Claremont Topology Seminar


The Claremont Topology Seminar meets on Tuesday's from 3:00-4:00 pm in Mudd Science Library 125, Pomona College. Mudd Science Library is located on the NE corner of College Avenue and 6th Street (just north of the construction site). 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.


2014-15 Schedule


Fall, 2014

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Sept 9

3:00 pm

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

Sept 16

3:00 pm

Sam Nelson

Claremont McKenna College

Title: Finite type enhancements of biquandle counting invariants

Abstract: Finite type invariants, also known as Vasiliev invariants, are integer-valued knot invariants satisfying a certain skein relation. Many of the coefficients of the Jones and Alexander polynomials, for example, are known to be Vassiliev invariants, and the set of all Vassiliev invariants dtermines a powerful invariant known as the Kontsevich integral. We adapt a scheme for computing finite type invariants due to Goussarov, Polyak and Viro to enhance the biquandle counting invariant. The simplest nontrivial case has connections to the concept of parity in virtual knot theory. This is joint work with Pomona student Selma Paketci.

Tuesday

Sept 23

3:00 pm

Tuesday

Sept 30

3:00 pm

Matt Rathbun

CSU Fullerton

Title: Monodromy action on unknotting tunnels in fiber surfaces and applications for DNA

Abstract: DNA encodes the instructions used in the development and functioning of all living organisms. The DNA molecule, however, often becomes knotted, linked, and generally entangled during normal biological processes like replication and recombination. The subject of Knot Theory, correspondingly, can inform our understanding of these processes. I will introduce Knot Theory, and some of the myriad of tools that mathematicians use to understand knots and links. In particular, I will focus on a special class of link called fibered links. I will explain some recent results, joint with Dorothy Buck, Kai Ishihara, and Koya Shimokawa, about transformations from one fibered link to another, and explain how these results are relevant to microbiology.

Tuesday

Oct 7

3:00 pm

Arielle Leitner

UCSB

Title: Geometric Transitions of the Cartan Subgroup in SL(n,R)

Abstract: A geometric transition is a continuous path of geometries which abruptly changes type in the limit. We explore geometric transitions of the Cartan subgroup in SL(n,R))$. For n=3, it turns out the Cartan subgroup has precisely 5 limits, and for n=4, there are 15 limits, which give rise to generalized cusps on convex projective 3-manifolds. When n>6, there is a continuum of non conjugate limits of the Cartan subgroup, distinguished by projective invariants. To prove these results, we use some new techniques of working over the hyperreal numbers.

Tuesday

Oct 14

3:00 pm

Leyda Almodovar

University of Iowa

Title: Clustering and topological analysis of brain structuresp> Abstract: Topological data analysis is a relatively new area that uses several disciplines in conjunction such as topology, statistics and computational geometry. The idea behind topological data analysis is to describe the “shape” of data by recovering the topology of the sampled space. Also, it is useful to find topological attributes that persist in the data, helping us gain a better understanding of how different properties of the data interact. Data was collected from MRI experiments with 96 subjects between the ages of 0 and 18, some of them predisposed to Huntington’s disease. Data analysis is performed via different topological approaches including clustering and persistent homology with the goal of identifying whole networks of points in the brain. The main purpose of this work is to compare the structure of brain networks of healthy subjects versus subjects predisposed to Huntington’s disease.
Tuesday

Oct 21

3:00 pm

No Meeting Fall Break
Tuesday

Oct 28

3:00 pm

Tuesday

Nov 4

3:00 pm

Cornelia Van Cott

University of San Francisco

Title: Surfaces and iterated Bing doubles

Abstract: We consider the classical problem of finding minimal genus Seifert surfaces for knots and links. In particular, we will consider the problem in the case of iterated Bing doubles, and we will describe a construction of minimal genus surfaces for these links. Next, we will broaden our perspective and consider the problem of finding minimal genus surfaces for iterated Bing doubles in the four-ball.

Tuesday

Nov 11

3:00 pm

Tuesday

Nov 18

3:00 pm

Faramarz Vafaee

Cal Tech

Title: Heegaard Floer homology and L-space knots

Abstract: Heegaard Floer theory consists of a set of invariants of three- and four-dimensional manifolds. Three-manifolds with the simplest Heegaard Floer invariants are called L-spaces and the name stems from the fact that lens spaces are L-spaces. The primary focus of this talk will be on the question of which knots in the three-sphere admit L-space surgeries. We will also discuss about possible characterizations of L-spaces that do not reference Heegaard Floer homology.

Tuesday

Nov 25

3:00 pm

Subhojoy Gupta

Cal Tech

Title: Riemann surfaces, projective structures and grafting

Abstract: A complex projective surface is obtained by gluing pieces of the Riemann sphere using Mbius maps. In this talk I'll introduce these, and discuss ways of deforming such a geometric structure by the cut-and-paste operation of "grafting". Recent joint work with Shinpei Baba shows that complex projective surfaces with any fixed holonomy are dense in the moduli space of Riemann surfaces. I shall talk of some ingredients of the proof, including Thurston's notion of "train-tracks on surfaces". This talk will be aimed towards a general audience.

Tuesday

Dec 2

3:00 pm

Tuesday

Dec 9

3:00 pm

Maria Trnkova

Cal Tech


Spring 2015 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Jan 27

Tuesday

Feb 3

Tuesday

Feb 10

Tuesday

Feb 17

Tuesday

Feb 24

Tuesday

Mar 3

Tuesday

Mar 10

Tuesday

Mar 17

3:00 pm

No Meeting Spring Break
Tuesday

Mar 24

Tuesday

Mar 31

Tuesday

Apr 7

Tuesday

Apr 14

Tuesday

Apr 21

Tuesday

Apr 28

Tuesday

May 5



Archived Schedules

2013-2014

2012-2013

2011-2012

2010-2011

2009-2010

2008-2009

2007-2008

2006-2007

2005-2006

2004-2005

2003-2004