We are pleased to announce this week’s Research Scholar Seminar.

Seminar Details:

• Speaker: Patil Jatin Suresh

• Title: A Short Look at Braids in Knot Theory

• Date & Time: Wednesday, 23 September 2025 , 5:00 – 6:00 PM

• Venue: A-507

Abstract:

Braids show up in many walks of life. These can be formulated, in geometric and algebraic ways, to mimic the real-life braids. This specific formulation of braids and their closures, ends up being relevant in representing Knots and Links. We would be looking at this formulation in the specified forms, and seeing how it relates to knots and links. Specifically, we would be looking at:

1. Alexander’s Theorem, which states that every knot or link can be represented by a braid, and

2. Markov’s Theorem, which, similar to Reidemeister’s Theorem for Equivalence for Knots/Links, states that closures of two braids are equivalent iff they can be connected via a sequence of moves.

References:

[1] Colin C. Adams. The knot book. An elementary introduction to the mathematical theory of knots, Revised reprint of the 1994 original. American Mathematical Society, Providence, RI, 2004, pp. xiv+307.
[2] Gerhard Burde, Heiner Zieschang, and Michael Heusener. Knots. Berlin, Boston: De Gruyter, 2013. isbn: 9783110270785. doi: doi : 10 . 1515 /9783110270785. url: https://doi.org/10.1515/9783110270785.
[3] Joan S. Birman and Tara E. Brendle. Braids: A Survey. 2005. arXiv: math/0409205 [math.GT]. url: https://arxiv.org/abs/math/0409205.

All are cordially invited to attend the seminar.