Claremont Topology Seminar

Founded 1989


The Claremont Topology Seminar meets on-line using Zoom on Tuesday's from 3:00-4:00 pm. If you would like to attend, request a Zoom link from Sam Nelson .

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.



Spring 2022 Schedule

special days, times or locations are in red

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 theory-based 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 surface-links 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 3-space. 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 3-space. 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 surface-links in 4-space.

Tuesday

Feb 22

Tuesday

Mar 1

Thomas Mattman

California State University, Chico

Title: Title: Two-bridge knots admit no purely cosmetic surgeries

Abstract: (Joint with Ichihara, Jong, and Saito). We show that two-bridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3-manifolds 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 McLoud-Mann. 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 Mazel-Gee

California Institute of Technology

Title: Towards knot homology for 3-manifolds

Abstract: The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin--Turaev 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 3-manifolds. 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 2-representations 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 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However, computing the KBSM of a 3-manifold 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 finite-volume cusped hyperbolic manifolds and other manifolds with well-controlled 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 Non-orientable 4-genus of Double Twist Knots, Part II: Lower Bounds

Abstract: The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball 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 non-orientable spanning surfaces. In this talk I describe methods for establishing lower bounds using linking forms on 4-manifolds and a major result of Donaldson. These methods suffice to compute the non-oprientable 4-genus of several infinite families of double twist knots.



Archived Schedules

2018-2019

2017-2018

2016-2017

2015-2016

2014-2015

2013-2014

2012-2013

2011-2012

2010-2011

2009-2010

2008-2009

2007-2008

2006-2007

2005-2006

2004-2005

2003-2004