Seminars Sorted by Series

Dislocations are line defects in crystals, and can be modeled using non-local operators. In this talk we will consider a related reaction-diffusion equation with a half-Laplacian. We show that the limit dynamics is characterized by a system of ODEs...

We construct new solutions to the $\sigma_k$-Yamabe problem on compact manifolds by considering the connected sum of two nondegenerate solutions $(M^n_1,g_1)$ and $(M^n_2,g_2)$, for any $2 \leq 2k < n$.

In this talk, I will first give an overview of recent progress on the scattering conjecture and rigidity conjecture for mass critical NLS. Then I will describe our recent results concerning both conjectures for L_2 initial data. I will also discuss...

We formulate several new boundary value problems for the 2D Navier-Stokes system. In all cases, we obtain quantitative decay estimates of the Fourier modes for both the vorticity and the velocity. In some special cases we found that the Fourier...

In this talk, I will discuss several topics related to transverse knots in contact 3-manifolds. I will introduce a conjecture on the maximal self-linking number of a topological knot in the standard contact 3-sphere. I will show how to apply braid...

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...

We will discuss methods of decomposing knot and link complements into polyhedra. Using hyperbolic geometry, angled structures, and normal surface theory, we analyze geometric and topological properties of knots and links.

The non-orientable genus (a.k.a crosscap number) of a knot is the smallest genus over all non-orientable surfaces spanned by the knot. In this talk, I’ll describe joint work with Christine Lee, in which we obtain two-sided linear bound of the...

Sageev associated to a codimension 1 subgroup $H$ of a group $G$ a cube complex on which $G$ acts by isometries, and proved this cube complex is always CAT(0). Haglund and Wise developed a theory of special cube complexes, whose fundamental groups...

We prove that if a hyperbolic group $G$ acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then $G$ is virtually special. This generalizes Agol's Theorem (the case when the action is proper)...

We give a brief introduction to random walks on groups with hyperbolic properties.

Let $G$ be a group acting by isometries on a Gromov hyperbolic space, which need not be proper. If $G$ contains two hyperbolic elements with disjoint fixed points, then we show that a random walk on $G$ converges to the boundary almost surely. This...

In this first talk, we give an introduction to Penner’s construction of pseudo-Anosov mapping classes. Penner conjectured that all pseudo-Anosov maps arise from this construction up to finite power. We give an elementary proof (joint with Hyunshik...

We consider questions that arise naturally from the subject of the first talk. The have two main results: 1. In genus $g$, the algebraic degrees of pseudo-Anosov stretch factors include all even numbers between $2$ and $6g - 6$; 2. The Galois...

From a complex analytic perspective, Teichmüller spaces and symmetric spaces can be realised as contractible bounded domains, which have several features in common but also exhibit many differences. In this talk we will study isometric maps between...

For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimension spectrum. I'll discuss and pose some questions which also in particular will imply a conjecture due to...

A theorem of Borel's asserts that for any positive real number $V$, there are at most finitely many arithmetic lattices in ${\rm PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at most finitely many arithmetic hyperbolid $3$-orbifolds...

A theorem of Borel's asserts that for any positive real number $V$, there are at most finitely many arithmetic lattices in ${\rm PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at most finitely many arithmetic hyperbolid $3$-orbifolds...

I will discuss a proof that a complete, non-compact hyperbolic 3- manifold $M$ with finite volume contains an immersed, closed, quasi-Fuchsian surface that separates a given pair of points in the sphere at infinity. Joint with David Futer.

Thurston's hyperbolization of fibered 3-manifolds is based on his classification theorem for isotopy classes of surface homeomorphisms. This classification has also been extremely important to the study of dynamical systems on surfaces. The...

I will talk about bilipschitz geometry of complex algebraic sets, focusing on the local geometry in dimension 2 (complex surface singularities), where the topological classification has long been understood in terms of 3-manifolds, while the...

This talk will discuss the question: To what extent are the fundamental groups of compact 3-manifolds determined (amongst the fundamental groups of compact 3-manifolds) by their finite quotients. We will discuss work that provides a positive answer...

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...