Date  Speaker  Title and Abstract 
Tuesday
Sept 9 3:00 pm 
Organizational Meeting  
Tuesday
Sept 16 3:00 pm 
Sam Nelson Claremont McKenna College 
Title: Semiquandles and flat knots Abstract: We define a new algebraic structure we call a semiquandle and use it to define invariants of Kauffman's flat singular knots. This type of object has potential applications to link homotopy and knotted graphs. This is joint work with Allison Henrich. 
Tuesday
Sept 23 3:00 pm 
Jiajun Wang Cal Tech 
Title: On combinatorial Floer homology Abstract: Heegaard Floer homology is introduced by Peter Ozsvath and Zoltan Szabo, which is defined from the Heegaard splitting of a threemanifold. On a "nice" Heegaard diagram, Heegaard Floer homology can be computed combinatorially. In this talk, we discuss how to make it a combinatorial theory. 
Tuesday
Sept 30 3:00 pm 
Dongping Zhuang Cal Tech 
Title: Large
scale geometry of commutator subgroups Abstract: Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsionfree nonelementary wordhyperbolic group, C is oneended. Hence (in this case), the asymptotic dimension of C is at least 2. 
Tuesday
Oct 7 3:00 pm 
Emily Stark Pomona College 
Title: Intrinsically Linked and TripleLinked graphs in RP^3 Abstract: It has been shown that the complete set of minorminimally intrinsically linked graphs in arbitrary 3manifolds are characterized by the seven Petersenfamily graphs. We explore a weaker definition of unlinks in projective space, which leads to two distinct twocomponent unlinks. The number of minorminimal intrinsically linked graphs increases and we begin to characterize such graphs up to connectivity 3. In particular, K6 , the complete graph on 6 vertices is unlinked in RP^3 , and 7 is the smallest n for which Kn is intrinsically linked in RP^3 . In contrast, Flapan, Naimi, and Pommersheim showed that every spatial embedding of K10 contains a nonsplit threecomponent link, and 10 is also the smallest n for which Kn is intrinsically triplelinked in RP^3. 
Tuesday
Oct 14 3:00 pm 
Sandra Ritz USC 
Title: A Categorification of the Burau Representation via Contact Geometry Abstract: We will begin with an overview of the Burau representation of the braid group. This will be followed by an introduction to a contact category on 3manifolds, with a brief discussion of its relation to the braid group. 
Tuesday
Oct 21 
No Seminar Fall Break 

Tuesday
Oct 28 3:00 pm 
Roman Golovko USC 
Title: The Sutured Embedded Contact Homology of S^1 x
D^2 Abstract: We will define the sutured embedded contact homology for contact oriented 3manifolds with convex boundary. After that, we will show that the sutured embedded contact homology of S^1 x D^2, equipped with 2n sutures of integral or infinite slope on the boundary, coincides with the sutured Floer homology. 
Tuesday
Nov 4 3:00 pm 
Davie Bachman Pitzer College CANCELLED 
Title: Topological index theory for surfaces in
3manifolds Abstract: We define an isotopy invariant index of a surface in a 3manifold, and show that it mimics the index of a (unstable) minimal surface. This allows us to find purely topological analogues to familiar techniques from geometry, such as barrier arguments. Deep results follow concerning Heegaard splittings, bridge positions of knots, and normal surfaces. In addition, this new viewpoint opens up a host of exciting new questions for the field of 3manifold topology. 
Tuesday
Nov 11 3:00 pm 
Alex
Hoffnung UC Riverside 
Title: Multisymplectic Geometry Abstract: A Lie 2algebra is a "categorified" version of a Lie algebra: that is, a category equipped with structures analogous to those of a Lie algebra, for which the usual laws hold up to isomorphism. In the classical mechanics of point particles, the phase space is often a symplectic manifold, and the Poisson bracket of functions on this space gives a Lie algebra of observables. Multisymplectic geometry describes an ndimensional field theory using a phase space that is an "nplectic manifold": a finitedimensional manifold equipped with a closed nondegenerate (n+1)form. Here we consider the case n = 2. For any 2plectic manifold, we construct a Lie 2algebra of observables. 
Tuesday
Nov 18 3:00 pm 
Cornelia Van Cott University of San Francisco 
Title: Obstructions to slicing Bing doubles Abstract: We will begin by introducing slice knots and links and reviewing several important related results. Next we will introduce a particular family of links called Bing doubles. Much recent attention has focused on characterizing when a Bing double is slice. We will discuss recent progress toward achieving this goal using a new tool called covering link calculus. 
Tuesday
Nov 25 3:00 pm 
Juan OrtizNavarro 
Title: A volume form on the Khovanov Invariant Abstract: The Reidemeister torsion construction can be applied to the chain complex used to compute the Khovanov homology of a knot or a link. This denes a volume form on Khovanov homology. The volume form transforms correctly under Reidemeister moves to give an invariant volume on the Khovanov homology. In this talk, I will start with some basic facts about knot theory and algebraic topology which will lead us to Khovanov Homology and the construction and invariance of this volume form. Also, some examples of the invariant are presented for particular choices for the bases of homology groups to obtain a numerical invariant of knots and links. In these examples, the algebraic torsion seen in the Khovanov Chain complex when homology is computed over Z is recovered. 
Tuesday
Dec 2 3:00 pm 

Tuesday
Dec 9 3:00 pm 
Liam Watson Universite du Quebec a Montreal, et Centre Interuniversitaire de Recherches en Geometrie et Topologie 
Title: Involutions on 3manifolds and Khovanov homology Abstract: Given a manifold with torus boundary, together with an appropriate involution, it is possible give obstructions to certain exceptional surgeries using Khovanov homology. In particular, obstructions to lens space surgeries, as well as obstructions to finite fillings may be obtained. This talk will explain how these obstructions arise, and attempt to compare them with strong obstructions arising in HeegaardFloer homology. 
Date  Speaker  Title and Abstract 
Tuesday
January 27 3:00 pm 
Sangbum Cho UC Riverside 
Title: Goeritz groups for lens spaces Abstract: Given a lens space (or the 3sphere) with its Heegaard splitting of genus two, the Goeritz group is defined to be the group of isotopy classes of orientation preserving homeomorphisms of the space that preserve the splitting. In this talk, we consider each of the Goeritz groups for lens spaces L = L(p, 1) and the 3sphere. We construct a tree on which the group acts, and give an explicit presentation of each group. 
Tuesday
February 3 3:00 pm 
Julie Bergner UC Riverside 
Title: Model categories and homotopy theories Abstract: In classical homotopy theory, two topological spaces are considered to be the same if they have a weak homotopy equivalence, or map inducing isomorphisms on homotopy groups, between them. Thus, we have a notion of equivalence which is weaker than isomorphism. A similar phenomenon occurs when we consider quasiisomorphisms between chain complexes. The structures possessed by the category of topological spaces and by the category of chain complexes can be axiomatized via a model category structure, thus enabling us to consider more general "homotopy theories". In this talk, we'll consider the advantages and difficulties with model categories as well as more modern approaches to the study of homotopy theories. 
Tuesday
February 10 3:00 pm 
Dave Bachman Pitzer College 
Title: Topological index theory for surfaces in
3manifolds Abstract: We define an isotopy invariant index of a surface in a 3manifold, and show that it mimics the index of a (unstable) minimal surface. This allows us to find purely topological analogues to familiar techniques from geometry, such as barrier arguments. Deep results follow concerning Heegaard splittings, bridge positions of knots, and normal surfaces. In addition, this new viewpoint opens up a host of exciting new questions for the field of 3manifold topology. 
Tuesday
February 17 3:00 pm 
Fangyun Yang UC Riverside 
Title: An Index Theorem for Singular Dirac Operators Abstract: We study Dirac Operators with singularities on a codimension $2$ submanifold. Suppose $M$ is a manifold of dimension $2n$, $B$ is a submanifold of dimension $2n  2$, and $Mbackslash B$ has a spin structure, which can not be extended to $M$. The metric we consider on $Mbackslash B$ is the restriction of a smooth metric on $M$. Then we show that if we put some APStype boundary conditions along the submanifold $B$, the associated Dirac operator is Fredholm. We also obtain an explicit Index formula for the Dirac operator. One immediate application of the Index formula is that it gives us an analytic proof of the generalized Rohklin congruence formula. 
Tuesday
February 24 3:00 pm 

Tuesday
March 3 3:00 pm 
Julien Roger USC 
Title: Quantum Teichmuller Spaces and Modular Functors Abstract: Let S be a surface with punctures. The quantum Teichmuller space T^q(S) is a deformation of the algebra of rational functions on the classical Teichmuller space T(S). Bonahon and Liu obtained a classification of the representations of T^q(S). Using this classification one can construct a vector bundle over the moduli space M(S). I will describe the first steps in trying to extend this construction to the DeligneMumford compactification of M(S). It involves looking at families of hyperbolic metrics where the length of a finite number of geodesics tends to 0, and the way this affects ideal triangulations on S. I will also explain how it relates to the notion of a modular functor. 
Tuesday
March 10 3:00 pm 
Emille Davie UC Santa Barbara 
Title: Detecting Veering Information of 3Braids using the Burau Representation Abstract: We will give a brief introduction to the braid group, to the Burau representation of the braid group, and to rightveering diffeomorphisms of surfaces with boundary. We will also discuss how the Burau representation can be used to detect rightveering 3braids. 
Tuesday
March 17 
No Seminar Spring Break 

Tuesday
March 24 3:00 pm 
Carmen Caprau CSU Fresno 
Title: On the universial sl(2) foam cohomology Abstract: We introduce and describe the features of the euniversalf sl(2)link cohomology via foams, also called singular cobordisms, modulo local relations. If time permitting, we will also discuss the tools that lead to efficient computations of the corresponding cohomology groups, even for big knots and links. 
Tuesday
March 31 3:00 pm 
Matt Day Cal Tech 
Title: Topological interpretation and extension of Morita's homomorphisms Abstract: In 1993, S. Morita defined a series of homomorphisms from subgroups of the mapping class group of a surface to abelian groups. This definition is entirely algebraic. We will discuss a topological interpretation of these homomorphisms due to A. Heap. Then we will use this topological interpretation to extend Morita's homomorphisms to crossed homomorphisms on the entire mapping class group. 
Tuesday
April 7 3:00 pm 
Alex Coward UC Davis 
Title: Unknotting, algorithms and genus one knots.
(Joint work with Marc Lackenby) Abstract: There is no known algorithm for determining whether a knot has unknotting number one, practical or otherwise. Indeed, there are many explicit knots that are conjectured to have unknotting number two, but for which no proof of this fact is currently available. For many years the knot 810 was in this class, but a celebrated application of Heegaard Floer homology by Ozsvath and Szabo established that its unknotting number is in fact two. In this talk we will see how tools from sutured manifold theory can be used to characterize unknotting crossing changes. We shall use these tools to address the following question: 'If a knot has unknotting number one, are there finitely many unknotting crossing changes and, if so, can one find them?'. We completely answer this question for genus one knots. Apart from sutured manifold theory, the proof utilizes some classical topology and an analysis of the arc complex of the once punctured torus. 
Tuesday
April 14 3:00 pm 
Tim Carrell Pomona College 
Title:The Surface Biquandle Abstract: Knot invariants are an important technique of knot theory that associate comparatively easy to study algebraic objects with knots. One such invariant, the biquandle, is constructed as the minimal structure needed to label the semiarcs of a knot. In this talk, we construct an invariant of surface knots similar to the biquandle by labeling semisheets. We also examine the relationship between such a surface biquandle and the classical biquandle. 
Tuesday
April 21 3:00 pm 

Tuesday
April 28 3:00 pm 
Dorothy Buck

Title: Knots and Links arising from Protein Action on DNA Abstract: The central axis of the famous DNA double helix is often topologically constrained or even circular. The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function is to change the DNA axis topology  for example converting a torus link into an unknot. Additionally, there are several protein families that change the axis topology as a byproduct of their interaction with DNA. This talk will describe two areas where 3manifold topology methods have been useful in predicting which types of knots and links arise from the action of these proteins on DNA. The first is joint work with Erica Flapan, and the second is joint work with Ken Baker and Andrew Lobb. 
Tuesday
May 5 3:00 pm 
Alice Stevens UC Davis 
Title: Kstable equivalence for knots in Heegaard surfaces Abstract: Let K be a knot embedded in a Heegaard surface S for a closed orientable 3manifold M. Two pairs (S, K) and (S', K') are equivalent in M if there is an ambient isotopy of M that maps (S, K) onto (S', K'). We define Kstabilization, which is essentially the addition of an unknotted tube to the surface SK, and we prove that any two pairs (S, K) and (S', K') are Kstably equivalent in M if they have the same surface slope. 