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Forthcoming events in this series
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Wick Rotation in Quantum Field Theory
Abstract
Physical space-time is a manifold with a Lorentzianmetric, but the more mathematical treatments of the theory usually prefer toreplace the metric with a positive - i.e. Riemannian - one. The passage fromLorentzian to Riemannian metrics is called 'Wick rotation'. In my talk I shallgive a precise description of what is involved, and shall explain some of itsimplications for physics.
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Cohomology jump loci, sigma-invariants, and fundamental groups of alge-
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Upper bounds onReidemeistermoves
Abstract
Given any two diagrams of the same knot or link, we
provide an explicit upper bound on the number of Reidemeister moves required to
pass between them in terms of the number of crossings in each diagram. This
provides a new and conceptually simple solution to the equivalence problem for
knot and links. This is joint work with Marc Lackenby.
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Characters and pushforward for differential K-theory with the Index theorem interpretation
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The virtual fibering conjecture and related questions
Abstract
Thurston asked a bold question of whether finite volume hyperbolic 3-manifolds might always admit a finite-sheeted cover which fibers over the circle. This talk will review some of the progress on this question, and discuss its relation to other questions including residual finiteness and subgroup separability, the behavior of Heegaard genus in finite-sheeted covers, CAT(0) cubings, the RFRS condition, and subgroups of right-angled Artin groups. In particular, hyperbolic 3-manifolds with LERF fundamental group are virtually fibered. Some applications of the techniques will also be mentioned.
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The Blob Complex
Abstract
We define a chain complex B_*(C, M) (the "blob complex") associated to an n-category C and an n-manifold M. This is in some sense the derived category version of a TQFT. Various special cases of the blob complex are
familiar: (a) if M = S^1, then the blob complex is homotopy equivalent to the Hochschild complex of the 1-category C; (b) for * = 0, H_0 of the blob complex is the Hilbert space of the TQFT based on C; (c) if C is a commutative polynomial ring (viewed as an n-category), then the blob complex is homotopy equivalent to singular chains on the configuration (Dold-Thom) space of M. The blob complex enjoys various nice formal properties, including a higher dimensional generalization of the Deligne conjecture for Hochschild cohomology.
If time allows I will discuss applications to contact structures on 3-manifolds and Khovanov homology for links in the boundaries of 4-manifolds. This is joint work with Scott Morrison.
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Decomposition complexity of metric spaces
Abstract
I shall describe the notion of finite decomposition complexity (FDC), introduced in joint work with Romain Tessera and Guoliang Yu on the Novikov and related conjectures. The talk will focus on the definition of FDC and examples of groups having FDC.
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The asymptotic geometry of mapping class groups and application
Abstract
I shall describe the asymptotic geometry of the mapping class
group, in particular its tree-graded structure and
its equivariant embedding in a product of trees.
This can be applied to study homomorphisms into mapping class
groups defined on groups with property (T) and on lattices in semisimple groups.
The talk is based upon two joint works with J. Behrstock, Sh. Mozes and M. Sapir.
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