HTLW01
16 January 2017 to 20 January 2017
The first event of the INI program Homology theories in low-dimension will be a week-long winter school, running January 16-20 2017, targeted at graduate students and early career researchers. There will be three distinct streams, organized to reflect the focus of the program as a whole. The anticipated streams are as follows:
Topics in Floer homology
Stream leader: Adam Levine, (Princeton University)
Additional lectures by: Liam Watson (University of Glasgow)
This lecture stream will begin with an overview of Heegaard Floer homology, before turning to the main focus: bordered Floer homology. This relatively new suite of invariants gives rise to powerful cut-and-paste tools for studying the Heegaard Floer homology of closed three-manifolds. Particular focus will be given to the case of manifolds with torus boundary, towards describing applications to knot Floer homology and to the study of L-spaces — those manifolds with simplest possible Heegaard Floer homology.
Structures on three-manifolds
Stream leader: Cameron Gordon, (University of Texas at Austin)
Additional lectures by: Rachel Roberts (Washington University in St-Louis), Andy Wand (University of Glasgow)
This lecture stream will give an overview of foliations and left-orderable three-manifold groups, with a view to describing the state of the art in an emerging relationship: for a closed, orientable, prime three-manifold Y, it is conjectured that the existence of a taut foliation foliation on Y, the existence of a left-order on the fundamental group of Y, and the condition that Y not be an L-space are equivalent. This latter condition comes from Heegaard Floer homology, and this will result in an important point of interaction with the stream Topics in Floer homology.
Aspects of geometric representation theory
Stream leader: Anthony Licata, (Australian National University)
Additional lectures by: Eli Grigsby (Boston College), Jacob Rasmussen (University of Cambridge)
This lecture stream aims to describe some of the representation theory which motivates and is used in constructions of knot homology theories. We will focus on the representation theory of sl(2) and its quantized enveloping algebra, and the first lectures will recall the structure theory of finite dimensional Lie algebras, quantum groups and skew Howe duality. We will then explain how in the case of sl(2), this representation theory gives rise to the Jones polynomial, and how constructions in geometric and categorical representation theory can be used to upgrade constructions of the Jones polynomial to constructions of Khovanov homology. The latter part of the lecture series will describe how sl(2) appears again as an internal structure in the annular version of Khovanov homology.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Winter school workshop, where work on this paper was undertaken. This work was supported by EPSRC grant EP/K032208/1.
Monday 16th January 2017 | |||
---|---|---|---|
09:00 to 09:50 | No Room Required | ||
09:50 to 10:00 | No Room Required | ||
10:00 to 11:00 |
Adam Levine Princeton University |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Cameron Gordon University of Texas at Austin |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:30 to 15:30 |
Cameron Gordon University of Texas at Austin |
Room 1 | |
15:30 to 16:00 | No Room Required | ||
16:00 to 17:00 |
Andy Wand University of Glasgow |
Room 1 | |
17:00 to 18:00 | No Room Required |
Tuesday 17th January 2017 | |||
---|---|---|---|
09:00 to 10:00 |
Adam Levine Princeton University |
Room 1 | |
10:00 to 11:00 |
Adam Levine Princeton University |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Cameron Gordon University of Texas at Austin |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:30 to 15:30 |
Anthony Licata Australian National University |
Room 1 | |
15:30 to 16:00 | No Room Required | ||
16:00 to 17:00 |
Andy Wand University of Glasgow |
Room 1 |
Wednesday 18th January 2017 | |||
---|---|---|---|
09:00 to 10:00 |
Adam Levine Princeton University |
Room 1 | |
10:00 to 11:00 |
Adam Levine Princeton University |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Eli Grigsby Boston College |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:30 to 15:30 |
Anthony Licata Australian National University |
Room 1 | |
15:30 to 16:00 | No Room Required | ||
16:00 to 17:00 |
Rachel Roberts Washington University in St. Louis |
Room 1 | |
19:30 to 22:00 | Room 1 |
Thursday 19th January 2017 | |||
---|---|---|---|
09:00 to 10:00 |
Adam Levine Princeton University |
Room 1 | |
10:00 to 11:00 |
Adam Levine Princeton University |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Eli Grigsby Boston College |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:30 to 15:30 |
Eli Grigsby Boston College |
Room 1 | |
15:30 to 16:00 | No Room Required | ||
16:00 to 17:00 |
Rachel Roberts Washington University in St. Louis |
Room 1 |
Friday 20th January 2017 | |||
---|---|---|---|
09:00 to 10:00 |
Liam Watson |
Room 1 | |
10:00 to 11:00 |
Liam Watson |
Room 1 | |
11:00 to 11:30 | No Room Required | ||
11:30 to 12:30 |
Jacob Rasmussen University of Cambridge |
Room 1 | |
12:30 to 13:30 | No Room Required | ||
13:30 to 14:30 | Room 1 | ||
14:30 to 15:30 |
Anthony Licata Australian National University |
Room 1 | |
15:30 to 16:00 | No Room Required | ||
16:00 to 17:00 |
Rachel Roberts Washington University in St. Louis |
Room 1 |
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