Claremont Topology Seminar


The Claremont Topology Seminar meets on Tuesday's from 3:00-4:00 pm in Mudd 125, Pomona College. Mudd is located just north of 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.


2013-14 Schedule


Fall, 2013

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Sept 10

3:00 pm

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

Sept 17

3:00 pm

Tuesday

Sept 24

3:00 pm

Tuesday

Oct 1

3:00 pm

Tuesday

Oct 8

3:00 pm

Tuesday

Oct 15

4:15 in Mudd 125

Renata Gerecke Title: Factor Groups of Knot and LOT Groups

Abstract: It is difficult to determine whether, given a finite, balanced group presentation, the group is finite or infinite. We study this problem in the context of knot groups and label orientated tree (LOT) groups. More specifically, we are looking at factor groups of knot and LOT groups by powers of meridians. This is in the spirit of Coxeter's work on the factor groups of braid groups. Indeed, our findings generalize Coxeter's work from the three-strand braid groups to knot groups.

Tuesday

Oct 22

3:00 pm

No Meeting Fall Break
Tuesday

Oct 29

3:00 pm

Sam Nelson

Claremont McKenna College

Title: Augmented Birack Homology

Abstract: We introduce a homology theory for augmented biracks. 2-cocyles in the cohomology of a coloring birack define enhancements of the birack counting invariant; we will see some examples.

Tuesday

Nov 5

3:00 pm

Tuesday

Nov 12

3:00 pm

Henry Segerman

University of Melbourne

Title: Regular triangulations and the index of a cusped hyperbolic 3-manifold

Abstract: Recent work by Dimofte, Gaiotto and Gukov defines the "index" (a collection of Laurent series) associated to an ideal triangulation of an oriented cusped hyperbolic 3-manifold. "Physics tells us" that this index should be a topological invariant of the manifold, not just of the triangulation of it. The problem is that the index is not well defined on all triangulations. We define a class of triangulations of a 3-manifold, depending only on the topology of the manifold, such that the index is well-defined and has the same value for each triangulation in the class. A key requirement is that the class of triangulations be connected by local moves on the triangulations, since we can prove invariance of the index under these moves. To achieve this requirement we import a result from the theory of regular triangulations of Euclidean point configurations due to Gelfand, Kapranov and Zelevinsky.

Tuesday

Nov 19

3:00 pm

Tuesday

Nov 26

4:15 at CMC, room TBA

Karly Brint

Pitzer College

Title: Stick Number of Torrified Rational Links

Abstract: Using the idea of supercoiling of DNA, it is possible to represent knots and links containing large numbers of twists with relatively small numbers of sticks. We use this approach to place an upper bound on stick number for a large class of links we call torrified rational links.

Tuesday

Dec 3

3:00 pm

Dave Bachman

Pitzer College

Title: Limits on concentrated instability

Abstract: Minimal surfaces typically have places where their instability is concentrated. We show that if all of this instability is concentrated in one place, then there is a limit to how unstable the surface is.

Tuesday

Dec 10

3:00 pm


Spring 2014 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Jan 28

3:00 pm

Eleni Panagiotou

UCSB

Title: Entanglement in systems of curves with Periodic Boundary Conditions

Abstract: Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems of open and closed curve models of polymers or vortex lines in a fluid flow. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed curves in PBC, the periodic linking number is a topological invariant that depends on a finite number of components in the periodic system. For open curves, the periodic linking number depends upon the entire infinite system and we prove that it converges to a real number that varies continuously with the configuration. Finally, we define two cut-offs of the periodic linking number and we compare these measures when applied to a PBC model of polyethylene melts.

Tuesday

Feb 4

3:00 pm

Tuesday

Feb 11

3:00 pm

Tuesday

Feb 18

3:00 pm

Yin Tian

USC

Title: a categorification of a Clifford algebra via 3-dimensional contact topology

Abstract: Categorification, initiated in the work of Crane and Frenkel, describes richer ``higher-level" structures which aim to clarify objects on the decategorification level and to provide finer invariants. A celebrated example is Khovanov homology which categorifies the Jones polynomial. In this talk we describe a categorifcation of a Clifford algebra. The motivation is from the contact category C(D^2) of a disk D^2 introduced by Honda which describe contact structures on D^2 \times [0,1].

Tuesday

Feb 25

3:00 pm

Tuesday

Mar 4

3:00 pm

Kristen Hendricks

UCLA

Title: Periodic Knots and Heegaard Floer Homology

Abstract: We introduce periodic knots and discuss two classical obstructions to periodicity, Murasugi's condition on the Alexander polynomial of a periodic knot and Edmonds' condition on the genus. We then describe a generalization of these two results in the case of doubly-periodic knots which arises from the modern link invariant Heegaard Floer homology. We finish with an example in which our construction gives more information that the two classical theorems.

Tuesday

Mar 11

3:00 pm

Hugh Howards

Wake Forrest University

Title: Linked spheres in Higher dimensions and how it all shapes up.

Abstract: The Borromean Rings are one of the most famous links. A result of Freedman and Skora shows that they cannot be formed out of circles, but they can be formed from two circles and an ellipse. They, however, are the only Brunnian link of 3, 4, or 5 components that can be formed out of convex curves. We look at generalizations of Brunnian Links to higher dimensions and ask if it is possible to form these genralized Brunnian Links out of round spheres or convex components answering the first question in the negative and the second in the positive.

Tuesday

Mar 18

No Meeting Spring Break
Tuesday

Mar 25

3:00 pm

Allison Gilmore

UCLA

Title: Knot Floer homology and constituent knots of graphs

Abstract: Knot Floer homology for singular knots was developed by Ozsvath, Szabo, and Stipsicz using the usual techniques of Heegaard diagrams and counts of holomorphic disks. Much of the talk will be devoted to introducing this theory and discussing its basic properties. The remainder of the talk will discuss joint work in progress with Kristen Hendricks. We will describe spectral sequences from the knot Floer homology of a singular knot to the knot Floer homology of any of its oriented constituent knots. If time permits, some preliminary computations will be presented and potential implications sketched.

Tuesday

Apr 1

3:00 pm

Ryan Blair

CSU Long Beach

Title: Knots with compressible thin levels.

Abstract: Width is an integer invariant of knots that is affected by the number of maxima and minima of a knot as well as the relative heights of these critical points. Width has been a particularly useful invariant due to deep connections between a width minimizing embedding of a knot and the topology of the knot exterior. In particular, Wu showed that a thinnest thin level for a width minimizing embedding is incompressible. In this talk, I will present joint work with Alex Zupan in which we construct the first examples of a width minimizing embedding with compressible thin levels.

Tuesday

Apr 8

3:00 pm

Jeremy Pecharich

Pomona College

Tuesday

Apr 15

3:00 pm

Tuesday

Apr 22

3:00 pm

Ellie Grano

Pepperdine University

Tuesday

Apr 29

4:15-5:15

Shanahan B460, HMC

Tim Hsu

San Jose State Univ.

Tuesday

May 6

3:00 pm

Erkao Bao

UCLA



Archived Schedules

2012-2013

2011-2012

2010-2011

2009-2010

2008-2009

2007-2008

2006-2007

2005-2006

2004-2005

2003-2004