Seminars Sorted by Series

Through the work of Agol and Wise, we know that all closed hyperbolic 3-manifolds are finitely covered by a surface bundle over the circle. Thus the geometry of these bundles indicates the geometry of general hyperbolic 3-manifolds. But there are...

Min-max theory developed in the 80s by Pitts (using earlier work of Almgren) allows one to construct closed embedded minimal surfaces in 3-manifolds in great generality. The main challenge is to understand the geometry of the limiting minimal...

I will talk about convex-cocompact representations of finitely generated free group $F_g$ into $\mathrm{PSL}(2,\mathbb C)$. First I will talk about Schottky criterion. There are many ways of characterizes Schottky group. In particular, convex hull...

The Min-max Theory for the area functional, started by Almgren in the early 1960s and greatly improved by Pitts in 1981, was left incomplete because it gave no Morse index estimate for the min-max minimal hypersurface. Nothing was said also about...

We prove that any right-angled Coxeter group on $k$ generators admits a proper action by affine transformations on $\mathbb R^{k(k-1)/2}$. As a corollary, many interesting groups admit proper affine actions including surface groups, hyperbolic three...

This is joint work with Thomas Barthelme of Penn State University. There are Anosov and pseudo-Anosov flows so that some orbits are freely homotopic to infinitely many other orbits. An Anosov flow is $R$-covered if either the stable or unstable...

A classical property of pseudo-Anosov mapping classes is that they act on the space of projective measured laminations with north-south dynamics. This means that under iteration of such a mapping class, laminations converge exponentially quickly...

This talk will be about some phenomena that occur as (singular) hyperbolic structures on 3-manifolds collapse to and transition through other geometric structures. Typically, the collapsed structures are much more flexible than the hyperbolic...

(Joint with Henry Segerman.) It is a theorem of Moise that every three-manifold admits a triangulation, and thus infinitely many. Thus, it can be difficult to learn anything really interesting about the three-manifold from any given triangulation...

I will first describe a simple graph coloring problem and survey some examples of graphs for which the coloring problem has or has no solution. I will then give a quick introduction to Bestvina-Brady Morse theory. Finally, I will describe the...

In this talk we will discuss further the existence of knot complements with essential surfaces of unbounded Euler characteristics. More precisely, we show the existence of a knot with an essential tangle decomposition for any number of strings. We...

I will show that the groups of mixed 3-manifolds containing arithmetic hyperbolic pieces and the groups of certain noncompact arithmetic hyperbolic $n$-manifolds ($n > 3$) are not LERF. The main ingredient is a study of the set of virtual fibered...

In this talk I will overview two very different kinds of random simplicial complex, both of which could be considered higher-dimensional generalizations of the Erdos-Renyi random graph, and discuss what is known and not known about the expected...

Associated to any simplicial graph there is a right-angled Coxeter group. Invariants of the Coxeter group such as its growth series or its weighted L^2 Betti numbers can be computed from the graph's clique complex (i.e., its flag complex).

we will describe various models of sparse and planar graphs and the associated distributions of eigenvalues (and eigenvalue spacings) which come up. The talk will be light on theorems, and heavy on experimental data.

The cd-index is a noncommutative polynomial which compactly encodes the flag vector data of a polytope, and more generally, of a regular cell complex. Ehrenborg and Readdy discovered the cd-index has an inherent coalgebraic structure which...

The d-divisible partition lattice is the collection of all partitions of an n-element set where each block size is divisible by d. Stanley showed that the Mobius function of the d-divisible partition lattice is given (up to a sign) by the number of...

Polycrystalline materials, such as metals, ceramics and geological materials, are aggregates of single-crystal grains that are held together by highly defective boundaries. The structure of grain boundaries is determined by five geometric parameters...

Liquid crystals form layered structures, known as smectics. Modeling these structures as minimal surfaces gives a class of trial solutions from which we can estimate ground state energetics. In order to control the boundary conditions, or topology...

The blue phases are remarkable mesophases appearing in highly chiral liquid crystals; they exhibit three-dimensional crystalline orientational order whilst remaining fully fluid. I will survey the development of our understanding of these materials...

Many biological tissues behave like viscous fluids on long timescales and posses a macroscopic, measurable surface tension. This surface tension correlates strongly with tissue type and successfully explains cell sorting of embryonic tissues. Both...

Liquid crystals form layered structures, known as smectics. Modeling these structures as minimal surfaces gives a class of trial solutions from which we can estimate ground state energetics. In order to control the boundary conditions, or topology...

Perfectly dry foams coarsen by the diffusion of gas between bubbles according to laws proved by von Neumann in 2d and by MacPherson and Srolovitz in 3d. The remarkable feature in 2d is that a bubble grows or shrinks at a rate that does not depend on...

We will discuss the geometry of equilibrium surfaces for anisotropic surface energies. In particular, the shape of solutions of free boundary problems will be discussed when the total energy includes wetting energy and anisotropic line tension...

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally-spaced smectic layers is highly generic but, at the same time, difficult to work with. We have developed an...

I describe a unified theoretical approach to represent exactly an n-point "canonical" correlation function from which one can obtain and compute any of the various types of correlation functions that determine the bulk properties of many-particle...

After reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^0-distance of its flow from the identity. I will also show that, unlike the Hofer norm...

Legendrian contact homology (LCH) is a powerful holomorphic curves invariant for Legendrian submanifolds in contact manifolds. It is defined via a differential graded algebra (DGA), but the computation of its homology is often too difficult...

Seifert fibered 4-manifolds are the 4-dimensional analog of Seifert 3-manifolds in that these are the 4-manifolds which admit a fixed-point free smooth circle action. In this talk I'll first review what is known and then present some recent results...