Department of Mathematics

Uppsala University

These lectures are directed to a general audience of PhD students.

The series is named after Professor Matts Essén (1932-2003), who worked at Uppsala until his retirement 1997

Knot polynomials and knot homologies

POSTER

A knot polynomial is an invariant that assigns a polynomial to each knot in S^3. For a long time, only

one such invariant was known - the Alexander polynomial. In the early 80's the work of Jones, Witten,

Reshetikhin, and Turaev led to the systematic construction of many more knot polynomials.

In the last 20 years, there has been a great deal of research on "categorifying" these knot polynomials,

starting with Khovanov's famous categorification of the Jones polynomial.

In these lectures, I will first define some knot polynomials and give some of their classical

applications. Then, I'll explain some things about their categorifications, including Khovanov homology

and knot Floer homology, and give some applications of these as well.

**Schedule** (June 12-16, 2017):

10.15 - 11.00 Lecture

11.15 - 12.00 Lecture

13.30 - 14.30 Lecture/Problem Session

**Venue: **Room 4006, Ĺngströmlaboratoriet, Uppsala

There will be one written assignment. The course gives 3 ECTS credits.

**Event's Dinner: **Friday 17.00 at Peppar Peppar

**Lunches: **Monday-Friday 12.20 at Eklundshof

**Registration is closed.**

**Registered Participants:**

Johan Asplund (Uppsala)

Samuel Edwards (Uppsala)

Love Forsberg (Uppsala)

Oleksandra Gasanova (Uppsala)

Marco Golla (Uppsala)

Nikolaos Iakovidis (Uppsala)

Helena Jonsson (Uppsala)

Lisa Lokteva (Uppsala)

Maksim Maydanskiy (Uppsala)

Volodymyr Mazorchuk (Uppsala)

Filipe Mussini (Uppsala)

Gleb Nenashev (Stockholm)

Andrea Pasquali (Uppsala)

Jacob Rasmussen (Cambridge)

Andreas Rocén (Uppsala)

Johanna Strömberg (Uppsala)

Laertis Vaso (Uppsala)

Evgeny Volkov (Uppsala)

Tilo Wiklund (Uppsala)

Jakob Zimmermann (Uppsala)

Xiaoting Zhang (Uppsala)

--------------------------------------------------------------------------------------------------

Previous lectures:

2016 Christian Krattenthaler (Vienna) The art of bijection

2015 Wilhelm Schlag (Chicago) An introduction to nonlinear wave equation

2014 Francois Baccelli (Austin) Stochastic geometry

2013 Alexander Kleshchev (Oregon) The symmetric group: its combinatorics, representations and applications

2012 Jens Marklof (Bristol) Emerging applications of homogeneous dynamics: From discrete mathematics to statistical physics