College Avenue and 6th Street. Following the talk we go for coffee/tea in downtown Claremont. Sometimes we meet a little later and then go to dinner. (Look for special times on the calendar.) Click here for a map of the Pomona Campus.

To reach Pomona College from the 10 freeway, exit at Indian Hill, go north, turn right (east) on 6th street and then turn left (north) on College. To reach Pomona 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.

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

# Fall, 2015

special days, times or locations are in red

 Date Speaker Title and Abstract Tuesday Sept 8 3:00 pm Organizational Meeting Meet at Some Crust Bakery for organizational meeting. Tuesday Sept 15 3:00 pm Jim Hoste Pitzer College Title: Involutory quandles of Montesinos Links I will show how to compute the involutory quandle of the (1/2, 1/2, p/q;e)-Montesinos links and discuss some of he properties of these quandles. This is part of a larger project to classify all links with finite n-quandles. This is joint work with Patrick Shanahan. Tuesday Sept 22 3:00 pm Sam Nelson Claremnt McKenna College Title: Biquandle brackets Abstract: Given a finite biquandle X and a commutative ring with identity R, we define an algebraic structure known as a biquandle bracket. Biquandle brackets can be used to define a family of knot and link invariants known as quantum enhancements which include biquandle cocycle invariants and skein polynomials such as the Alexander, Jones and HOMFLYpt polynomials as special cases. As an application we will see a new skein invariant which is not determined by the knot group, the knot quandle or the HOMFLYpt polynomial. Tuesday Sept 29 3:00 pm Satyan Devadoss Williams College Title: Origami Folding and Evolutionary Trees Abstract: In the past 25 years, origami has seen a tremendous explosion, in the arts, the sciences, and in technology. The mathematical theory of origami, in many ways, is at its infancy. There is a simple relationship between origami folds and geometric trees, obtained simply by looking at the crease lines of a piece of folded polygonal paper. In genetics, such trees play an important role in capturing the evolutionary process of species. We try to show a natural map between these worlds, of spaces of polygons and spaces of metric trees, and ask some foundational questions about this map. The heavy lifting of our work is done by an analogous version of a beautiful rigidity result of Cauchy from 1813. Tuesday Oct 6 3:00 pm Caitlin Leverson Duke University Title: Legendrian knots and links Abstract: qGiven a plane field $dz-xdy$ in $\mathbb{R}^3$. A Legendrian knot is a knot which at every point is tangent to the plane at that point. One can similarly define a Legendrian knot in any contact 3-manifold (manifold with a plane field satisfying some conditions). In this talk, we will explore Legendrian knots in $\mathbb{R}^3$, $J^1(S^1)$, and $\#^k(S^1\times S^2)$ as well a few Legendrian knot invariants. We will also look at the relationships between a few of these knot invariants. No knowledge of Legendrian knots will be assumed though some knowledge of basic knot theory would be useful. Tuesday Oct 13 3:00 pm Jeremy Toulisse University of Southern California Title: Anti-de Sitter geometry and Teichmüller theory. Abstract: In the nineties, G. Mess discovered deep connections between anti-de Sitter (AdS) geometry and the theory of hyperbolic surfaces. In particular, there exists an equivalence between maximal surface in AdS space-time and minimal Lagrangian map between hyperbolic surfaces. In this talk, we will explain this equivalence and extend it to manifolds with cone singularities. Tuesday Oct 20 3:00 pm No Meeting Fall Break Tuesday Oct 27 3:00 pm Kenji Kozai UC Berkeley Title: Regenerating hyperbolic structures from Sol Abstract: Suppose f is a pseudo-Anosov homeomorphism of a surface S, and that M is the mapping torus of f. Thurston's double-limit theorem implies that M admits a hyperbolic structure. However, M also admits a more natural singular Sol structure coming from the invariant measured foliations on S induced by f. When S is a punctured torus, Heusener-Porti-Suarez showed that the Sol structure can be deformed to nearby hyperbolic cone structures on M. By considering these geometries as special cases of projective structures, the result extends to mapping tori of surfaces of higher genus, provided that the pseudo-Anosov map f satisfies some additional properties. Tuesday Nov 3 12:15-1:10 pm Alissa Crans Loyola Marymount College Title: Hom Quandles Abstract: Analogous to the case for groups, the collection of quandle homomorphisms, Hom(Q, X), has no natural quandle structure. However, if X is an abelian quandle, then the hom set does become a quandle with the obvious pointwise operation. We will consider examples and investigate properties of this hom quandle. Tuesday Nov 10 3:00 pm Faramarz Vafaee California Institute of Technology Title: A slicing obstruction from the 10/8 theorem Abstract: A knot K in S^3 is smoothly slice if it bounds a disk that is smoothly embedded in the four-ball. From Furuta's 10/8 theorem, we derive a smooth slicing obstruction for knots in S^3 using a spin 4-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots (i.e. a knot in S^3 which bounds a locally flat disk in D^4) which are not smoothly slice. This work is joint with Andrew Donald. Tuesday Nov 17 3:00 pm Diana Hubbard Boston College Title: The hunt for effective transverse invariants Abstract: A central aim of modern contact geometry is to find effective invariants of transverse knots, that is, invariants that give more information than classical invariants. In this talk I will describe the background of this problem, explain why a fruitful way to understand transverse knots is via braids, and outline some progress towards defining an effective invariant in the setting of Khovanov homology. This work is joint with Adam Saltz. Tuesday Nov 24 3:00 pm Kyle ChapmanUCSB Title: Ergodicity in the space of polygonal Knots Abstract: Equilateral polygonal knots are often used as a model for molecules and polymers. Additionally, one can use information about equilateral polygonal knots to gather insight into the space of smooth tame knots. Because of these facts, it is often useful to be able to randomly sample the space of equilateral polygonal knots. This has posed a problem, as until recently, the primary methods of random generation have been used without knowing some basic facts about the validity of the method. We will discuss what it means for a random generation method to be ergodic, and what methods have actually been shown to be so. Tuesday Dec 1 3:00 pm Julie Bergner UC Riverside Tuesday Dec 8 3:00 pm Andy Manion UCLA

# Spring 2016 Schedule

special days, times or locations are in red

 Date Speaker Title and Abstract Tuesday Jan 26 Tuesday Feb 2 Tengren Zhang California Institute of Technology Tuesday Feb 9 Mimi TsurugaUC Davis Tuesday Feb 16 Tuesday Feb 23 Tuesday Mar 1 Tuesday Mar 8 Tuesday Mar 15 3:00 pm No Meeting Spring Break Tuesday Mar 22 Tuesday Mar 29 George MossessianUC Davis Tuesday Apr 5 Tuesday Apr 12 Tuesday Apr 19 Tuesday Apr 26 Tuesday May 3

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