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Winter school workshop


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16th January 2017 to 20th January 2017
Liam Watson University of Glasgow
Cameron Gordon
Adam Levine
Anthony Licata

Workshop Theme

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.

Deadline for applications: 1 November 2016

Apply now

Please note members of Cambridge University are welcome to turn up and sign in as a non-registered attendee on the day(s) during the workshop and attend the lecture(s). Please note that we cannot provide you with any support including name badge, meals or accommodation.

In addition to visiting the INI, there are multiple ways in which you can participate remotely.



Registration Only
  • Registration Package: £227
  • Student Registration Package: £177

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only
  • Formal Dinner: £50

Participants on the Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, the above charge will apply.


Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation. Please see the Hotels Combined website for a list of local hotels and guesthouses.



Lunch will be served at Wolfson Court in the Cafeteria from 12:30 to 13:30 on days that lectures take place.

  • Accommodation Package and Registration Package participants should present their badge as payment for their meal
  • Those issued with a blue Institute door entrance card can add money onto the card via the Porters' Lodge at Wolfson Court
  • Other participants must purchase their meal using their dining card via the Porters' Lodge (forms can be found on the registration desk or at the Porters' Lodge)

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner will take place On Wednesday 18th January, at Trinity College. Participants on the Registration Package, including organisers and speakers, are automatically included in this event.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons