# 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.

# 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 SegermanUniversity 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 HowardsWake 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 Tuesday Apr 8 3:00 pm Jeremy Pecharich Pomona College Tuesday Apr 15 3:00 pm Tuesday Apr 22 3:00 pm Ellie GranoPepperdine University Tuesday Apr 29 4:15-5:15 Shanahan B460, HMC Tim Hsu San Jose State Univ. Tuesday May 6 3:00 pm

2012-2013

2011-2012

2010-2011

2009-2010

2008-2009

2007-2008

2004-2005