Martin Bobb (UT Austin)
TBA
TBA
The talk will concentrate on open questions related to the optimal bounds for the discrepancy of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl, K. Roth, and many others, […]
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 […]
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 […]
Abstract TBA
Abstract TBA
The bridge distance and the topological index are measures of the complexity of the bridge splitting of a knot. In 2016, Johnson and Moriah gave a formula for the bridge distance of the canonical bridge sphere of a knot in a highly twisted plat projection in terms of the height and the width of the […]
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, […]
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 […]
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 […]
Title: Biquandle Brackets and Knotoids Abstract: Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein relations with coefficients which are functions of biquandle colors at a crossing. In this talk we use biquandle brackets to enhance the biquandle counting matrix […]
One of the main drivers of current research in geometry is the classification of Calabi-Yau threefolds. Towards this effort, a particular approach in algebraic geometry is via the study of stability conditions. In this talk, I will explain what constitutes a notion of stability in algebraic geometry, and what the challenges are in studying them.