Low Dimensional Topology: Invariants of Links, Homology Theories, and Complexity

David Wood

  •  3 Jun 2024 - 21 Jun 2024
     8:00 am - 2:00 pm

Dionne Ibarra (Monash University)
Joan Licata (Australian National University)
Gabriel Montoya-Vega (CUNY Graduate Center, USA)

Program Description:
The three-week research program will bring together world leading specialists in different areas of knot theory, both from Australia and internationally, for a focused research program that will encourage collaboration between mathematicians at all career stages.

The first two weeks will be focused exclusively on research between small groups between five to seven people consisting of PhD students, early career researchers, and renowned scientists. Some of the research topics included are the generalization of the Kauffman-Harary conjecture, the long exact sequence of Khovanov homology, complexity of computing extreme Khovanov homology, and the interplay between characteristic varieties, skein modules, ?-polynomials, quantum invariants, and hyperbolic geometry.

The third week will consist of a conference with up to twenty participants in total. Specifically, the conference will focus on studying the latest trends on link invariants including virtual links, Khovanov homology, the colored Jones polynomial, and links in 3−manifolds. The participants and key speakers are carefully chosen considering their likely future research collaboration. Aiming to strengthen the diversity and gender equity in the scientific collaborations between the knot theory community in Australia and the rest of the world, amongst the participants there will be female early career researchers and female senior researchers, PhD students, and scientists from Australia, Europe, Asia, and the USA.

Program Structure: TBD


  • Deadline: 7 April 2024
  • Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
  • Arrival date: 2 June 2024
  • Departure date: 21 June 2024

This MATRIX research program is partially supported by AMSI and AustMS through the AMSI-AustMS Workshop Funding program, and benefits from the SMRI International Visitor Program.

MATRIX Wine and Cheese Afternoon 4 June 2024
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.