Claremont Topology Seminar

Founded 1989


The Claremont Topology Seminar meets on Tuesday's from 3:00-4:00 pm in Millikan 2099, Pomona College. Millikan 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.

To reach Pomona College from the 10 freeway, exit at Indian Hill, go north, turn right (east) on 6th street and then turn left (north) on College. To reach Pomona College from the 210 freeway, if traveling East, exit at Towne Avenue, turn right (south) on Towne, turn left (east) on Foothill Blvd, and turn right (south) onto College Avenue. If traveling West on the 210 freeway, exit at Baseline/Padua, turn right (west) onto Baseline, turn left (south) onto Padua at the first light, turn right (west) onto Foothill Blvd at the third light, turn left (south) onto College Avenue.

Parking on College Avenue is free.

For more information about the Seminar, or to suggest speakers, contact Jim Hoste , Dave Bachman , Sam Nelson , Erica Flapan or Vin de Silva.


2017-18 Schedule


Fall, 2017

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Sept 5, 2017

3:00 pm

Organizational Meeting Meet at Some Crust Bakery for organizational meeting.
Tuesday

Sept 12, 2017

3:00 pm

Title:

Abstract:

Tuesday

Sept 19, 2017

3:00 pm

Allison K Henrich

Seattle University

Title: An Intransitive Relation on Knots

Abstract: In this talk, we will introduce and explore the following relation on knots. A knot D is said to be a descendant of another knot P if there is a minimal crossing diagram of P on which some subset of crossings can be changed to produce a diagram of D. In this case, P is said to be a parent of D. The descendant-parent relation has many interesting properties--for instance, intransitivity--and it enjoys useful connections with other previously studied relations on knots. We explore several such properties and connections, and we provide a variety of computational results. This is joint work with Jason Cantarella, Elsa Magness, Oliver O’Keefe, Kayla Perez, Eric Rawdon, and Briana Zimmer.

Tuesday

Sept 26, 2017

3:00 pm

Sam Nelson

Claremont McKenna College

Title: Psyquandles, Singular Knots and Pseudoknots

Abstract: Singular knots are 4-valent spatial graphs considered up to rigid vertex isotopy. Pseudoknots are knots with some precrossings, classical crossings where we don't know which strand is on top. Psyquandles are a new algebraic structure which defines invariants of both singular and pseudoknots. In particular we will define the Jablan Polynomial, a generalization of the Alexander polynomial for singular/pseudoknots arising from psyquandles. This is joint work with Natsumi Oyamaguchi (Shumei University) and Radmila Sazdanovic (NCSU).

Tuesday

Oct 3, 2017

3:00 pm

Ellie Dannenberg

Pomona College

Title: Circle Packings on Surfaces with Complex Projective Structures.

Abstract: The classical circle packing theorem of Koebe, Andreev, and Thurston says that given a triangulation $\tau$ of a closed, orientable surface, there is a unique constant curvature Riemannian metric on the surface so that the surface with this metric admits a circle packing with dual graph $\tau$. Kojima, Mizushima, and Tan give a definition of a circle packing on surfaces with complex projective structures. Unlike in the metric case, there is a deformation space of complex projective circle packings with combinatorics given by $\tau$. They conjecture that this space is homeomorphic to Teichmuller space. I'll present progress towards this conjecture for certain classes of triangulations.

Abstract:

Tuesday

Oct 10, 2017

3:00 pm

Teddy Einstein

Cornell University

Title: Hierarchies of Non-Positively Curved Cube Complexes

Abstract: A non-positively curved (NPC) cube complex is a combinatorial complex constructed by gluing Euclidean cubes along faces in a way that satisfies a combinatorial local non-positive curvature condition. A hierarchy is an inductive method of decomposing the fundamental group of a cube complex. Cube complexes and hierarchies of cube complexes have been studied extensively by Wise and feature prominently in Agol's proof of the Virtual Haken Conjecture for hyperbolic 3-manifolds.

Abstract:

Tuesday

Oct 17, 2017

3:00 pm

No Meeting Fall Break
Monday

Oct 23, 2017

3:00 pm

John Stillwell

University of San Francisco

History of Mathematics Seminar
Tuesday

Oct 24, 2017

3:00 pm

Aaron Mazel-Gee

USC

Title:K-theory and traces

Abstract: A vector bundle over a topological space X is a family of vector spaces parametrized by X. The study of spaces through their vector bundles is called topological K-theory. If the space has a more algebraic flavor, then we can also study its algebraic K-theory; for example, on a complex manifold we can restrict to holomorphic vector bundles. As K-theory can be very difficult to compute, we are quite lucky to have an assortment of ``trace maps'' (in the sense of traces of matrices) that compare it to more computable invariants. In particular, the cyclotomic trace is responsible for the vast majority of computations of algebraic K-theory. However, despite its importance, there has been no geometric basis for the cyclotomic trace: it has just served as an extremely useful but conceptually unmotivated tool. In this talk, I will give an overview of K-theory and traces, with the end goal of explaining forthcoming joint work with David Ayala and Nick Rozenblyum that provides a precise geometric explanation of the cyclotomic trace.

Tuesday

Oct 31, 2017

3:00 pm

Iris Yoon Title:

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Tuesday

Nov 7, 2017

3:00 pm

Radmila Sazdanovic

North Carolina State University

Title:

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Tuesday

Nov 14, 2017

3:00 pm

Dmitri Gekhtman

Cal Tech

Title: Holomorphic retractions onto Teichmuller disks.

Abstract: A complex manifold is a space built by gluing patches of complex coordinate coordinate space using holomorphic transition maps. There is a finite-dimensional space of ways to equip a closed surface with the structure of a complex manifold. This space of complex structures is called the Teichmuller space of the surface. It turns out that the Teichmüller space is itself a complex manifold. In this talk, we will see how the topology and geometry of a surface is reflected in the complex-analytic structure of its Teichmuller space. We will see how polygonal decompositions of the surface give rise to holomorphically embedded copies of the unit disk inside of Teichmuller space. These embedded disks are called Teichmuller disks. We will describe some recent results which give partial answers to the following question: Which Teichmuller disks are holomorphic retracts of Teichmuller space?

Tuesday

Nov 21, 2017

3:00 pm

Yen Duong

Title:

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Tuesday

Nov 28, 2017

3:00 pm

James Conant Title:

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Tuesday

Dec 5, 2017

3:00 pm

Dave Bachman

Pitzer College

Title:

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Spring 2018 Schedule

special days, times or locations are in red

Date Speaker Title and Abstract
Tuesday

Jan 23, 2018

3:00 pm

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Tuesday

Jan 30, 2018

3:00 pm

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Tuesday

Feb 6, 2018

3:00 pm

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Tuesday

Feb 13, 2018

3:00 pm

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Tuesday

Feb 20, 2018

3:00 pm

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Tuesday

Feb 27, 2018

3:00 pm

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Tuesday

Mar 6, 2018

3:00 pm

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Tuesday

Mar 13, 2018

3:00 pm

No Meeting Spring Break
Tuesday

Mar 20, 2018

3:00 pm

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Tuesday

Mar 27, 2018

3:00 pm

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Tuesday

Apr 3, 2018

3:00 pm

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Tuesday

Apr 10, 2018

3:00 pm

no seminar this week
Tuesday

Apr 17, 2018

3:00 pm

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Tuesday

Apr 24, 2018

3:00 pm

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Tuesday

May 1, 2018

3:00 pm

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Archived Schedules

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