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.

Monday 12

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.

  • Slides are here.

    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.

  • Slides are here.

    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.

  • Slides are here.

    Tuesday 13

    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.

  • Papers about compression are here and here ,
  • The paper about dimension growth is here,
  • Slides of a related talk are here,
  • The video of a related talk is here.

    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.

  • Slides are here.


    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.

  • Slides are here.

    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.

  • Slides are here.

    5:00 Yves de Cornulier

    Title: On QI-classification of Lie groups

    Abstract: 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?

    Wednesday 14

    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.

  • Slides are here.

    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.

  • Related notes are here.

    Thursday 15

    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.

  • Slides are here.

    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?

  • Slides are here

    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.

    Related links:

  • Permanence in coarse geometry is here,
  • Discrete groups with finite decomposition complexity is here,
  • A notion of geometric complexity and its application to topological rigidity is here.

    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.

  • Slides are here.

    Friday 16

    9:30 Erik Guentner

    11:00 Alireza Salehi Golsefidy