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DTSTAMP;TZID=America/Vancouver:20221205T140000
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UID:20221205T140000@prima2022.primamath.org
SUMMARY:Khovanov homology and four-dimensional topology
DESCRIPTION:Over the last forty years, most progress in four-dimensional topology came
from gauge theory and related invariants. Khovanov homology is an invariant of
knots in R^3 of a different kind: its construction is combinatorial, and
connected to ideas from representation theory. There is hope that it can tell
us more about smooth 4-manifolds; for example, Freedman, Gompf, Morrison and
Walker suggested a strategy to disprove the 4D Poincare conjecture using
Rasmussen’s invariant from Khovanov homology. It is yet unclear whether their
strategy can work. I will explain a new attempt to pursue it (joint work with
Lisa Piccirillo) and some of the challenges we encountered. I will also review
other topological applications of Khovanov homology, with regard to smoothly
embedded surfaces in 4-manifolds.

STATUS:CONFIRMED
LOCATION:Grand Ballroom
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