Workshop on Volume Conjecture and related topics in Knot Theory

IISER Pune

Dec 17-21, 2018


Futher Reading

Schedule of Talks
Abstracts

Day: Monday Dec 17, Tuesday Dec 18, Wednesday Dec 19
Name: Abhijit Champanerkar, CUNY

Title: Hyperbolic knot theory

Further Reading:

Expository articles
Notes/Papers
  • Hyperbolic Geometry: The first 150 years by John Milnor
  • Hyperbolic Geometry by Cannon, Floyd, Kenyon, and Parry
  • Geometries of 3-manifolds by Peter Scott, Bulletin of LMS, 15 (1983) online.
  • Geometric structures on 3-manifolds by Francis Bonahon, Handbook of Geometric Topology, available online.
  • Hyperbolic knots by Colin Adams, http://arxiv.org/abs/math/0309466
  • Computation of Hyperbolic Structures in Knot Theory by Jeff Weeks, http://arxiv.org/abs/math/0309407
  • Hyperbolic Structures on Knot Complements by Callahan and Reid
  • Notes on Geometry and 3-Manifolds by Walter Neumann
Books
  • Thurston's Notes http://library.msri.org/books/gt3m/
  • An introduction to Geometric Topology by Bruno Martelli, available online.
  • Lectures on Hyperbolic Geometry by Benedetti and Petronio Springer-Verlag, ISBN 3-540-55534
  • Low-Dimensional Geometry by Francis Bonahon
  • Hyperbolic Knot Theory by Jessica Purcell
Computer Programs
Day: Tuesday Dec 18, Wednesday Dec 19
Name: Stefan Friedl, University of Regensburg

Title: An introduction to twisted Alexander polynomials

Further Reading:
Day: Thursday Dec 20, Friday Dec 21
Name: Shashank Kanade, University of Denver

Title: Rogers-Ramanujan-type identities and asymptotics

Further Reading:
    Books:

  • George E. Andrews, "The theory of partitions"
  • Andrew V. Sills, "An invitation to the Rogers-Ramanujan identities"


    • Surveys and Papers:

  • Basil Gordon and Richard J. McIntosh, "A survey of classical mock theta functions"
  • Richard J. McIntosh, "Some asymptotic formulae for q-hypergeometric series"
  • Masha Vlasenko and Sander Zwegers, "Nahm's conjecture: asymptotic computations and counterexamples"
  • Don Zagier, "The dilogarithm function",
  • Don Zagier, "Vassiliev invariants and a strange identity related to the Dedekind eta-function"
Day: Monday Dec 17, Tuesday Dec 18, Wednesday Dec 19
Name: Ilya Kofman, CUNY

Title: An introduction to the colored Jones polynomial

Further Reading:
  • Cromwell: Knots and links by Peter Cromwell
  • Lickorish: An introduction to knot theory by W.B.Raymond Lickorish.
  • Ohtsuki: Quantum Invariants by Tomotada Ohtsuki
  • Prasolov-Sossinsky: Knots, links, braids and 3-manifolds by V.V.Prasolov and A.B.Sossinsky
Day: Thursday Dec 20
Name: Rama Mishra, IISER Pune

Title: State Sum models for Colored Jones Polynomial

Further Reading:
Day: Wednesday Dec 19, Thursday Dec 20, Friday Dec 21
Name: Hitoshi Murakami, Tohoku University

Title: An Introduction to the Volume Conjecture and its generalizations, I, II, and III

Slides of talks: Talk 1   Talk 2   Talk 3  

Further Reading:
  • An Introduction to the Volume Conjecture by Hitoshi Murakami, arXiv:1002.0126
  • The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot by Hitoshi Murakami, arXiv:1402.2714
  • Volume conjecture for knots by Murakami, Hitoshi; Yokota, Yoshiyuki. SpringerBriefs in Mathematical Physics, 30. Springer, Singapore, 2018. ISBN: 978-981-13-1149-9
  • Formulas for computing colored Jones polynomials
Day: Monday Dec 17, Tuesday Dec 18
Name: Speaker: Visakh Narayanan, IISER Pune

Title: "Ribbon categories": invariant generating machines! I & II

Further Reading: Further Reading:
Day: Tuesday Dec 18, Wednesday Dec 19, Thursday Dec 20
Name: Kate Petersen, Florida State University

Title: Characters, Representations and the A-polynomial

Further Reading:
  • Thurston's Notes http://library.msri.org/books/gt3m/
  • Dunfield "Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds." Invent math 136 (1999) no. 3. 623-657.
  • Shalen: Representations of 3-manifold groups in the Handbook of Geometric Topology. (pdf on his webpage)
  • Cooper, Culler, Gillet, Long, Shalen: ”Plane curves associated to character varieties of 3-manifolds.” Invent. Math ('94).
  • Culler, Shalen "Varieties of group representations and splittings of 3-manifolds' Annals of math (2) 117 (1983) no. 1, 109-146.
Day: Monday Dec 17
Name: P. Ramadevi, IIT Mumbai

Title: Twist Knot Invariants and Volume Conjecture

Further Reading:
Day: Friday Dec 21
Name: Mahendar Singh, IISER Mohali

Title: Knot invariants from quandles.

Further Reading:

Organizers:

Rama Mishra (IISER Pune),

Abhijit Champanerkar (CUNY)

Tejas Kalelkar (IISER Pune)

Contact: ramamishra64 at gmail dot com