Special Session on Geometric TopologyAMS 2008 Spring Eastern MeetingCourant Institute of Mathematical SciencesNew York University, March 15 to 16, 2008 |
This event is also part of the festivities organized in New York City to celebrate the sixtieth birthday of Sylvain Cappell, which include a conference on Singularities in Geometry and Topology also at the Courant Institute immediately following the AMS Meeting, from March 17 to 20.
All talks in the Special Session will be in room 208, Silver Center. Invited Addresses will be in room 109, Warren Weaver Hall. The registration desk will be in the lobby, Warren Weaver Hall, and will be open 7:30 am-4 pm on Saturday, March 15, and 8 am-noon on Sunday, March 16.
The list of confirmed participants includes: Sylvain Cappell, James F. Davis, Pisheng Ding, Wojciech Dorabiala, Christopher Dwyer, Brad Forrest, Ian Hambleton, Mark W. Johnson, Keith Jones, Qayum Khan, Seonhee Lim, Wolfgang Lück, Gerald Marchesi, Francesco Matucci, Stephen F. Sawin, Rob Scheiderman, Dirk Schütz, Shmuel Weinberger, and Anna Wienhard.
David Rosenthal (St. John's University) and Marco Varisco (Binghamton University, SUNY) [e-mail].
from | to | Saturday, March 15 | Sunday, March 16 |
---|---|---|---|
8:30 am | 8:50 am | Qayum Khan | Stephen F. Sawin |
9:00 am | 9:20 am | James F. Davis | Wolfgang Lück |
9:30 am | 9:50 am | ||
10:00 am | 10:20 am | Brad Forrest | Mark W. Johnson |
10:30 am | 10:50 am | Francesco Matucci | Dirk Schütz |
11:00 am | 11:50 am | Invited Address: Ravi Vakil | Invited Address: Weinan E |
1:30 pm | 2:20 pm | Invited Address: Ovidiu Savin | Invited Address: Ilya Kapovich |
2:30 pm | 2:50 pm | Rob Scheiderman | Wojciech Dorabiala |
3:00 pm | 3:20 pm | Ian Hambleton | Sylvain Cappell |
3:30 pm | 3:50 pm | ||
4:00 pm | 4:20 pm | Seonhee Lim | Anna Wienhard |
4:30 pm | 4:50 pm | Christopher Dwyer | Shmuel Weinberger |
5:00 pm | 5:20 pm | Pisheng Ding | |
5:30 pm | 6:20 pm | Erdős Lecture: Timothy Gowers |
Abstract: I will explain joint work with Shmuel Weinberger on invariants of closed manifolds whose universal covers have no L^{2} harmonic forms.
Abstract: We explain consequences of recent work of Frank Quinn for computations of Nil groups in algebraic K-theory, in particular the Nil groups occurring in the K-theory of polynomial rings, Laurent polynomial rings, and the group ring of the infinite dihedral group.
Abstract: We show that the symbol classes of the de Rham operator and the signature operator on a closed manifold of dimension 4n are equivalent mod 2 as KO-theory elements.
Abstract: Let p be a smooth bundle of compact manifolds. We will show that if the fundamental group of the base acts trivially on the rational homology of the fibers, then the bundle p gives rise to a secondary transfer map defined on the level of Whitehead spaces. This secondary transfer map can be used to give an alternative construction of the smooth torsion invariant of the bundle p defined by Dwyer, Weiss and Williams. As an application of this secondary transfer, we obtain a composition formula for the smooth torsion invariant.
Abstract: I will discuss a decomposition of twisted K-theory in the case of a discrete group acting properly. This is work in progress in proving a conjecture by Alejandro Adem and Yongbin Ruan for twisted orbifold K-theory.
Abstract: Auter space, a cousin of Marc Culler and Karen Vogtmann's Outer space, was introduced by Allen Hatcher and Vogtmann in 1998. In this introduction, Hatcher and Vogtmann defined subspaces of Auter space called the degree complexes, which act like skeleta for Auter space. In this talk, I will present applications of the degree complexes including a presentation for Aut(F_{n}) and discuss minimality properties of these complexes.
Abstract: The talk will discuss the classification up to s-cobordism of closed, oriented, topological 4-manifolds whose fundamental groups have geometric dimension 2.
Abstract: The category of Pi-algebras is the category of universal algebras containing, i.e. the natural categorical home for, the graded homotopy groups of a pointed topological space. Given a homotopy commutative diagram of pointed spaces, applying the graded homotopy groups functor yields a diagram of Pi-algebras of the same shape. One can then ask if there is a strictly commutative diagram of pointed spaces which yields the same diagram of Pi-algebras, called a realization of the diagram of Pi-algebras. In work which recently appeared, the authors established an obstruction theory for realizing diagrams of Pi-algebras, with the obstructions landing in Andre-Quillen cohomology groups. In the work to be discussed, the authors have since constructed various “local-to-global” spectral sequences for computing this Andre-Quillen cohomology in terms of the previously studied case of Andre-Quillen cohomology of a single Pi-algebra. Higher homotopy operations, such as Toda brackets, can also be described as obstructions to realizing certain diagrams of Pi-algebras. Thus, the broader collaborative project seeks to use the cohomology of diagrams as a tool to organize higher homotopy operations.
Abstract: Bass defined an exotic Nil-summand of the algebraic K-theory of a polynomial extension. Later, Waldhausen extended the definition to tensor algebras and defined an exotic Nil-summand of the algebraic K-theory of an injective amalgam of groups. Our Nil-Nil theorem states, under a certain finiteness condition, that there is a natural isomorphism from the amalgam Nil to a tensor Nil.
Abstract: Volume entropy of a Riemannian manifold is the exponential growth rate of the volumes of balls. Entropy rigidity for rank-1 Riemannian manifolds is known: a theorem of Besson-Courtois-Gallot says that the locally symmetric metrics attain minimal volume entropy among all Riemannian metrics. In this talk, we are interested in entropy rigidity for buildings, especially hyperbolic ones. We will give several characterizations of the volume entropy, analogous to the ones for trees, that will help us to find some lower bound on volume entropy.
Abstract: In a paper from 2005 we propose several definitions for the Burnside ring of an infinite discrete group. We introduce stable equivariant cohomotopy for proper cocompact G-CW-complexes. We formulate a version of the Segal Conjecture for infinite groups in this setting. We have now finished the proof of it in the setting of infinite discrete groups. This is the topic of the talk.
Abstract: We give a classification of centralizers of elements in R. Thompson's groups F, T and V . This is achieved by using solutions of the ordinary conjugacy problem both from a dynamical perspective, seeing elements as piecewise-linear homeomorphisms, and a combinatorial one, using tree pairs and strand diagrams. We give combinatorial and topological applications of this description.
Abstract: We restrict the action for N=1 Supersymmetric Quantum Mechanics (SUSY QM) to the subset of all paths which are the concatenation of n short geodesic segments. On this subspace the path integral representing the time evolution operator is a perfectly rigorous finite-dimensional supersymmetric integral. Its kernel is represented by an n-fold kernel product of a simple kernel called the approximate kernel. The limit as n goes to infinity exists and can be naturally interpreted as the infinite-dimensional path integral that defines the time evolution operator and partition function of the theory. When applied to loops instead of paths, the action can also be interpreted as the infinite-dimensional Mathai-Quillen form one uses to get a “proof” of the Gauss-Bonnet-Chern theorem. We prove that this large n limit converges to the heat kernel for the Laplace-Beltrami operator on forms. We use this convergence to give a rigorous version of the nonrigorous proof using the Mathai-Quillen formalism (or equivalently using SUSY QM) of Gauss-Bonnet Chern. We suggest how the same techniques may be used to make rigorous the SUSY QM “proof” of the Local Index Theorem and some other nonrigorous math integral arguments.
Abstract: Concordance invariants for knots in 3-manifolds can be defined by applying intersection invariants to a singular (immersed) concordance. Besides fitting into a general theory of Whitney towers, the resulting knot invariants generalize the Arf invariant and classify knots up to stable concordance, which allows taking connected sums with copies of S^{2}xS^{2}.
Abstract: We study the topology of the moduli space of polygonal planar curves with given side-length vector. By a conjecture of Walker the side-lengths are determined by the cohomology ring of the moduli space. We show that this conjecture is true for a large class of length vectors, and that an analogous conjecture holds if one considers polygonal curves in 3-space.
Abstract: Away from the prime 2, there is a quite good understanding of equivariant surgery for finite group actions, assuming certain gap hypotheses, or of isovariant surgery, without the usual gap hypothesis, that is quite parallel to the classical surgery theory of manifolds. This talk will explain some of the issues involved in going beyond these cases: i.e. understanding the prime 2, equivariant surgery without the gap hypothesis, and infinite compact groups. I plan to discuss concrete examples where the phenomena can be described without any reference to surgery theory.
Abstract: I will explain a construction of rotation numbers which generalizes both the classical rotation number of a homeomorphism of the circle as well as the symplectic rotation number. For Lie groups of Hermitian type these rotation numbers are intimately related to a generalization of the Maslov index and play an important role when studying the varieties of representations of such groups.