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Timetable (HTLW03)

Physics and knot homologies

Monday 10th April 2017 to Thursday 13th April 2017

Monday 10th April 2017
09:00 to 09:50
Registration
09:50 to 10:00
Welcome from Christie Marr (INI Deputy Director)
10:00 to 11:00
Cumrun Vafa (Harvard University); (Harvard University)
String Theory and Homological Invariants for 3-Manifolds
In this talk I review the recent progress made in defining homological invariants for 3-manifold using string theory constructions.  This generalizes the constructions of homological invariants for knots using M5 branes, to the case of 3-manifolds.
INI 1
11:00 to 11:30
Morning Coffee
11:30 to 12:30
Daniel Roggenkamp (Universität Mannheim); (Universität Mannheim)
tba
INI 1
12:30 to 13:30
Lunch @ Wolfson Court
13:30 to 14:30
Andrea Brini (Imperial College London); (CNRS (Centre national de la recherche scientifique))
tba
INI 1
15:30 to 16:00
Afternoon Tea
16:00 to 17:00
Anna Beliakova (Universität Zürich)
tba
INI 1
17:00 to 18:00
Welcome Wine Reception
Tuesday 11th April 2017
10:00 to 11:00
Jørgen Andersen (Aarhus Universitet)
tba
INI 1
11:00 to 11:30
Morning Coffee
11:30 to 12:30
Matthew Hogancamp (University of Southern California)
tba
INI 1
12:30 to 13:30
Lunch @ Wolfson Court
13:30 to 14:30
Piotr Kucharski (University of Warsaw)
Knots, (extremal) A-polynomials, and BPS invariants
Co-author: Piotr Sulkowski (University of Warsaw, Caltech)

In this talk I will introduce a new class of algebraic curves called extremal A-polynomials of a knot and use it to describe BPS invariants introduced by Labastida, Marino, Ooguri, and Vafa.

I will present results obtained from the analysis of both classical and quantum extremal A-polynomials. The first lead to exact formulas for BPS invariants imposing nontrivial integrality statements in number theory. The latter enabled us to construct the combinatorial model for calculating BPS invariants.

I will also indicate how these results relate to the formalism of quivers introduced in the talk by Piotr Sulkowski.
INI 1
14:30 to 15:30
Ramadevi Pichai (Indian Institute of Technology)
Arborescent knots, mutants - current status on their invariants
Computation of colored HOMFLY-PT polynomials for knots carrying arbitrary representations is still a challenging problem. First I will recapitulate the necessary tools for determining the colored knot invariant within Chern-Simons theory. Then, I will present our results on quantum Wigner 6j useful for writing polynomial form of the knot invariant. Further, we will discuss our results for mutant knot pairs. Finally, we summarize the current status on these polynomials which we periodically update on the website http://knotebook.org
INI 1
15:30 to 16:00
Afternoon Tea
16:00 to 17:00
Paul Wedrich (Imperial College London)
tba
INI 1
Wednesday 12th April 2017
10:00 to 11:00
Pavel Putrov (Institute for Advanced Study, Princeton)
tba
INI 1
11:00 to 11:30
Morning Coffee
11:30 to 12:30
Tobias Ekholm (Uppsala Universitet); (Institut Mittag-Leffler)
Higher genus knot contact homology and recursion for the colored HOMFLY polynomial
We present a conjectural description of Legendrian symplectic field theory for the conormal of a knot ("higher genus knot contact homology") and discuss its relation to the recursion relation for the colored HOMFLY polynomial. This reports on joint work with Lenny Ng. 
INI 1
12:30 to 13:30
Lunch @ Wolfson Court
13:30 to 17:00
Free Afternoon
19:30 to 22:00
Formal Dinner at Trinity College
Thursday 13th April 2017
10:00 to 11:00
Mohammed Abouzaid (Columbia University)
tba
INI 1
11:00 to 11:30
Morning Coffee
11:30 to 12:30
Piotr Sulkowski (Universiteit van Amsterdam)
BPS states, knots and quivers
I will present a surprising relation between knot invariants and quiver representation theory, motivated by various string theory constructions involving BPS states. Consequences of this relation include the proof of the famous Labastida-Marino-Ooguri-Vafa conjecture, explicit (and unknown before) formulas for colored HOMFLY polynomials for various knots, new viewpoint on knot homologies, new dualities between quivers, and many others.
INI 1
12:30 to 13:30
Lunch @ Wolfson Court
13:30 to 14:30
Alexey Sleptsov (ITEP (Institute for Theoretical and Experimental Physics))
tba
INI 1
14:30 to 15:30
Amer Iqbal (Abdus Salam School of Mathematical Sciences GC University)
tba
INI 1
15:30 to 16:00
Afternoon Tea
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons