3. Postdoctoral Program - MSRI

2 REPORT ON THE MSRI WORKSHOP “HOMOLOGY THEORIES OF KNOTS AND LINKS”
the subject continues to interact with classical questions in low-dimensional topology,
shedding new light on and solving old problems.
The aim of this program was both to explore progress within these three streams,
but also to study their interactions. It also benefitted greatly from its interactions
with the symplectic geometry program.
Owing in part to its richness and its promise as a new tool in low-dimensional
topology, link homology has attracted a large number of talented young mathematicians.
Thus, the program, bringing together these young researchers from all over
the world, along with the leaders in the field, proved to be beneficial both to the
professional development of those young researchers, and to to the development of
the subject.
2. Introductory workshop
The program began with a Connections to Women” workshop (Jan 21-22nd), organized
by Elisenda Grigsby, Olga Plamenevskaya, and Katrin Wehrheim. The program
Survey talks in the mornings will placed Khovanov and Heegaard Floer homology
in a broader context, focusing on both their applications to classical questions in
low-dimensional topology, and also connections to contact and symplectic topology.
Research talks in the afternoons will highlight the range of current activity in the
field. Speakers were (in chronological order): Eli Grigsby, Dusa McDuff, Heather
Russel, Carmen Caprau, Shelley Harvey, Gordana Matić, Vera Vértesi, Joan Licata,
Ina Petkova, and Sinem Onaran. Lectures included “Introduction to Floer Theory”
(by McDuff) “Contact Invariants in Heegaard Floer homology”(Matić), and “Introduction
to knot homology theories and categorification” (Grigsby).
This was followed by an introductory workshop (Jan 25-Jan 29th). oragnized
by Aaron Lauda, Robert Lipshitz, and Dylan Thurston. This workshop had three
mini-courses: one knot Floer homology and related topics, another on Khovanov and
Khovanov-Rozansky homology; and the third on categorification of quantum groups.
There were several stand-alone lectures in addition. For the mini-course on Heegaard
Floer homology, the speakers were Matt Hedden, Lenhard Ng, and András Juhász.
For the mini-course on Khovanov and Khovanov/Rozansky homology, the speakers
were Scott Morrison and Ben Webster. For the mini-course on Categorication of
Quantum Groups, the speakers were Sabin Cautis and Aaron Lauda.
We plan a format of no more than four talks each day to allow ample time for presentation
opportunities for younger researchers and formal and informal discussions.
3. Presentations and Seminars
The program included a post-doc seminar, and a research seminar, several learning
seminars (including a “Bordered Floer homology seminar working group”) and a
graduate students’ seminar. These seminars benefitted greatly from their interactions