Knot Theory

Efficient Generation of Large Random Polygons

Efficient Generation of Large Random Polygons

Direct Sampling of Confined Polygons in Linear Time

Balancing Graphs Using Geometric Invariant Theory

Finding Good Coordinates for Sampling: The Importance of Geometry

Matrix Optimization Informed by Geometric Invariant Theory and Symplectic Geometry

Optimization Informed by Geometric Invariant Theory and Symplectic Geometry

Math 105

Complex Analysis

Generating (and Computing with) Very Large Ensembles of Random Polygonal Knots

Optimization and Normal Matrices

RMHS

Geometric Approaches to Frame Theory

Introduction to Knot Theory

Frames as Loops

Applications of Grassmannians and Flag Manifolds

Frames, Optimization, and Geometric Invariant Theory

Hodge and Gelfand Theory in Clifford Analysis and Tomography

Topological Polymers and Random Embeddings of Graphs

Finding Good Coordinates for Sampling Configuration Spaces

Geometric Approaches to Frame Theory

Geometric Approaches to Frame Theory

Animations

Some Applications of Symplectic Geometry

A Lie Algebraic Perspective on Frame Theory

Random Graph Embeddings with General Edge Potentials

What is a Random Knot? And Why Do We Care?

The (Symplectic) Geometry of Spaces of Frames

Generating (and Computing with) Very Large Ensembles of Random Polygonal Knots

An Introduction to Symplectic Geometry and Some Applications

New Stick Number Bounds from Random Sampling of Confined Polygons

What is (Applied) Symplectic Geometry?

New Stick Number Bounds from Random Sampling of Confined Polygons

Hamiltonian Group Actions on Frame Spaces

Modeling Topological Polymers

Symplectic Geometry and Frame Theory

Stiefel Manifolds and Polygons

Visualizing Higher Dimensions

Tensors in Differential Geometry

Symplectic Geometry and Frame Theory

Using Differential Geometry to Model Complex Biopolymers

What’s the Probability a Random Triangle is Obtuse?

For MATH 161

What’s the Probability a Random Triangle is Obtuse?

An Introduction to Geometric Probability, Shape Spaces, Group Actions, and Grassmannians

Modeling Topological Polymers

Symplectic Geometry and Frame Theory

The Geometry of Topologically Constrained Random Walks

Symplectic Geometry and Frame Theory

Random Walks are Almost Closed

Loop closure is surprisingly non-destructive

Random Walks are Almost Closed

Loop closure is surprisingly non-destructive