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

June 12-16, 2017: Jacob Rasmussen (Cambridge)

Knot polynomials and knot homologies


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:

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