Topology Seminar

Mon, 14/01/2008 14:45	Jessica Purcell (Oxford)	Topology Seminar	L3
	Volumes of knot complements
	The complement of a knot or link is a 3-manifold which admits a geometric structure. However, given a diagram of a knot or link, it seems to be a difficult problem to determine geometric information about the link complement. The volume is one piece of geometric information. For large classes of knots and links with complement admitting a hyperbolic structure, we show the volume of the link complement is bounded by the number of twist regions of a diagram. We prove this result for a large collection of knots and links using a theorem that estimates the change in volume under Dehn filling. This is joint work with Effie Kalfagianni and David Futer

Mon, 21/01/2008 14:45	Saul Schleimer (Warwick)	Topology Seminar	L3
	The arc complex is Gromov hyperbolic
	The arc complex is a combinatorial moduli space, very similar to the curve complex. Using the techniques of Masur and Minsky, as well as new ideas, I'll sketch the theorem of the title. (Joint work with Howard Masur.) If time permits, I'll discuss an application to the cusp shapes of fibred hyperbolic three-manifolds. (Joint work with David Futer.) We are planning to have dinner at Chiang Mai afterwards. If anyone would like to join us, please can you let me know today, as I plan to make a booking this evening. (Chiang Mai can be very busy even on a Monday.)

Mon, 28/01/2008 14:45	Ulrike Tillmann (Oxford)	Topology Seminar	L3
	n-categories in topology : paths and cobordisms

Mon, 04/02/2008 14:45	Tim Riley (Bristol)	Topology Seminar	L3
	Hydra groups
	I will describe a new family of groups exhibiting wild geometric and computational features in the context of their Conjugacy Problems. These features stem from manifestations of "Hercules versus the hydra battles." This is joint work with Martin Bridson.

Mon, 11/02/2008 14:45	Teruji Thomas (Oxford)	Topology Seminar	L3
	Quadratic forms and cobordisms
	Taking the intersection form of a 4n-manifold defines a functor from a category of cobordisms to a symmetric monoidal category of quadratic forms. I will present the theory of the Maslov index and some higher-categorical constructions as variations on this theme.

Mon, 18/02/2008 14:45	Luis Paris (Bourgogne)	Topology Seminar	L3
	Small index subgroups of the mapping class group

Mon, 25/02/2008 13:15	Jorgen Anderson (Aarhus)	Topology Seminar	L3
	Hitchin's connection and Kazhdan's property T

Mon, 25/02/2008 14:45	Arthur Bartels (Imperial)	Topology Seminar	L3
	Topological rigidity and word-hyperbolic groups
	The Borel conjecture asserts that aspherical manifolds are topologically rigid, i.e., every homotopy equivalence between such manifolds is homotopic to a homeomorphism. This conjecture is strongly related to the Farrell-Jones conjectures in algebraic K- and L-theory. We will give an introduction to these conjectures and discuss the proof of the Borel conjecture for high-dimensional aspherical manifolds with word-hyperbolic fundamental groups.

Mon, 25/02/2008 16:00	Eric Opdam (Amsterdam)	Topology Seminar	L3
	Representation theory of affine Hecke algebras and K-theory
	In recent joint work with Maarten Solleveld we could give a complete classification of the set the irreducible discrete series characters of affine Hecke algebras (including the non simply-laced cases). The results can be formulated in terms of the K-theory of the Schwartz completion of the Hecke algebra. We discuss these results and some related conjectures on formal dimensions and on elliptic characters.

Mon, 03/03/2008 14:45	Alex Muranov (Lyon)	Topology Seminar	L3
	Finitely generated simple groups of infinite commutator width.
	If $G$ is a group and $g$ an element of the derived subgroup $[G,G]$ , the commutator length of $g$ is the least positive integer $n$ such that $g$ can be written as a product of $n$ commutators. The commutator width of $G$ is the maximum of the commutator lengths of elements of $[G,G]$ . Until 1991, to my knowledge, it has not been known whether there exist simple groups of commutator width greater than $1$ . The same question for finite simple groups still remains unsolved. In 1992, Jean Barge and Étienne Ghys showed that the commutator width of certain simple groups of diffeomorphisms is infinite. However, those groups are not finitely generated. Finitely generated infinite simple groups of infinite commutator width can be constructed using "small cancellations." Additionally, finitely generated infinite boundedly simple groups of arbitrarily large (but necessarily finite) commutator width can be constructed in a similar way.

Forthcoming Seminars

Mon, 20/05/2013 - 2:15pm

Eigenvalues of large random matrices, free probability and beyond.

Speaker: CAMILLE MALE
Mon, 20/05/2013 - 2:15pm

Four-manifolds, surgery and group actions

Speaker: Ian Hambleton
Mon, 20/05/2013 - 3:45pm

Fibering 5-manifolds with fundamental group Z over the circle

Speaker: Yang Su
Mon, 20/05/2013 - 3:45pm

Random Wavelet Series

Speaker: STEPHANE JAFFARD
Mon, 20/05/2013 - 4:00pm

The Hasse Principle for the Equation Polynomial=Norm: An Approach Using Sieve Theory

Speaker: Alastair Irving
Mon, 20/05/2013 - 5:00pm

Analysis of some nonlinear PDEs from multi-scale geophysical applications

Speaker: Bin Cheng
Tue, 21/05/2013 - 12:00pm

Quantum information processing in spacetime

Speaker: Ivette Fuentes (Nottingham)