Topology Seminar (past)
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Mon, 26/10/2009 15:45 |
Alex Coward (Oxford) |
Topology Seminar  |
L3 |
| 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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Mon, 19/10/2009 15:45 |
Dennis Sullivan (CUNY and Stony Brook) |
Topology Seminar |
L3 |
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Mon, 12/10/2009 15:45 |
Iain Aitchison (Melbourne) |
Topology Seminar |
L3 |
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Mon, 05/10/2009 15:45 |
Jacob Lurie |
Topology Seminar |
L3 |
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Thu, 18/06/2009 11:00 |
Ian Agol (Berkeley) |
Topology Seminar |
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| 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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Mon, 15/06/2009 15:45 |
Kevin Walker (Microsoft) |
Topology Seminar |
L3 |
| 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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Mon, 08/06/2009 15:45 |
Eric Guenter (Hawaii) |
Topology Seminar |
L3 |
| 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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Mon, 01/06/2009 15:45 |
Dr Cornelia Drutu (Oxford) |
Topology Seminar |
L3 |
| 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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Mon, 25/05/2009 00:00 |
Topology Seminar |
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Mon, 18/05/2009 15:45 |
Carl-Friedrich B¨odigheimer (Bonn) |
Topology Seminar |
L3 |
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Mon, 11/05/2009 15:45 |
Stefan Schwede (Bonn) |
Topology Seminar |
L3 |
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Mon, 04/05/2009 15:45 |
George Raptis (Oxford) |
Topology Seminar |
L3 |
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Mon, 27/04/2009 15:45 |
Andras Juhasz (Cambridge) |
Topology Seminar |
L3 |
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Mon, 30/03/2009 15:45 |
Soren Galatius (Stanford) |
Topology Seminar |
L3 |
| Let G be a compact semisimple Lie group. A classical paper of Atiyah and Bott (from 1982) studies the moduli space of flat G-bundles on a fixed Riemann surface S. Their approach completely determines the integral homology of this moduli space, using Morse theoretic methods. In the case where G is U(n), this moduli space is homotopy equivalent to the moduli space of holomorphic vector bundles on S which are "semi-stable". Previous work of Harder and Narasimhan determined the Betti numbers of this moduli space using the Weil conjectures. 20 years later, a Madsen and Weiss determined the homology of the moduli space of Riemann surfaces, in the limit where the genus of the surface goes to infinity. My talk will combine these two spaces: I will describe the homology of the moduli space of Riemann surfaces S, equipped with a flat G-bundle E -> S, where we allow both the flat bundle and the surface to vary. I will start by reviewing parts of the Atiyah-Bott and Madsen-Weiss papers. Our main theorem will then be a rather easy consequence. This is joint work with Nitu Kitchloo and Ralph Cohen. | |||
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Thu, 26/03/2009 14:00 |
Chen QingTao ((UC Berkeley)) |
Topology Seminar |
L3 |
| The colored HOMFLY polynomial is a quantum invariant of oriented links in S³ associated with a collection of irreducible representations of each quantum group U_q(sl_N) for each component of the link. We will discuss in detail how to construct these polynomials and their general structure, which is the part of Labastida-Marino-Ooguri-Vafa conjecture. The new integer invariants are also predicted by the LMOV conjecture and recently has been proved. LMOV also give the application of Licherish-Millet type formula for links. The corresponding theory of colored Kauffman polynomial could also be developed in a same fashion by using more complicated algebra method. In a joint work with Lin Chen and Nicolai Reshetikhin, we rigorously formulate the orthogonal quantum group version of LMOV conjecture in mathematics by using the representation of Brauer centralizer algebra. We also obtain formulae of Lichorish-Millet type which could be viewed as the application in knot theory and topology. By using the cabling technique, we obtain a uniform formula of colored Kauffman polynomial for all torus links with all partitions. Combined these together, we are able to prove many interesting cases of this orthogonal LMOV conjecture. | |||
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Thu, 26/03/2009 11:00 |
Jacob Lurie (MIT) |
Topology Seminar |
L3 |
| In this lecture, I will illustrate the cobordism hypothesis by presenting some examples. Exact content to be determined, depending on the interests of the audience. | |||
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Wed, 25/03/2009 11:00 |
Jacob Lurie (MIT) |
Topology Seminar |
L3 |
| In this lecture, I will give a more precise statement of the Baez-Dolan cobordism hypothesis, which gives a description of framed bordism (higher) categories by a universal mapping property. I'll also describe some generalizations of the cobordism hypothesis, which take into account the structure of diffeomorphism groups of manifolds and which apply to manifolds which are not necessarily framed. | |||
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Tue, 24/03/2009 11:00 |
Jacob Lurie (MIT) |
Topology Seminar |
L3 |
| In this lecture, I'll give an overview of some ideas from higher category theory which are needed to make sense of the Baez-Dolan cobordism hypothesis. If time permits, I'll present Rezk's theory of complete Segal spaces (a model for the theory of higher categories in which most morphisms are assumed to be invertible) and explain how bordism categories can be realized in this framework. | |||
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Mon, 23/03/2009 15:45 |
Jacob Lurie (MIT) |
Topology Seminar |
L2 |
| In this lecture, I will review Atiyah's definition of a topological quantum field theory. I'll then sketch the definition of a more elaborate structure, called an "extended topological quantum field theory", and describe a conjecture of Baez and Dolan which gives a classification of these extended theories. | |||
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Mon, 16/03/2009 15:45 |
Mike Hopkins (Harvard) |
Topology Seminar |
L3 |
