Claremont Topology Seminar

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.


2016-17 Schedule


Fall, 2016

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Sept 6

3:00 pm

Organizational Meeting Meet at Some Crust Bakery for organizational meeting.
Tuesday

Sept 13

3:00 pm

Christopher Tuffley

Massey University Manawatu

Title: Intrinsic linking in higher dimensions, and with linking numbers divisible by q.

Abstract: In 1983 Conway and Gordon proved that every embedding of the complete graph K_6 in 3-space contains a pair of disjoint cycles that form a non-separable link --- a fact that is expressed by saying K_6 is intrinsically linked. Since then, a number of authors have shown that embeddings of larger complete graphs necessarily exhibit more complicated linking behaviour, such as links with many components and/or large pairwise linking numbers.

With some adaptions to the proofs, similar results can be established for embeddings of large n-complexes in (2n+1)-space. We will look at some of the adaptions required, in the context of proving the existence of two component links with linking number a nonzero multiple of a given integer q. In the course of this we will obtain an improved bound for n greater than or equal to 1 on the number of vertices needed to force a two component link with linking number at least q in absolute value.

Tuesday

Sept 20

3:00 pm

Catherine Pfaff

UC Santa Barbara

Title: When Outer Space behaves like a hyperbolic space & how we can use this to understand the group Out(F_n).

Abstract: A common strategy for studying a group is to study some object that it acts on and how it acts on this object. My favorite group is the outer automorphism group of the free group (or Out(F_n)). I will introduce this group and the object, Culler-Vogtmann Outer Space, that it acts on. I will also relate the study of this group acting on Culler-Vogtmann Outer Space to the study of the group SL(2,Z) acting on the hyperbolic plane.

Tuesday

Sept 27

3:00 pm

Dave Bachman

Pitzer College

Title: Heegaard Genus is NP-Hard

Abstract: In joint work with Ryan Derby-Talbot and Eric Sedgwick, we show that the problem of determining the Heegaard genus of a 3-manifold is NP hard.

Tuesday

Oct 4

3:00 pm

Jieon Kim

Osaka City University

Title : On biquandle cocycle invariants from marked graphs

Abstracts: A quandle is a set equipped with a binary operation satisfying certain axioms derived from the Reidemeister moves in knot theory. Quandle homology and cohomology theories have been studied extensively in recent years. L.H. Kauffman and D.E. Radford introduced a generalization of quandles, called biquandles and J.S. Carter, M. Elhamdadi and M. Saito defined a (co)homology theory and cocycle invariants for biquandles. J.S. Carter, S. Kamada and M. Saito defined shadow quandle colored diagrams and shadow quandle cocycle invariants of oriented links and surface-links. Surface-links are represented by broken surface diagrams and marked graph diagrams. In this talk, we'd like to introduce shadow biquandle colorings of oriented broken surface diagrams and those of oriented marked graph diagrams, and describe shadow biquandle cocycle invariants of oriented surface-links via broken surface diagrams and marked graph diagrams. This is a joint work with S. Kamada, A. Kawauchi, and S.Y. Lee.

Tuesday

Oct 11

3:00 pm

Brittany Fasy

Montana State University

Title: Persistent Local Homology in Road Network Analysis

Abstract: Topological data analysis (TDA) has rapidly grown in popularity in recent years. One of the emerging tools is persistent local homology, which can be used to extract local structure from a dataset. In this talk, we provide a definition of this new tool, along with a few applications. In particular, we investigate its use in road network analysis.

Tuesday

Oct 18

No Meeting Fall Break
Tuesday

Oct 25

3:00 pm

Amanda Curtis

UC Santa Barbara

Title: Projectors for SL(3)

Abstract: The Temperley-Lieb algebra is known for its usefulness in topological quantum computation and in certain knot invariants. In today's talk, I discuss my work with a similar algebra, the algebra of SL(3) spiders, and a particularly useful set of diagrams within it. As these diagrams have analogous diagrams in the Temperley-Lieb algebra, I offer a summary of the Temperley-Lieb algebra and springboard from there into my discussion of the projectors for the SL(3) spider.

Tuesday

Nov 1

3:00 pm

Jim Hoste

Pitzer College

Title: Diagramatic Moves on 3-diagrams

Abstract: The classical theory of knots and links is often approached via link diagrams and Reidemeister moves. The important result is that two diagrams represent the same link if and only if they are related by a sequence of Reidemeister moves.

Recently, several papers have explored the topic of link diagrams with multi-crossings. In these diagrams, n strands are allowed to cross at a single point in the plane, creating what is known as an n-crossing. Many of the obvious results analogous to classical diagrams have been proven. For example, given any n>1, every link has an n-diagram, that is, one with only n-crossings. However, until now, no analog of the Reidemeister moves have yet to be found for multicrossing diagrams. In this talk I will describe a set of 3-diagram moves and prove that they are sufficient to pass between any two 3-diagrams of the same knot.

This is joint work with Colin Adams and Martin Palmer.

Tuesday

Nov 8

3:00 pm

Sam Nelson

Claremont McKenna College

Title: Biquasiles and Dual Graph Diagrams

Abstract: Dual graph diagrams are an alternative way to present oriented knots and links with roots in statistical mechanics. Biquasiles are algebraic structures which can be used to color dual graph diagrams analogously to quandle colorings of standard knot diagrams. In this talk we will see examples of biquasiles including a finite biquasile whose counting invariant detects the mirror image of 9_32.

Tuesday

Nov 15

3:00 pm

Danielle O'Donnol

University of Indiana.

Title: Legendrian theta-graphs

Abstract: We will work in three-space with the standard contact structure. An embedded graph is Legendrian if it is everywhere tangent to the contact structure. I will give an overview of the invariants used in this area. Then I will talk about our recent work on classification of planar Legendrian theta-graphs. This is joint with Peter Lambert-Cole (Indiana).

Tuesday

Nov 22

3:00 pm

Jose Ceniceros

Louisiana State Univ.

Title: Legendrian/Transverse Knots and Knot Floer Homology

Abstract: We will give an overview of knot theory supported in a contact 3-manifold with a focus on invariants of Legendrian and transverse knots that take values in knot Floer homology. We will also extend the definition of the BRAID invariant defined by Baldwin, Vela-Vick, Vertesi and define a new invariant that also takes values in knot Floer homology.

Tuesday

Nov 29

3:00 pm

Kanako Oshiro

Sophia University

Title: Up-down colorings of virtual-link diagrams and RII-detectors

Abstract: In this talk, we introduce an up-down coloring of a virtual-link diagram. For two 2-component virtual-link diagrams D and D', their up-down colorabilities give a lower bound of the minimum number of RII-moves which are needed to transform D to D'. By using the notion of a quandle cocycle invariant, we determine the necessity of RII-moves for a pair of diagrams of the trivial virtual-knot. This implies that for any virtual-knot diagram D, there exists a diagram D' representing the same virtual-knot such that any sequence of generalized Reidemeister moves between D and D' includes at least one RII-move. This is a joint work with Ayaka Shimizu and Yoshiro Yaguchi.

Tuesday

Dec 6

3:00 pm

Burak Ozbagci

Koc University

Title: Symplectic fillings of contact 3-manifolds

Abstract: In the first half of my talk, I will introduce various types of symplectic fillings of three dimensional contact manifolds, and give a brief overview of the results in the literature. In the second half of the talk, I will concentrate on fillings of the unit cotangent bundles of closed surfaces equipped with their canonical contact structures. In particular, I will explain my recent joint work with Youlin Li where the surfaces at hand are non-orientable.


Spring 2017 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Jan 24

3:00 pm

Tuesday

Jan 31

3:00 pm

Tuesday

Feb 7

3:00 pm

Tuesday

Feb 14

3:00 pm

Tuesday

Feb 21

3:00 pm

Tuesday

Feb 28

3:00 pm

Tuesday

Mar 7

3:00 pm

Tuesday

Mar 14

No Meeting Spring Break
Tuesday

Mar 21

3:00 pm

Tuesday

Mar 28

3:00 pm

Tuesday

Apr 4

3:00 pm

Tuesday

Apr 11

3:00 pm

Tuesday

Apr 18

3:00 pm

Tuesday

Apr 25

3:00 pm

Tuesday

May 2

3:00 pm



Archived Schedules

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