Graduate Student Seminars

Fall 2018

Title:Khovanov homology and the PS braid conjecture

Speaker: Sujoy Mukherjee - GWU
Date and TimeFriday, November 16, 2:00-3:00pm
Place: Rome 206
Abstract: In 1984, knot theory was revolutionized with the discovery of the Jones polynomial. Fifteen years later, with several questions about it still unanswered, the polynomial was categorified into what is presently known as Khovanov homology (KH). The idea of KH is to associate a bigraded chain complex to a link whose homology is an invariant of the link itself. Additionally, the Euler characteristic of this chain complex, when interpreted appropriately, is the Jones polynomial.

Parts of the PS braid conjecture state that the order of the torsion subgroups in the KH of a closed braid is less or equal to its braid index. In 2017, with the discovery of links with large even torsion subgroups in their KH, this statement was resolved. At the same time, for the case of odd torsion subgroups, the first infinite families of knots and links with odd torsion subgroups up to \mathbb{Z}_7 were introduced.

In this talk, after providing a short introduction to KH, we will focus on knots and links with larger odd torsion subgroups than \mathbb{Z}_7, like \mathbb{Z}_9, \mathbb{Z}_{27}, and \mathbb{Z}_{25}. Additionally, we will discuss other recent developments in the study of torsion in KH.

Speakers: Valentina Harizanov, Xiaofeng Ren, GWU
Date and Time: Friday, November 2, 2-3PM
Place: Rome Hall (801 22nd Street), Room 206
Abstract: Professors Valentina Harizanov and Xiaofeng Ren will each give half hour talks about their research interests intended to give graduate students thoughts about for future areas of research.

Title:give us an idea of their research interests

Speaker: Lowell Abrams and Joel Lewis - GWU
Date and TimeFriday, October 26, 2:00-3:00pm
Place: Rome 206
Abstract:Professors Abrams and Lewis will each speak for a half hour to give us an idea of their research interests

Title:Utilizing Mathematica, Wolfram|Alpha, and other Wolfram technologies for teaching and research

Speaker: Andrew Dorsett of Wolfram Research about the Mathematica software
Date and TimeFriday, September 28, 2:00-3:00pm
Place: Rome 206
Abstract: I will begin with a technical overview of Mathematica, as well as briefly touching on the creation of Wolfram|Alpha. Next, we can discuss emerging trends in technology and what is currently available (or being developed) to support those trends. Then, to give you a sense of what's possible, I'll discuss how other organizations use these tools for teaching and research.