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May 01, 2009
Group Theory

Morse theory and conjugacy classes of finite subgroups II

We construct a hyperbolic group with a finitely presented subgroup, which has infinitely many conjugacy classes of finite-order elements. We also u…
Aug 19, 2009
Geometric Topology
Quantum Algebra

Integral TQFT for a one-holed torus

We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from …
May 14, 2010
Analysis of PDEs

Boundary behavior p-harmonic functions in the Heisenberg group

We study the boundary behavior of nonnegative p-harmonic functions which vanish on a portion of the boundary of a domain in the Heisenberg group H^n.…
Dec 19, 2013
Geometric Topology
Symplectic Geometry

Braids and combinatorial knot Floer homology

We present a braid-theoretic approach to combinatorially computing knot Floer homology. To a knot or link K, which is braided about the standard disk…
Jan 31, 2009
Group Theory
Geometric Topology

Super-exponential 2-dimensional Dehn functions

We produce examples of groups of type F_3 with 2-dimensional Dehn functions of the form exp^n(x) (a tower of exponentials of height n), where n is an…
Jul 12, 2011
Geometric Topology

In this section, we compute Kh(G) and ˜Kh(G) for a ribbon graph G. We first compute Kh(G) via the cube of resolutions complex. Although ˜Kh(G) can also be computed from the cube of resolutions complex, we instead compute ˜Kh(G) via the spanning quas…

A Turaev surface approach to Khovanov homology

We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a li…
Dec 09, 2009
Optimization and Control
Data Structures and Algorithms

An exact algorithm for graph partitioning

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to…
May 12, 2010
Optics

Tunable Double Negative Band Structure from Non-Magnetic Coated Rods

A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-co…
Oct 21, 2015
Algebraic Geometry
Geometric Topology

Signatures of real algebraic curves via plumbing diagrams

We define and calculate signature and nullity invariants for complex schemes for curves in the real projective plane. We use an analog of the Murasug…
Aug 30, 2013
Number Theory
Combinatorics

Asymptotic formulas for stacks and unimodal sequences

We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known res…
Apr 15, 2008
Geometric Topology
Symplectic Geometry

Smooth surfaces with non-simply-connected complements

We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim s…
Nov 27, 2007
Functional Analysis
Representation Theory

In this section we will give some examples of coorbit spaces and also show that the generalization presented in this paper is in fact a generalization of the theory by Feichtinger and Gröchenig.

Examples of Coorbit Spaces for Dual Pairs

In this paper we summarize and give examples of a generalization of the coorbit space theory initiated in the 1980's by H.G. Feichtinger and K.H. Gr\…
Apr 05, 2017
Representation Theory
Operator Algebras

For a detailed exposition of the results mentioned below, we refer to the forthcoming paper [NÓ17].

Antiunitary representations and modular theory

Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, ant…
Dec 09, 2009
Optimization and Control

Gradient-based methods for sparse recovery

The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (…
Apr 09, 2016
Optimization and Control

Inexact alternating direction multiplier methods for separable convex…

Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear const…
Jan 11, 2017
Numerical Analysis

Numerical analysis of nonlocal fracture models in Hölder space

In this work, we calculate the convergence rate of the finite difference approximation for a class of nonlocal fracture models. We consider two point…
Jul 30, 2014
Geometric Topology

Even and odd Kauffman bracket ideals for genus-1 tangles

This paper refines previous work by the first author. We study the question of which links in the 3-sphere can be obtained as closures of a given 1-m…
Dec 17, 2011
Geometric Topology

The head and tail conjecture for alternating knots

We investigate the coefficients of the highest and lowest terms (also called the head and the tail) of the colored Jones polynomial and show that the…
Aug 30, 2017
Geometric Topology

Lifting Lagrangian immersions in $\mathbb{C} P^{n-1}$ to Lagrangian …

In this paper we show how to lift Lagrangian immersions in $\mathbb{C} P^{n-1}$ to produce Lagrangian cones in $\mathbb{C} ^n$, and use this process …
Jan 18, 2014
Geometric Topology

The colored Kauffman skein relation and the head and tail of the colo…

Using the colored Kauffman skein relation, we study the highest and lowest $4n$ coefficients of the $n^{th}$ unreduced colored Jones polynomial of al…
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