Homology theories in low dimensional topology
Created: | 2017-02-03 13:41 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |
Editors' group: | SMS Editors group for the Newton Institute |
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 |
Media items
This collection contains 88 media items.
Media items
2-representations of braid groups, continued
53 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
13 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
31 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
33 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
17 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
48 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
40 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
17 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
26 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
12 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
77 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
25 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
29 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
36 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
61 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
30 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
42 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
20 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
58 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
28 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