The conference will be held in the Laskey Building in Scarritt-Bennett center on the 2nd Floor in room Laskey C.
1008 19th Ave S, Nashville, TN 37212.
1:00 pm Shmuel Weinberger
Title: From aggregation on networks to a problem of Wall.
Abstract: I will start by discussing the problem of aggregation of
preferences in an abstract setting (coming from economics and
engineering) and then move from there towards more abstract problems
and theorems (of other people) regarding operators and quadratic forms
on infinite graphs, and will give applications to problems related to
the meaning of Poincare duality for discrete groups.
(My second talk will fill in gaps in the presentation from the first.)
2:00 pm Stanley Chang
Title: Positive scalar curvature and noncompact manifolds
Abstract: Scalar curvature, the weakest form of curvature that can be assigned pointwise to a manifold, was once imagined to be a possible tool in the classification of higher dimension manifolds. Efforts to understand positive scalar curvature have culminated in the so-called Gromov-Lawson-Rosenberg Conjecture, which is now known to be false. In this talk, we will discuss the progress made in both the compact and noncompact venues to understand the scalar curvature properties of manifolds.
3:30 pm Russell Lyons
Title: Uniform Spanning Forests, the First l2-Betti Number, and
Uniform Isoperimetric Inequalities
Abstract: Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area, intimately related to random walks and electrical networks. It turns out that they are also related to the first l2-Betti numbers of groups. We illustrate this by proving a uniform isoperimetric inequality for Cayley graphs.
4:30 pm Simon Thomas
Title: Bratteli Diagrams and the Unitary Duals of Locally Finite Groups
Abstract: I will discuss an attempt to understand the unitary duals of discrete countable groups from the point of view of descriptive set theory.
9:30 Guoliang Yu
Title: The Novikov conjecture and metric geometry
Abstract: I will give an introductory talk on how metric geometry can be used to study the Novikov conjecture.
If time permits, I will explain a localization technique introduced in my recent joint work with Rufus Willett.
11:00 Mark Sapir
Title: Embedding Cayley graphs into Hilbert spaces and related questions
Abstract: I will talk about the Hilbert space compression functions of finitely generated groups.
12:00 Remi Coulon
Title: Embedding expanders into a group.
Abstract: In 2003, M. Gromov provided a construction to embed certain expanders into a finitely generated groups. He obtained in this way a "monster" with surprising properties. In particular it does not coarsely embed into a Hilbert space. In this talk I will try to explain the main ideas of this construction involving random walks and small cancellation theory.
2:30 Russell Lyons
Title: Determinantal Probability Measures
Abstract: It turns out that the uniform spanning tree measure on a finite graph and its extensions to infinite graphs can be described via determinants. More generally, the uniform measure on regular matroids can be described via determinants. But other probability measures on the set of bases of a matroid arise in a similar way via determinants as well. Exterior algebra turns out to provide the proper framework to give easy proofs of various results.
4:00 Steve Ferry
Title: Deforming manifolds in Gromov-Hausdorff space
Abstract: If two manifolds are close to each other in some appropriate sense, must they be homeomorphic? We will discuss situations where this form of "rigidity" holds and other situations where it fails.
5:00 Yves de Cornulier
On QI-classification of Lie groups
I'll survey results about the quasi-isometry classification of locally compact groups, with an emphasis on the following question: given a Lie group G, which locally compact groups are quasi-isometric to G?
9:30 Rufus Willett
Title: Expanders and Baum-Connes type conjectures.
Abstract: Thanks to work of Guoliang Yu, it has been known for almost fifteen years that the existence of a coarse embedding into Hilbert space has 'good' consequences for Baum-Connes and Novikov type conjectures. On the other hand, expanders are known not to admit such a coarse embedding, and are known to be counterexamples to some of these conjectures (in some cases). A lot still remains unclear, however. I will discuss what can be said for certain classes of expanders (in particular, those with large girth which are used in the construction of 'exotic' groups), and how this relates to coarse embeddings into Hilbert space. This is joint work with Guoliang Yu.
11:00 Shmuel Weinberger
12:00 Miklós Abért
Title: Groups and graph limits
Abstract: In the talk I will try to explain why the notion of graph
convergence is important in group theory, and more surprisingly, why
group theory is relevant for the theory of graph convergence.
2:30 Steve Ferry
Title: Volume Growth, DeRham Cohomology, and the Higson Compactification
Abstract: We construct a variant of DeRham cohomology and use it to
prove that the Higson compactification of R^n has uncountably
generated n^th integral cohmology. We also explain that there is,
nevertheless, a way of using the Higson compactification to prove the
Novikov conjecture for a large class of groups and give a proof, due
to Dranishnikov, that the Higson compactification of n-dimensional
hyperbolic space is acyclic in even dimensions.
4:00 Yuliy Baryshnikov
Title: Packings and coverings
Abstract: I will discuss several natural questions related to packings and coverings in Euclidean spaces:
- does there exist a graph with quadratic ball growth, which cannot be packed in in the plane?
- what is the optimal Holder exponent of a continuous map of a square onto a cube?
- what is the topology of the packing and covering configuration spaces?
5:00 James Lee
Title: Geometric analysis on graphs, algorithms, and complexity
Abstract: I will talk start by discussing some problems in geometric spectral graph theory and their applications to algorithms and computational complexity. I will also touch on some of the relevant analogies between graphs and manifolds, and how these problems show up in other areas like geometric group theory.
9:30 Russell Lyons
Title: Random Complexes via Topologically-Inspired Determinants
Abstract: Uniform spanning trees on finite graphs and their analogues on infinite graphs have a higher-dimensional analogue on finite and infinite CW-complexes. On finite complexes, they relate to (co)homology, while on infinite complexes, they relate to (the higher) l2-Betti numbers. One use is to get uniform isoperimetric inequalities.
11:00 James Lee
Title: Eigenvalues, flows, and metric uniformization
Abstract: This will be the low-dimensional talk, and will largely address the spectrum of the graph Laplacian on planar graphs and their generalizations. The main theme is: How do we do something like conformal uniformization when we have no conformal structure?
12:00 Alireza Salehi Golsefidy
Title: Expanders and finite quotients of linear groups
Abstract: I will talk about a necessary and sufficient condition for a finitely generated subgroup of SL(n,Q) under which the Cayley graphs of such a group modulo square free integers form a family of expanders (joint with Varju). As an application the fundamental theorem of affine sieve (joint with Sarnak) will be mention.
2:30 Yuliy Baryshnikov
4:10 Colloquium talk by Lewis Bowen
5:20 Erik Guentner
Title: Coarse geometry of linear groups
Abstract: I will outline a proof, highlighting the role of permanence properties, that linear groups are coarsely embeddable in Hilbert space. In the first talk, I will focus on the permanence properties themselves, and will explain why, for example, the free product of coarsely embeddable groups is itself coarsely embeddable. The second talk will be devoted to linear groups.
6:30 James Lee
Title: Higher-order Cheeger inequalities
Abstract: I will address general graphs, and the connection between higher eigenspaces and expansion of small sets. This turns out to have interesting applications, both to computational complexity, and to the rigorous analysis of certain graph partitioning heuristics.
9:30 Erik Guentner
11:00 Alireza Salehi Golsefidy