Date  Speaker  Title and Abstract 
Tuesday Sept 6  Dave Bachman Pitzer College 
Title: Heegaard splittings and tori Abstract: I will present joint work with Ryan DerbyTalbot, where we almost completely characterize those Seifert Fibered Spaces that admit infinitely many nonisotopic Heegaard splittings of the same genus. 
Tuesday Sept 13  Sam Nelson UC Riverside 
Title: Recent results on knots and quandles Abstract: In this talk, we'll see some recent results on the relationship between knot diagrams and quandles as well as recent results on the structure of finite quandles. 
Tuesday Sept 20  Sam Nelson UCR 
Title: More recent results on knots and finite quandles Abstract: Results surveyed will include quandle matrices, the orbit decomposition of finite quandles, symbolic computation with finite quandles and an algorithm for finding Alexander presentations of finite quandles. 
Tuesday Sept 27  Erica Flapan Pomona College 
Title: Intrinsic linking and knotting of graphs in arbitrary 3manifolds
(joint with: Hugh Howards, Don Lawrence, Blake Mellor) Abstract: We prove that a graph is intrinsically linked in an arbitrary 3manifold M if and only if it is intrinsically linked in S^3. Also, assuming the Poincare Conjecture, a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S^3. 
Tuesday Oct 4  Erica Flapan  continuation of last week 
Tuesday Oct 11  
Tuesday Oct 18  Fall Break, no meeting  
Tuesday Oct 25  Danny C. Calegari Cal Tech 
Title: Distortion in Transformation Groups (joint with M. Freedman) Abstract: An element g in a finitely generated group G is distorted if the word length of g^n grows sublinearly as a function of n. An element g in an arbitrary group G is distorted if it is distorted (as above) in some finitely generated subgroup H. We show that rigid rotations of spheres are distorted in groups of diffeomorphisms (C^1 or C^infty depending on the dynamics of the rotation). We also show that every homeomorphism of the sphere is arbitrarily badly distorted in the group of all homeomorphisms. A corollary, pointed out by Yves de Cornulier, is that the group of homeomorphisms of a sphere, thought of as a discrete group, has the *strongly bounded* property, introduced by G. Bergman. 
Tuesday Nov 1  Mike Krebs Cal State LA 
Title: Toledo invariants on 2orbifolds Abstract: To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3sphere into the Lie group U(2,1), we associate a real number called the ``orbifold Toledo invariant.'' Using the theory of Higgs bundles, we explicitly compute all values this invariant takes on. 
Tuesday Nov 8  Afra Zomorodian Stanford University 
Title: Localized Homology Theory
Abstract: In this talk, I introduce "localized homology", a theory for finding local geometric descriptions for topological attributes. Given a space and a cover of subspaces, we construct the blowup complex, a derived space that contains the local and global topologies at different scales. The persistent homology of the blowup complex localizes the topological attributes of the space. Our theory is general and applies in all dimensions. After giving an informal discussion, I formalize the approach for general spaces, adapt it for simplicial spaces, and develop a simple algorithm that works directly on the input and avoids the construction. I then show results using a complete implementation of the ideas presented. 
Tuesday Nov 15  Marty Scharlemann UCSB 
Title: Meditation on the Schoenflies Conjecture Abstract: The Schoenflies Conjecture remains unsolved only in one dimension and in that dimension only in the Diff/PL category. I'll give a brief overview both of the importance and history of the conjecture and discuss some recent developments and connections to problems in 3manifolds. 
Tuesday Nov 22  Lisa Hernandez UC Riverside 
Title: An application of TQFT: determining the girth of a knot. Abstract: A knot diagram can be divide by a circle into two parts, such that each part can be coded by a planar tree with integer weights on its edges. A half of the number of intersection points of this circle with the knot diagram is called the girth. The girth of a knot is then the minimal girth of all diagrams of this knot. The girth of a knot minus 1 is an upper bound of the Heegaard genus of the 2fold branched covering of that knot. We will use TQFTs coming from the Kauffman bracket to determine the girth of some knots. Consequently, our method can be used to determine the Heegaard genus of 2fold branched covering of some knots. 
Tuesday Nov 29  Blake Mellor Loyola Marymount University 
Title: Intrinsic linking and knotting in Virtual Spatial Graphs. (Joint with Tom Fleming) Abstract: Kauffman's theory of virtual knots can be extended to a theory of virtual spatial graphs. We look at what it means for a graph to be virtually intrinsically linked. We show that the space of intrinsically linked graphs can be decomposed into an infinite sequence of nested spaces of graphs, which are virtually intrinsically linked of various degrees. We also look at several examples of particular graphs, such as K_6 and the Petersen graph. Time permitting, we will also consider virtually intrinsically knotted graphs. 
Tuesday Dec 6  XiaoSong Lin UC Riverside 
Title: Loop braids and the motion group of the unlink in the 3space. Abstract: The motions of components of the unlink in the 3space can be described by loop braids. In this talk, we will give a complete description of the relations among loop braids. We shall also touch upon the question of finding representations of the group of loop braids. (Notes: The concept of a group of motions of a submanifold N in a manifold M was introduced by David Dahm in his unpublished Ph.D. thesis (Princeton, 1962). In the mathematics literature, this concept was almost only further explored in the work of Deboral Goldsmith published in 1981. More physicists seem to be aware of the work of Dahm and Goldsmith than mathematicians. It is our hope to offer a remedy to this situation through this talk.) 
Date  Speaker  Title and Abstract 
Tuesday Jan 24  Peter Milley UC Riverside 
Title: Constructing all 1cusped hyperbolic manifolds with volume less than 2.7
(Joint with D. Gabai and R. Meyerhoff) Abstract: Every 1cusped hyperbolic 3manifold with volume less than 2.7 can be obtained by Dehn surgery on one of 21 2cusped manifolds. This result, while simple in principle and easy to demonstrate, was surprisingly difficult to prove; the proof spans two papers currently in progress. In this talk I will sketch out the proof and explain the connection to the stillopen problem of finding the minimumvolume closed hyperbolic manifold. I will also describe some of the difficulties we had nailing down this result, including the hopefully amusing tale of Lemma 8.8, case 7, subcase 2, subsubcase 6, subsubsubcase 2. Finally, I will perform tricks with SnapPea. 
Tuesday Jan 31  Ko Honda University of Southern California 
Title: Rightveering diffeomorphisms of a compact surface with boundary Abstract: We initiate the study of the monoid of rightveering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions. This is joint work with W. Kazez and G. Mati\'c. 
Tuesday Feb 7  Stefano Vidussi UC Riverside 
Taubes' Conjecture and Twisted Alexander Polynomials Abstract: It is wellknown that the SeibergWitten invariants of a $4$manifold provide obstructions to the existence of a symplectic structure. When the $4$manifold is of the form $S^{1} \times N$, these obstructions can be described in terms of the Alexander polynomial of $N$. C. Taubes formulated the conjecture that, if $S^{1} \times N$ is symplectic, then $N$ fibers over the circle. P. Kronheimer studied the case where $N$ is obtained as $0$surgery along a knot $K \subset S^{3}$ and showed that the aforementioned constraints on the Alexander polynomial $\Delta_{N}$ give evidence to Taubes' conjecture, i.e. $\Delta_{N}$ must be monic and its degree must coincide with the genus of the knot. Still, these conditions are short of characterizing fibered knots. In this talk we discuss how to extend these ideas to the case of a general $3$manifold and how these conclusions can be strengthened by taking into account the twisted Alexander polynomials associated to an epimorphism of $\pi_{1}(N)$ into a finite group. This way we get new evidence to Taubes' conjecture and, practically, new obstructions to the existence of symplectic structures on $S^1 \times N$, even in the case of $0$surgery along a knot. As an application o! f these results we show that if $N$ is the $0$surgery along the pretzel knot $(5,3,5)$, a case that cannot be decided with the use of the Alexander polynomial, $S^1 \times N$ is not symplectic: this answers a question of Kronheimer. In a similar way, we show that Taubes' conjecture holds for knots up to $12$ crossings. (\textit{Joint work with Stefan Friedl of Rice University}) 
Tuesday Feb 14  Fumikazu Nagasato Tokyo Institute of Technology, Japan 
Title:
Algebraic varieties via a filtration of
the Kauffman bracket skein module Abstract: In this talk, we define an algebraic variety in an affine space $\mathbb{C}^N$ for a knot in 3sphere $S^3$, called the reduced character variety (RCV) of a knot, which is constructed via a filtration of the Kauffman bracket skein module (KBSM) of a knot exterior. For a braid $\sigma$, we can in fact construct a polynomial map $f_{\sigma}$ from $\mathbb{C}^N$ to itself by using a representation of the braid group into the automorphism group of the KBSM of a handlebody at $t=1$, which representation is closely related to the nonlinear Magnus representation of the braid group into a polynomial ring over $\mathhbb{Z}$. The RCV of a knot is defined as a subvariety of the set of fixed points of $f_{\sigma}$ for a braid presentation $\sigma$ of the knot. We can show that the RCV is an invariant of knots in $S^3$. (We note that a quantization of the nonlinear Magnus representation and the RCV can be derived from the above system at general $t$.) We try to get a better understanding of the RCV by focusing on ``the number of its irreducible components (*)''. First, we observe numerically a relationship of the quantity (*) with socalled the CassonLin invariant defined by X.S. Lin, which in fact inspired the RCV. Moreover we look into the quantity (*) and see that the quantity (*) is closely related to the knot determinant and moreover the highest degree of the Apolynomial $A_K(M,L)$ of a knot $K$ in terms of $L$.

Tuesday Feb 21  Jim Hoste Pitzer College  postponed to later in the semester 
Tuesday Feb 28  Jesse Johnson UC Davis 
Title: Heegaard Splittings and the Pants Complex Abstract: John Hempel defined a ``distance" for Heegaard splittings based on the complex of curves. I will describe two similar types of distance, using Hatcher and Thurston's pants complex and the dual graph to the curve complex, respectively. These distances prove to be more global notions of complexity for a Heegaard splitting in the sense that they behave nicely under stabilization and lead to nontrivial 3manifold invariants. 
Tuesday Mar 7  Thomas Mattman CSU Chico 
Title: Boundary slopes (nearly) bound cyclic slopes. Abstract: Let $r_m$ and $r_M$ be the least and greatest finite boundary slopes of a hyperbolic knot $K$ in $S^3$. We show that any cyclic surgery slopes of $K$ must lie in the interval ${[} r_m  1/2, r_M + 1/2 {]}$. 
Tuesday Mar 14  no meeting Spring Break  
Tuesday Mar 21  Jim Hoste Pitzer College 
Title: Boundary Slopes of 2Bridge Links Determine the Crossing
Number Albstract: A {\it diagonal} surface in a link exterior $M$ is a properly embedded, incompressible, boundary incompressible surface which furthermore has the same number of boundary components and same slope on each component of $\partial M$. We derive a formula for the boundary slope of a diagonal surface in the exterior of a 2bridge link which is analogous to the formula for the boundary slope of a 2bridge knot found by Hatcher and Thurston. Using this formula we show that the {\it diameter} of a 2bridge link, that is, the difference between the smallest and largest finite slopes of diagonal surfaces, is equal to the crossing number. 
Tuesday Mar 28  Sam Nelson UC Riverside 
Title: A quandletheoretic definition of linking number. Abstract: The study of knot and link invariants defined in terms of finite quandles has generally focused on connected quandles and singlecomponent links, i.e. knots. In this talk, we'll see how a particular kind of finite quandle can be used to give a purely algebraic definition of linking number, which can then be applied to arbitrary quandles. This is joint work with Natasha Harrell, an undergraduate at UCR. 
Tuesday Apr 4  no meeting  
Tuesday Apr 11  no meeting  
Tuesday Apr 18  Mohamed Ait Nouh Cal State Univ Channel Islands 
Title: A new invariant of knots via Kirby calculus. Abstract: A twisted knot is a knot obtained from the unknot by grabbing a handful of the unknot strands, cutting then all, then after twisting one set, reglue. This operation is equivalent to doing a certain type of Dehn surgery on an unknot in the complement of the original unknot. By using Kirby calculus, a twisted knot bounds a nice disk in a standard 4manifold. We introduce the notion of characteristic twisting of knots in the 3sphere, motivated by characteristic classes. We also define a new invariant of knots corresponding to the minimal number of characteristic twisting disks of a knot K. Parts of the proofs are inspired by Kirby calculus and old guage theory. 
Tuesday Apr 25  Marta Asaeda UC Riverside  Title: Skein Modules Based on Incompressible Surfaces 
Tuesday May 2  Vin de Silva Pomona College 
Title: Topological approximation by small simplicial complexes. Abstract: How does one obtain topological information about a data set? An obvious strategy is to attempt to approximate the configuration of data points by a suitable simplicial complex. I will explain one particular construction, "the witness complex" (due to Gunnar Carlsson and myself), which has been found to be useful and effective. There are two flavours, "strong" and "weak", and a central part of this work involves understanding the relationship between the two flavours. I will discuss the "weak witnesses theorem" which underpins this understanding. 