Discrete structure
Ramsey theory · thresholds
I study when sufficiently large unorganized objects are forced to contain ordered substructure, and when growing random objects acquire such structure with high probability.
Research
Structure, thresholds, and stability
My work ranges from Ramsey theory and random thresholds to nonlinear feedback stabilization and sparse neural networks.
Nonlinear dynamics
Feedback · stabilization
I investigate when nonlinear systems can be stabilized, and what topological or quantitative obstructions prevent feedback from working.
Sparse learning
Neural networks · lottery tickets
I develop methods for finding useful sparse subnetworks and study why capable structure emerges inside overparameterized models.
Publications & manuscripts
Research record
Journal articles, public preprints, technical reports, and doctoral work.
Double-Scoring: Reliable Extraction of Strong Lottery Tickets
A score-space method that lets a sparse neural network discover its own effective sparsity while searching for strong lottery tickets.
Project pageBrockett Openness Profiles and Gain-Limited Feedback Stabilization
A quantitative study of how openness near an equilibrium constrains the gain required from a stabilizing feedback law.
Project pageWhen do the Kahn–Kalai bounds provide nontrivial information?
Necessary conditions for when the Park–Pham estimate improves on the trivial upper bound, together with sufficient conditions for asymptotically exact information.
Project pageBounds on the Threshold Ramsey Multiplicity of Ramsey Numbers with Many Colors
Bounds for the number of monochromatic copies forced at critical multicolor Ramsey thresholds.
Project pageRamsey-Theoretic Characterizations of Classically Non-Ramseyian Problems
Ramsey-theoretic characterizations for problems that do not initially appear to be Ramsey problems.
Project pageConditional Park–Pham Bounds under Positive Correlation
A transfer principle showing when threshold bounds survive conditioning, with formulations for finite posets and permutation patterns.
Project pageContinuous Feedback Stabilization of Nonlinear Control Systems by Composition Operators
A composition-operator characterization that reduces continuous feedback stabilizability to stability of a system built from a local section.
Project pageArtificial Intelligence and Machine Learning Approaches for Enhanced SDA
Project West Wing Technical Operating Report TOR-2021-02533, The Aerospace Corporation, 22 pp.
Digital Threat Model Verification & Validation
Project West Wing Technical Operating Report TOR-2021-00810, The Aerospace Corporation, 17 pp.
A Variational Approach to Local Asymptotic and Exponential Stabilization of Nonlinear Systems
Variational characterizations of local asymptotic and exponential stabilization.
Project pageStability in Common and Uncommon Places
PhD dissertation on stabilization phenomena across several mathematical settings.
Mentoring
Students & research group
I advise graduate students and work with undergraduates on projects in combinatorics, control, and machine learning.
Graduate students
Current
- Darian Colgrove
- Jack Baretz
Graduate students
Past
- Ganesha Thondilege
- Tunde Alesinloye
- Daniel Atta Kwakye
- Jonathan Wirkkala
Undergraduate research group
Current
- Casia Steinhaus
- Taylor Valdez
Undergraduate research group
Past
- Jack Baretz
- Salah Dandan
- Augustus Tandberg
- Gabrielle Wahl
- Martin Epstein
- Liam Turman
- Josh Dorsam