For more information about the Seminar, to suggest speakers, or to volunteer to speak, contact Dave Bachman , Sam Nelson , Helen Wong or Vin de Silva.
Date  Speaker  Title and Abstract 
Tuesday
Jan 18 


Tuesday
Jan 25 
Organizational Meeting 

Tuesday
Feb 1 


Tuesday
Feb 8 
Sam Nelson Claremont McKenna College 
Title: Experimental Knot Music v2 Abstract: In this talk I will recount the history of my knot theorybased music project and show an example of my method for creating music from knot homsets. 
Tuesday
Feb 15 
Seonmi Choi Kyungpook Natl U in Korea 
Title : On invariants for surfacelinks in entropic magmas via marked graph diagrams Abstract : M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and constructed the invariant P of framed links in 3space. The invariant is closely related to the Kauffman bracket polynomial. The normalized bracket polynomial is obtained from the Kauffman bracket polynomial by the multiplication of indeterminate and it is an ambient isotopy invariant for links. In this talk, we reformulate the multiplication by using a map from the set of framed links to a Kauffman bracket magma in order that P is invariant for links in 3space. We define a generalization of a Kauffman bracket magma, which is called a marked Kauffman bracket magma. We find the conditions to be invariant under Yoshikawa moves except the first one and use a map from the set of admissible marked graph diagrams to a marked Kauffman bracket magma to obtain the invariant for surfacelinks in 4space. 
Tuesday
Feb 22 


Tuesday
Mar 1 
Thomas Mattman California State University, Chico 
Title: Title: Twobridge knots admit no purely cosmetic surgeries Abstract: (Joint with Ichihara, Jong, and Saito). We show that twobridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3manifolds that are homeomorphic as oriented manifolds. Our argument is based on a recent result by Hanselman and a study of signature and finite type invariants of knots as well as the SL(2,\C) Casson invariant.

Tuesday
Mar 8 
Hugh Howards Wake Forest University 
Title; Systematically Detecting Flypes and Hexagonal Mosaics Abstract: We talk about building knots using mosaics which were as introduced as a way of modeling quantum knots by Lomonaco and Kauffman and a newer variant, hexagonal mosaics, introduced by Jennifer McLoudMann. In the process we find a new bound on crossing numbers for hexagonal mosaics and find an infinite family of knots which do not achieve their hexagonal mosaic number while also in a projection which achieves their crossing number, extending a result of Lew Ludwig et al. In the process we introduce a new tool which makes it easier to systematically recognize when two knots differ by a sequence of Flypes (for example, giving a process to recognize that the Perko Pair were in fact the same knot). No background with mosaics or flypes is necessary. This is joint work with Jiong Li* and Xiotian Liu* (* indicates undergraduate students). 
Tuesday
Mar 15 
No Meeting  Spring Break 
Tuesday
Mar 22 
Aaron MazelGee California Institute of Technology 
Title: Towards knot homology for 3manifolds Abstract: The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3manifolds by ReshetikhinTuraev using quantum groups. Khovanov homology is a categorification of the Jones polynomial of a knot in R^3, analogously to how ordinary homology is a categorification of the Euler characteristic of a space. It is a major open problem to extend Khovanov homology to knots in 3manifolds. In this talk, I will explain forthcoming work towards solving this problem, joint with Leon Liu, David Reutter, Catharina Stroppel, and Paul Wedrich. Roughly speaking, our contribution amounts to the first instance of a braiding on 2representations of a categorified quantum group. More precisely, we construct a braided (infinity,2)category that simultaneously incorporates all of Rouquier's braid group actions on Hecke categories in type A, articulating a novel compatibility among them. 
Tuesday
Mar 29 
Rhea Palak Bakshi Institute for Theoretical Studies, ETH Zurich, Switzerland 
Title: Kauffman bracket skein modules and their structure Abstract: Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3sphere to arbitrary 3manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However, computing the KBSM of a 3manifold is notoriously hard, especially over the ring of Laurent polynomials. With the goal of finding a definite structure of the KBSM over this ring, several conjectures and theorems were stated over the years for KBSMs. We show that some of these conjectures, and even theorems, are not true. In this talk I will briefly discuss a counterexample to Marche's generalisation of Witten's conjecture. I will show that a theorem stated by Przytycki in 1999 about the KBSM of the connected sum of two handlebodies does not hold. I will also give the exact structure of the KBSM of the connected sum of two solid tori. 
Tuesday
Apr 5 


Tuesday
Apr 12 
Martin Bobb IHES 
Title: Cusps in Convex Projective Geometry Abstract: Convex real projective structures generalize hyperbolic structures in a rich way. We will discuss a class of manifolds introduced by Cooper Long and Tillmann, which include finitevolume cusped hyperbolic manifolds and other manifolds with wellcontrolled ends. These manifolds have nice deformation theoretic properties, and we will conclude with an existence theorem for novel structures on some hyperbolic manifolds. 
Tuesday
Apr 19 


Tuesday
April 26 


Tuesday
May 3 
Jim Hoste Pitzer College 
Title: On the Nonorientable 4genus of Double Twist Knots, Part II: Lower Bounds Abstract: The nonorientable 4genus of a knot K is the smallest first Betti number of any nonorientable surface in the 4ball spanning the knot. It is defined to be zero if the knot is slice. In joint work with Patrick Shanahan and Cornelia Van Cott, we attempt to determine the value of this invariant for double twist knots. In an earlier talk at this seminar, I presented methods of determining upper bounds by explicitly describing nonorientable spanning surfaces. In this talk I describe methods for establishing lower bounds using linking forms on 4manifolds and a major result of Donaldson. These methods suffice to compute the nonoprientable 4genus of several infinite families of double twist knots. 