MLADEN BESTVINA

*MEASURED LAMINATIONS AND GROUP THEORY*

- Abstract not available.

DANIEL BISS

*THE COMBINATORICS OF SMOOTH
MANIFOLDS: ORIENTED MATROIDS IN TOPOLOGY*

- The problem of finding a combinatorial formula for the rational Pontrjagin classes was solved in the early 90's by Gelfand and MacPherson; their solution makes essential use of combinatorial objects called oriented matroids. We show that the oriented matroids in question actually determine the tangent bundle of a smooth manifold; we will also discuss potiential applications of this result to the topology of diffeomorphism groups.

STEVE GERSTEN

*ISOPERIMETRIC INEQUALITIES FOR NILPOTENT GROUPS*

- This is joint research with D. F. Holt and T. R. Riley.
- We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function.
- Paper reference: arXiv:math.GR/0201261

DUSA McDUFF

*THE TOPOLOGY OF GROUPS OF SYMPLECTOMORPHISMS*

- A symplectomorphism is a diffeomorphism of a manifold that preserves a symplectic form. Ever since Gromov showed that the group of symplectomorphisms of the product of two 2-spheres of equal size has the homotopy type of an extension of SO(3) x SO(3) by Z/2Z, people have been interested in understanding the special properties of groups of symplectomorphisms. This survey talk will describe some ways in which the structure of a group of symplectomorphisms differs from that of an arbitrary diffeomorphism group.

YAIR MINSKY

*ON THURSTON'S ENDING LAMINATION CONJECTURE*

- The classification theory of hyperbolic 3-manifolds (with finitely generated fundamental group) hinges on Thurston's conjecture from the late 70's, that such a manifold is uniquely determined by its topological type and a finite number of invariants that describe the asymptotic structure of its ends.
- We will describe the recent proof of this conjecture, in the "incompressible boundary case", in joint work with J. Brock and R. Canary.

PETER OZSVATH

*HOLOMORPHIC DISKS AND LOW-DIMENSIONAL TOPOLOGY*

- I will discuss recent work with Zoltan Szabo, in which we use techniques from symplectic geometry -- holomorphic disks, and Lagrangian Floer homology -- to construct topological invariants for three-and four-manifolds. These invariants yield many of the four-dimensional results which have been proved using their gauge-theoretic predecessors (Donaldson-Floer and Seiberg-Witten theory), though the new invariants are constructed using more topological and combinatorial input, rendering them easier to calculate. I hope to focus on some of their applications to three-dimensional topological questions which have not been addressed by gauge theory.

GUOLIANG YU

*THE NOVIKOV CONJECTURE AND GEOMETRY OF GROUPS*

- I will explain what is the Novikov conjecture, why it is interesting and how it is related to geometry of groups.

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Last modified: Thu May 9 12:20:38 EDT 2002