Claremont Topology Seminar

Founded 1989


The Claremont Topology Seminar meets in person on Tuesdays from 3:00-4:30 pm in Estella 2099 in Spring 2024 at the Pomona College Campus of the Claremont Colleges. Estella Laboratory is located on the NE corner of College Avenue and 6th Street. Following the talk we go for coffee/tea in downtown Claremont. Sometimes we meet a little later and then go to dinner. (Look for special times on the calendar.) Click HERE for a map of the Pomona Campus.

Parking on College Avenue is free.


For more information about the Seminar, to suggest speakers, or to volunteer to speak, contact Bahar Acu, Dave Bachman, Sam Nelson, Helen Wong or Vin de Silva.


Spring 2024 Schedule (Upcoming)

special days, times or locations are in purple

Date Speaker Title and Abstract
Tuesday

January 23

Organizational Meeting

Tuesday

January 30

Song Yu

California Institute of Technology and Tsinghua Yau Mathematical Sciences Center

Title: Knot invariants, Gromov-Witten invariants, and integrality conjectures

Abstract: In this talk, we will take a peek at large N duality which is a deep correspondence between invariants of knots in 3-manifolds and enumerative geometry in symplectic 6-manifolds discovered in physics in the 1980-90s. On the numerical level, the correspondence relates Chern-Simons knot invariants to open Gromov-Witten invariants which are counts of bordered Riemann surfaces with Lagrangian boundary conditions, and has led to predictions on the integrality structures of both invariants. We will discuss recent progress on the enumerative geometry side and connections to known integrality properties in Gromov-Witten theory.

Tuesday

February 6

NO SEMINAR

Tuesday

February 13

Luya Wang

Stanford University

Title: Deformation inequivalent symplectic structures and Donaldson's four-six question

Abstract: Studying symplectic structures up to deformation equivalences is a fundamental question in symplectic geometry. Donaldson asked: given two homeomorphic closed symplectic four-manifolds, are they diffeomorphic if and only if their stabilized symplectic six-manifolds, obtained by taking products with CP^1 with the standard symplectic form, are deformation equivalent? I will discuss joint work with Amanda Hirschi on showing how deformation inequivalent symplectic forms remain deformation inequivalent when stabilized, under certain algebraic conditions. This gives the first counterexamples to one direction of Donaldson's "four-six" question and the related Stabilizing Conjecture by Ruan.

Tuesday

February 20

Puttipong Pongtanapaisan

Arizona State University

Title: Building Knotted Objects Efficiently

Abstract: Knotted objects can be constructed by gluing together standard pieces called handles. Understanding the minimum number of handles required for construction and their sequential attachment provides valuable insights into the complexity of entanglement. Certain knots require specific types of handles to be attached first, preventing them from fitting into small lattice tubes. This is particularly relevant as polymers in confinement are modeled as knots within lattice tubes. In this talk, I will discuss methods for studying these handles and their attachment order using coloring games applied to link diagrams.

Tuesday

February 27

Orsola Capovilla-Searle

UC Davis

CANCELED
Tuesday

March 5

Adam Yassine

Pomona College

Title: A Structural Approach to Classical Mechanics

Abstract: A structural approach to the study of classical mechanics clarifies the physical heuristics that physicists use in constructing mathematical models of classical mechanical systems. The focus of our current program is to develop a category theoretic framework that captures certain compositional features of classical mechanics. The framework is both flexible enough to support the description of a wide variety of systems and rigid enough to uniquely determine the physicists' models.

Tuesday

March 12

No Meeting Spring Break
Tuesday

March 19

Iris Yoon

Wesleyan College

Title: TBA

Abstract: TBA

Tuesday

March 26

Qing Zhang

UC Santa Barbara

Title: TBA

Abstract: TBA

Tuesday

April 2

Jim Hoste

Pitzer College

Title: TBA

Abstract: TBA

Tuesday

April 9

TBA Title: TBA

Abstract: TBA

Tuesday

April 16

Ryan Maguire

Dartmouth College

Title: TBA

Abstract: TBA

Tuesday

April 23

Joe Breen

University of Iowa

Title: TBA

Abstract: TBA

Tuesday

April 30

Elena Wang

Michigan State University

Title: A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance

Abstract: Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between graphs and present a metric to measure the distance between two geometric graphs via merge trees. In order to preserve as much useful information as possible from the original data, we introduce a way of rotating the sublevel set to obtain the merge trees via the idea of the directional transform. We represent the merge trees using a surjective multi-labeling scheme and then compute the distance between two representative matrices. Our distance not only has theoretically desirable qualities but can also be approximated in polynomial time. We illustrate its utility by implementation on a Passiflora leaf data set.


Fall 2023 Schedule

special days, times or locations are in purple

Date Speaker Title and Abstract
Tuesday

Sept 5

Organizational Meeting

Tuesday

Sept 12

Robert Bowden

Harvey Mudd College

Title: Chebyshev Threadings in Skein Algebras for Punctured Surfaces

Abstract: Skein algebras are algebras of links in a surface quotiented by diagram-based equivalence relations based on the Kauffman bracket. In the case of surfaces with punctures, the skein algebra is generated by links as well as arcs between the punctures, and there are additional skein relations for the arcs. We examine the algebraic structure of the punctured case, finding a description of the central elements at certain roots of unity. Our construction is closely related to the one for the usual skein algebra, where central elements come from threading links by Chebyshev polynomials.

Tuesday

Sept 19

Reginald Anderson

Claremont McKenna College

Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks

Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more restrictive condition than being smooth), which can also be extended to smooth toric varieties and global quotient toric DM stacks of a smooth toric variety by a finite abelian group, if we allow our resolution to have cokernel which is supported only along the vanishing of the irrelevant ideal. Here we show implications for exceptional collections of line bundles and a positive example for the modified King's conjecture by giving a strong, full exceptional collection of line bundles on a smooth, non-unimodular nef-Fano complete toric surface.

Tuesday

Sept 26

Reginald Anderson

Claremont McKenna College

Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks - Continued

Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more restrictive condition than being smooth), which can also be extended to smooth toric varieties and global quotient toric DM stacks of a smooth toric variety by a finite abelian group, if we allow our resolution to have cokernel which is supported only along the vanishing of the irrelevant ideal. Here we show implications for exceptional collections of line bundles and a positive example for the modified King's conjecture by giving a strong, full exceptional collection of line bundles on a smooth, non-unimodular nef-Fano complete toric surface.

Tuesday

Oct 3

Julian Chaidez

USC

Title: Quantum 4-Manifold Invariants Via Trisections

Abstract: I will describe a new family of potentially non-semisimple invariants for compact a 4-manifold whose boundary is equipped with an open book. The invariant is computed using a trisection, along with some additional combing data, and a piece of algebraic data called a Hopf triple. The relationship with other recent works on non-semisimple 4-manifold invariants, like the work of Costantino-Geer-Patureau-Mirand-Virelizier, is not yet clear. This talk is based on joint work with Shawn Cui (Purdue) and Jordan Cotler (Harvard).

Tuesday

Oct 10

Christopher Perez

Loyola University New Orleans

Title: Towers and elementary embeddings in total relatively hyperbolic groups

Abstract: In a remarkable series of papers, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloe Perin that if H is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G, then G is a tower over H. We prove a generalization of Perin's result to toral relatively hyperbolic groups using JSJ and shortening techniques.

Tuesday

Oct 17

No Meeting Fall Break
Tuesday

Oct 24

Wenyuan Li

USC

Title: Generating families on Lagrangian cobordisms

Abstract: An important question in contact topology is to understand Legendrian knots and their relations given by Lagrangian cobordisms. In the contact manifold T*M x R, an important tool to study Legendrian knots and their Lagrangian cobordisms is called generating families or generating functions, which are generalizations of the defining functions f of graphical Legendrians of the form {(x, df(x), f(x))}. When there exists a generating family with good control at infinity, interesting Legendrian invariants can be extracted. We try to understand the following basic question: when can a generating function on the Legendrian knot be extended to the Lagrangian cobordism? We will give a necessary and sufficient condition to the problem for generating families with good control at infinity. In particular, we show that such an extension always exists in the case of Lagrangian concordances.

Tuesday

Oct 31

Konstantinos Varvarezos

UCLA

Title: Cosmetic Surgeries on Knots and Heegaard Floer Homology

Abstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is called purely cosmetic if the resulting 3-manifolds are homeomorphic as oriented manifolds, whereas it is said to be chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. An outstanding conjecture predicts that no nontrivial knots admit any purely cosmetic surgeries. We apply certain obstructions from Heegaard Floer homology to show that (nontrivial) knots which arise as the closure of a 3-stranded braid do not admit any purely cosmetic surgeries. Furthermore, we find new obstructions to the existence of chirally cosmetic surgeries coming from Heegaard Floer homology; in particular, we make use of immersed curve formulations of knot Floer homology and the corresponding surgery formula. Combining these with other obstructions involving finite type invariants, we completely classify chirally cosmetic surgeries on odd alternating pretzel knots. Moreover, we rule out cosmetic surgeries for L-space knots along slopes with opposite signs.

Tuesday

Nov 7

Hyunki Min

UCLA

Title: Contact structures and the mapping class group of lens spaces

Abstract: One important problem in contact topology is to classify contact structures on a given manifold. Around 20 years ago, Giroux and Honda classified contact structures on lens spaces. A natural question to ask after that is how the transformations on lens spaces interact with the contact structures. In this talk, we study contactomorphisms on lens spaces, which are diffeomorphisms preserving the contact structure. We show that the contact mapping class group of a standard contact lens space is a subgroup of the mapping class group of the lens space.

Tuesday

Nov 14

Claremont Colleges Course Previews for Spring 2024 Title: Geometry Topology Course Previews for Spring 2024

Abstract: Geometry and Topology Seminar invites students and faculty to a course preview session devoted to a discussion and presentations about upcoming Spring 2024 courses in geometry, topology and/or with applications in geometry and topology to help students make their enrollment choices.

Tuesday

Nov 21

No Meeting Thanksgiving Week
Tuesday

Nov 28

Melody Molander

UC Santa Barbara

Title: Skein Theory of Affine ADE Subfactor Planar Algebras

Abstract: Subfactor planar algebras first were constructed by Vaughan Jones as a diagrammatic axiomatization of the standard invariant of a subfactor. These planar algebras also encode two other invariants of the subfactors: the index and the principal graph. The Kuperberg Program asks to find all diagrammatic presentations of subfactor planar algebras. This program has been completed for index less than 4. In this talk, I will introduce subfactor planar algebras and give some presentations of subfactor planar algebras of index 4 which have affine ADE Dynkin diagrams as their principal graphs.


Archived Schedules

2022-2023

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


This site is maintained by Bahar Acu who received the (34yo) baton from Jim Hoste.