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We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and th...
We prove that the set of quadratic growths attainable by integervalued superharmonic functions on the lattice Z2 has the structure of an Apollonian circle packing. This completely characterizes the PD...
We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (op-amps). We observe that a wide variety of design objectives and constraints have ...
We present two novel algorithms at the ingress and egress of packet switches with QoS provisioning and fairness constraints. We first provide a suite of generalized weighted fair queuing formulations ...
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
We first consider the problem of determining the doping profile that minimizes base transit time in a (homojunction) bipolar junction transistor. We show that this problem can be formulated as a geome...
This tutorial paper concerns a method for digital circuit sizing based on formulating the problem as a geometric program (GP), a special type of mathematical optimization problem that can be very effi...
This tutorial concerns a method for solving a variety of circuit sizing and optimization problems, which is based on formulating the problem as a geometric program (GP), or a generalized geometric pro...
Commonly-used subdivision schemes require manifold control meshes and produce manifold surfaces. However, it is often necessary to model nonmanifold surfaces, such as several surface patches meeting a...
We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are h...
We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering numbe...
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp r...
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various ext...
Hypoelliptic estimates in radiative transfer.
Double Hurwitz numbers count branched covers of CP1 with fixed branch points, with simple branching required over all but two points 0 and ∞, and the branching over 0 and ∞ specified by ...

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