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February 2017

Peter Lambert-Cole (Indiana), Triangle Topology Seminar

February 21, 2017 @ 3:00 pm - 4:00 pm

There will be two talks; one at 3:00 pm and the second talk will be at 4:15 pm. Title: Conway mutation and knot Floer homology Abstract: Mutant knots are notoriously hard to distinguish. Many, but not all, knot invariants take the same value on mutant pairs. Khovanov homology with coefficients in Z/2Z is known to be mutation-invariant, while the bigraded knot Floer homology groups can distinguish mutants such as the famous Kinoshita-Terasaka and Conway pair. However, Baldwin and Levine conjectured that…

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March 2017

Laura Starkson (Stanford University), Triangle Topology Seminar

March 6, 2017 @ 3:15 pm - 4:15 pm

Title:  Manipulating singularities of Weinstein skeleta Abstract: Weinstein manifolds are an important class of symplectic manifolds with convex ends/boundary. These 2n dimensional manifolds come with a retraction onto a core n-dimensional stratified complex called the skeleton, which generally has singularities. The topology of the skeleton does not generally determine the smooth or symplectic structure of the 2n dimensional Weinstein manifold. However, if the singularities fall into a simple enough class (Nadler’s arboreal singularities), the whole Weinstein manifold can be recovered…

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April 2017

Dorothy Buck (Imperial College London), Triangle Topolgy Seminar

April 4, 2017 @ 4:30 pm - 5:30 pm

Title:  Knotted DNA Abstract: The central axis of the famous DNA double helix is often topologically constrained or even circular. The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function is to change the DNA axis topology -- for example converting a torus link into an unknot. Additionally, there are several protein families that change the axis topology as a by-product of their interaction with DNA.…

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October 2017

Slava Krushkal (University of Virginia), Triangle Topology Seminar

October 2, 2017 @ 4:30 pm - 5:30 pm

Location: SAS 1102 at North Carolina State University, 4:30 pm Title: Flow and Yamada polynomials, planar triangulations, and TQFT Abstract: In the 1960s Tutte observed that the value of the chromatic polynomial of planar triangulations at (golden ratio +1) obeys a number of remarkable properties. In this talk I will explain how TQFT gives rise to a conceptual framework for studying planar triangulations. I will discuss several extensions of Tutte's results and applications to the structure of the chromatic and flow polynomials…

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November 2017

Faramarz Vafaee (California Institute of Technology), Triangle Topology Seminar

November 7, 2017 @ 4:30 pm - 5:30 pm

Title: The prism manifold realization problem Abstract:  The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in the three-sphere. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized by a pair of relatively prime integers p > 1 and q. We determine a complete list of prism…

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January 2018

, Triangle Topology Seminar

January 23, 2018 @ 4:30 pm - 5:00 pm

Speaker: Title: Abstract:

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March 2018

Adam Saltz, University of Georgia – Topology Seminar

March 26, 2018 @ 3:15 pm - 4:30 pm

3:15 pm in Physics 119 at Duke University Title: Link homology and Floer homology in pictures by cobordisms Abstract: There are no fewer than eight link homology theories which admit spectral sequences from Khovanov homology. These theories have very different origins -- representation theory, gauge theory, symplectic topology -- so it's natural to ask for some kind of unifying theory. I will attempt to describe this theory using Bar-Natan's pictorial formulation of link homology. This strengthens a result of Baldwin, Hedden, and…

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April 2018

Melissa Zhang, Boston College – Triangle Topology Seminar

April 2, 2018 @ 3:15 pm - 4:30 pm

Physics 119 at Duke University, at 3:15 pm Speaker: Melissa Zhang, Boston College Title: Annular Khovanov homology and 2-periodic links Abstract: I will exhibit a spectral sequence from the annular Khovanov homology of a 2-periodic link to that of its quotient, which in turn proves rank inequalities and decategorifies to polynomial congruences. While previous work used heavier algebraic machinery to prove this rank inequality in a particular sl_2 weight space grading, we instead mimic Borel's construction of equivariant cohomology and employ grading…

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September 2018

Matt Stoffregen, MIT – Triangle Topology Seminar

September 25, 2018 @ 4:30 pm - 5:30 pm

Location: 332 Phillips Hall, 4:30 pm - 5:30 pm Speaker: Matt Stoffregen, MIT Title: Localization in Khovanov Homology Abstract: For periodic links, we show that the Khovanov space of Lipshitz-Sarkar admits a natural cyclic group action, and identify its fixed point set. As an application, we prove that the Khovanov homology (with coefficients in the field of p elements) of a p-periodic link has rank greater than or equal to that of the annular Khovanov homology of the quotient link. This is joint…

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October 2018

Adam Lowrance, Vassar College, & Min Hoon Kim, Korea Institute for Advanced Study – Triangle Topology Seminar

October 16, 2018 @ 3:30 pm - 6:00 pm

Triangle Topology Seminar Location: SAS 2102, North Carolina State University 3:30 pm – 4:30 pm Speaker: Adam Lowrance, Vassar College Title: Gordian distance and spectral sequences in Khovanov homology Abstract: The Gordian distance between two knots is the fewest number of crossing changes necessary to transform one knot into the other. Khovanov homology is a categorification of the Jones polynomial that comes equipped with several spectral sequences. In this talk, we show that the page at which some of these…

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