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.
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 integervalued 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 3manifolds. 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 fourball. 
Tuesday
Nov 11 3:00 pm 


Tuesday
Nov 18 3:00 pm 
Faramarz Vafaee Cal Tech 
Title: Heegaard Floer homology and Lspace knots Abstract: Heegaard Floer theory consists of a set of invariants of three and fourdimensional manifolds. Threemanifolds with the simplest Heegaard Floer invariants are called Lspaces and the name stems from the fact that lens spaces are Lspaces. The primary focus of this talk will be on the question of which knots in the threesphere admit Lspace surgeries. We will also discuss about possible characterizations of Lspaces 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 cutandpaste 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 "traintracks 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 
Title: Thurston's spinning construction. Abstract: Thurston defined the spinning construction for hyperbolic 3manifolds. It is a way how to get an ideal triangulation from a regular one. In this talk I will demonstrate different points of view on this construction and explain what is its importance. The talk is accessible to general audience. 
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 
