Events
Department of Mathematics and Statistics
Texas Tech University
 | Wednesday
Sep. 30
4 PM
online
|
| Applied Mathematics and Machine Learning
TBA
Amirpasha Kamalhedayat
Department of Aerospace Engineering, University of Michigan
|
Abstract: TBA
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied
The Links–Gould (LG) polynomials are two-variable link invariants arising from the quantum supergroup $U_q(\mathfrak{sl}(2|1))$, exhibiting hybrid behavior between the Jones and Alexander polynomials. I will survey some recent results illustrating this theme.
The basic LG invariant provides a lower bound on the Seifert genus and this bound extends to its colored versions. It has been verified by Garoufalidis and Li that the 2-colored Links–Gould polynomial detects the genus for all 352.2 million prime knots with up to 19 crossings. We also prove a conjecture of Geer and Patureau-Mirand that the Links–Gould invariant admits a specialization to the Akutsu–Deguchi–Ohtsuki (ADO) invariant at a sixth root of unity. Finally, we establish analogs of Jones–Wenzl idempotents for LG and formulate an analog of the Fox conjecture, supported by computational evidence.
This is joint work, in various combinations, with Stavros Garoufalidis, Rinat Kashaev, Ben-Michael Kohli, Jiebo Song, Guillaume Tahar, and Emmanuel Wagner.
 | Thursday
Oct. 1
6:30 PM
Math 010
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| Mathematics Education
Math Circle
Burak Avsar
Mathematics and Statistics, Texas Tech University
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Outreach program for advanced middle and high school math students