Student 3-manifold seminar, Spring 2024

Meeting time: Wednesdays 10-11am @ 732 Evans

Organizers: Ethan Dlugie and Qiuyu Ren

Date	Speaker	Title
24 Jan 2024		Organizational meeting
31 Jan 2024	Ethan Dlugie	The Burau representation and shapes of polyhedra
7 Feb 2024	Qiuyu Ren	Generalized Poincaré conjectures and Milnor's exotic 7-spheres
14 Feb 2024	Audrey Rosevear	The Giroux correspondence
21 Feb 2024	Ethan Dlugie	Isogenies, ping-pong, and Banach-Tarski
28 Feb 2024	Gabriel Beiner	The Casson invariant and instanton Floer homology for homology 3-spheres
13 Mar 2024	Qiuyu Ren	Constructions of homotopy 4-spheres
3 Apr 2024	Galen Liang	Defining ECH with examples and applications I
10 Apr 2024	Matthew Palani Lideros	A Survey of quantum invariants
17 Apr 2024	Galen Liang	Defining ECH with examples and applications II
24 Apr 2024	Audrey Rosevear	Geodesic laminations and the Thurston-Nielsen classification theorem

Past semesters

Fall 2023

This semester we have quantum topology as a central theme.

Date	Speaker	Title
31 Aug 2023		Organizational meeting
7 Sep 2023	Ethan Dlugie	Knots and braids, in preparation for quantum invariants
14 Sep 2023	Qiuyu Ren	Jones polynomial as a trace
21 Sep 2023	Nancy Eagles	Unknotting knots and the Jones polynomial
28 Sep 2023	John Nolan	The Jones polynomial for a torus knot
5 Oct 2023	John Lentfer	Hecke algebra representations and Ocneanu’s trace
12 Oct 2023	Elliot Kienzle	Gauge theory for knots: three perspectives on the linking number
19 Oct 2023	Elliot Kienzle	Topological quantum field theories and the Jones Polynomial
26 Oct 2023	Larsen Linov	How to make a rubber band bracelet
2 Nov 2023	Gabriel Beiner	Chern-Simons theory and the Wess-Zumino-Witten model
9 Nov 2023	Matthew Palani Lideros	Quantum representations of mapping class groups
16 Nov 2023	Qiuyu Ren	Witten-Reshetikhin-Turaev invariants via skein theory, colored Jones polynomial, and related conjectures
30 Nov 2023	Qiuyu Ren	Witten-Reshetikhin-Turaev invariants via skein theory, colored Jones polynomial, and related conjectures II

References: (* indicates expository papers or lecture notes)

Jones polynomial:
V. Jones, Jones polynomial for dummies*
V. Jones, A polynomial invariant for knots via von Neumann algebras
V. Jones, Hecke algebra representations of braid groups and link polynomials
S. Sawin, Links, Quantum Groups, and TQFT's*
(Witten-)Reshetikhin-Turaev invariants:
N. Yu. Reshetikhin, V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups
R. C. Kirby, P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,C)
E. Witten, Quantum field theory and the Jones polynomial
Colored Jones polynomial:
N. Yu. Reshetikhin, V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups
S. Garoufalidis, T. T. Lê, The colored Jones function is q-holonomic
Volume conjecture:
H. Murakami, An Introduction to the Volume Conjecture*
A blog post* by D. Moskovich
R. M. Kashaev, A link invariant from quantum dilogarithm
H. Murakami and J. Murakami, The colored Jones polynomials and the simplicial volume of a knot
Q. Chen, T. Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants
(Kauffman bracket) skein modules of 3-manifolds:
J. H. Przytycki, Fundamentals of Kauffman bracket skein modules*
J. H. Przytycki, Skein modules of 3-manifolds
Skein TQFT:
C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Topological quantum field theories derived from the Kauffman bracket
C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Three-manifold invariants derived from the Kauffman bracket
General/Miscellancy:
L. H. Kauffman, S. L. Lins, Temperley–Lieb recoupling theory and invariants of 3-manifolds*
T. Ohtsuki, Quantum invariants. A study of knots, 3-manifolds, and their sets*
L. Kauffman, Quantum topology and quantum computing*
E. Witten, Quantum field theory and the Jones polynomial
M. F. Atiyah, The geometry and physics of knots*
S. Sawin, Links, Quantum Groups, and TQFT's*
B. Bakalov, A. Kirillov jun., Lectures on tensor categories and modular functors*

Ancient semesters

You can find lists of further past talks in the student 3-manifold seminar here (Fall 2021 - Spring 2023) and here (Spring 2019 - Spring 2020).