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.

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 HenrichSeattle 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: Abstract: Tuesday Nov 7, 2017 3:00 pm Radmila Sazdanovic North Carolina State University Title: Abstract: 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: Abstract: Tuesday Nov 28, 2017 3:00 pm James Conant Title: Abstract: Tuesday Dec 5, 2017 3:00 pm Dave Bachman Pitzer College Title: Abstract:

Spring 2018 Schedule

special days, times or locations are in red

 Date Speaker Title and Abstract Tuesday Jan 23, 2018 3:00 pm Title: Abstract: Tuesday Jan 30, 2018 3:00 pm Title: Abstract: Tuesday Feb 6, 2018 3:00 pm Title: Abstract: Tuesday Feb 13, 2018 3:00 pm Title: Abstract: Tuesday Feb 20, 2018 3:00 pm Title: Abstract: Tuesday Feb 27, 2018 3:00 pm Title: Abstract: Tuesday Mar 6, 2018 3:00 pm Title: Abstract: Tuesday Mar 13, 2018 3:00 pm No Meeting Spring Break Tuesday Mar 20, 2018 3:00 pm Title: Abstract: Tuesday Mar 27, 2018 3:00 pm Title: Abstract: Tuesday Apr 3, 2018 3:00 pm Title: Abstract: Tuesday Apr 10, 2018 3:00 pm no seminar this week Tuesday Apr 17, 2018 3:00 pm Title: Abstract: Tuesday Apr 24, 2018 3:00 pm Title: Abstract: Tuesday May 1, 2018 3:00 pm Title: Abstract:

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