Homology theories in low dimensional topology

Homology theories in low dimensional topology's image
Created: 2017-02-03 13:41
Institution: Isaac Newton Institute for Mathematical Sciences
Description: The subject of homology theories in low-dimensional topology dates back to the work of Floer, and gained new breadth and vigour with the introduction of Khovanov homology fifteen years ago. Since then, these theories have had a far-reaching impact both in topology and more widely with analysts, algebraists, geometers, and physicists all contributing to and benefiting from their development. This programme will follow three broad themes:

The meaning of Floer homology: The programme will pursue and uncover intimate connections of Floer homology with underlying topological data. For example: the connection of Floer homology with the fundamental group by way of orderable groups, foliations, and related structures.
The meaning of quantum knot homologies: In comparison to Floer homology, the geometrical meaning of quantum knot homologies such as Khovanov homology remains relatively obscure. One natural place to look for such meaning is in physics, which has played an important role in this field ever since Witten interpreted the Jones polynomial in terms of Chern-Simons theory.
Quantum 3-manifold invariants: We hope to make significant progress towards, for example, lifting the numerical Reshetikhin-Turaev 3-manifold invariants to homological invariants. This should then provide a quantum counterpart to analytic invariants of smooth 4-manifolds.

Tying these three themes together will be a central focus of the programme. It has become apparent in recent years that one should think of quantum invariants as first-order approximations to Floer invariants. The programme aims to make relationships such as these more precise and general.



Figure from Ken Baker's Sketches of Topology blog
 

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2-representations of braid groups, continued

   39 views

Licata, A (Australian National University)
Friday 20th January 2017 - 14:30 to 15:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 7 Feb 2017


2-Verma modules and the Khovanov-Rozansky link homologies

   6 views

Vaz, P (Université Catholique de Louvain)
Thursday 29th June 2017 - 10:00 to 11:00

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 11 Jul 2017


3-manifold groups epimorphisms and rigidity

   30 views

Boileau, M (Université de Provence Aix Marseille 1)
Thursday 2nd February 2017 - 11:30 to 12:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 14 Feb 2017


A Gordon-Litherland form for ribbon surfaces

   26 views

Owens, B (University of Glasgow)
Thursday 2nd February 2017 - 15:30 to 16:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 14 Feb 2017


An Upsilon-like invariant from Khovanov-Rozansky homology

   4 views

Lewark, L
Tuesday 27th June 2017 - 13:30 to 14:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Thu 20 Jul 2017


Annular Khovanov-Lee theory and representation theory

   39 views

Grigsby, E (Boston College)
Thursday 19th January 2017 - 11:30 to 12:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 7 Feb 2017


Annular Khovanov-Lee theory of braid closures and braided surfaces

   36 views

Grigsby, E (Boston College)
Thursday 19th January 2017 - 14:30 to 15:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 7 Feb 2017


Arborescent knots, mutants - current status on their invariants

   13 views

Pichai, R (Indian Institute of Technology)
Tuesday 11th April 2017 - 14:30 to 15:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 18 Apr 2017


Around Chebyshev's polynomial and the skein algebra of the torus

   7 views

Queffelec, H
Monday 26th June 2017 - 16:00 to 17:00

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 19 Jul 2017


Bar Natan's deformation of Khovanov homology and involutive monopole Floer homology

   11 views

Lin, F (Princeton University)
Thursday 20th April 2017 - 15:15 to 16:15

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 28 Apr 2017


Bordered via curves and train tracks I

   68 views

Liam Watson
Friday 20th January 2017 - 09:00 to 10:00

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 7 Feb 2017


Boundary-reducing surgeries and bridge number

   24 views

Luecke, J (University of Texas at Austin)
Wednesday 1st February 2017 - 11:30 to 12:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 14 Feb 2017


BPS states of M5-brane on T^3

   26 views

Iqbal, A (Abdus Salam School of Mathematical Sciences GC University)
Thursday 13th April 2017 - 14:30 to 15:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 18 Apr 2017


BPS states, knots and quivers

   24 views

Sulkowski, P (Uniwersytet Warszawski, CALTECH (California Institute of Technology))
Thursday 13th April 2017 - 11:30 to 12:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 18 Apr 2017


Braid groups and their 2-representations

   49 views

Licata, A (Australian National University)
Tuesday 17th January 2017 - 14:30 to 15:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 6 Feb 2017


Braid monodromy, orderings, and transverse invariants

   27 views

Plamenevskaya, O (Stony Brook University)
Thursday 16th March 2017 - 15:15 to 16:15

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 20 Mar 2017


Branched covers of quasipositive links and L-spaces

   37 views

Boyer, S (UQAM - Université du Québec à Montréal)
Thursday 2nd February 2017 - 10:00 to 11:00

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 14 Feb 2017


Categorical diagonalization

   11 views

Hogancamp, M
Wednesday 28th June 2017 - 11:30 to 12:30

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Thu 20 Jul 2017


Categories of curved complexes for marked surfaces

   36 views

Zibrowius, C (University of Cambridge)
Thursday 18th May 2017 - 15:15 to 16:15

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 24 May 2017


Categorified knot invariants and algebraic geometry

   14 views

Negut, A (Massachusetts Institute of Technology)
Wednesday 28th June 2017 - 10:00 to 11:00

Collection: Homology theories in low dimensional topology

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 11 Jul 2017


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