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October 2019

Topology Seminar: Jesse Levitt (USC)

October 1, 2019 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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Title: Understanding Structure in the Single Variable Knot Polynomials Abstract: We examine the dimensionality and internal structure of the aggregated data produced by the Alexander, Jones, and Z0 polynomials using topological data analysis and dimensional reduction techniques. By examining several families of knots, including over 10 million distinct examples, we find that the Jones data is well described as a three dimensional manifold, the Z0 data as a single two dimensional manifold and the Alexander data as a collection of two dimensional manifolds. We confirm each of these…

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Topology Seminar: Mauricio Gomez Lopez (U. Oregon)

October 8, 2019 @ 3:00 pm - 4:00 pm

Title: Cobordism Categories and Spaces of Manifolds. Abstract: Cobordisms have been one of the central objects in topology since the pioneering work of Rene Thom, which provided the first link between manifolds and homotopy theory. In more recent years, there has been much focus on cobordism categories. These play a fundamental role in the study of topological quantum field theories and automorphism groups of manifolds.  A fundamental result in this field is the theorem of Galatius, Madsen, Tillmann, and Weiss,…

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November 2019

Paper Strip Knots (David Bachman)

November 5, 2019 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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I will discuss joint work with Jim Hoste, where we prove that a unique folded strip of paper can follow any polygonal knot with odd stick number. In the even stick number case there are either infinitely many, or none.

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Topology Triple-Header!

November 12, 2019 @ 2:30 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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This triple-header of topology talks will include three speakers: First, Hyeran Cho from The Ohio State University will speak about Derivation of Schubert normal forms of 2-bridge knots from (1,1)-diagrams. In this talk, we show that the dual (1, 1)-diagram of a (1, 1)-diagram (a.k.a. a two pointed genus one Heegaard diagram) D(a, 0, 1, r) with 1 ≤ r < 2a + 1 and gcd(2a + 1, r) = 1 is given by D(1/2r, 0, 2a+1-1/r, 1/r) when 1/r…

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December 2019

Dan Douglas (USC)

December 3, 2019 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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Abstract TBA

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Ryan Blair (Cal State Long Beach)

December 10, 2019 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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Abstract TBA

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January 2020

Stefano Vidussi (UCRiverside)

January 28 @ 3:00 pm - 4:00 pm

Title: The BNS invariant of the fundamental group of a surface bundle over a surface. Abstract: We will discuss some new results on the Bieri-Neumann-Strebel invariant of these groups, showing in particular that (with obvious exceptions) they algebraically fiber. As a corollary, we show that for "most" bundles these groups are not coherent.

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February 2020

Tommaso Cremaschi (USC)

February 4 @ 3:00 pm - 4:00 pm

Title: Volumes and filling collections of multicurves Abstract: In this talk we will be concerned with links L in a Seifert-Fibered space N such that their projection to the base surface is a collection of curves G in minimal position. After stating a hyperbolization result, for the complement of L, in terms of G we will study the volume of their complement and give combinatorial asymptotics. We will be particularly interested in the case where N is the projective tangent…

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Kenneth Millett (University of California, Santa Barbara)

February 18 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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Gordian Knots According to the legend of Phrygian Gordium, Alexander the Great cut the ``Gordian Knot’’ and eventually went on to rule Asia thereby fulfilling an ancient prophecy.  Where there are several descriptions of the precise nature of the Gordian Knot and Alexander’s action, an explicit mathematical treatment (the theory of thick knots) and the reasons for its contemporary interest will be discussed.  The first simple example of such a Gordian Knotted Structure supported by a rigorous mathematical analysis will be presented.…

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March 2020

Martin Bobb (UT Austin)

March 31 @ 3:00 pm - 4:00 pm
Millikan 2099, Pomona College, 610 N. College Ave.
Claremont, CA 91711 United States
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