Research
Optimization
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Current research uses polyhedral lifts and flow decompositions on layered graphs to effeciently solve variants of the two-person Blotto game from game theory using a polynomial size linear program, supervised by Professor Pablo Parrilo
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Integer Programming Solutions to Graph Coloring, May 2022, P. Hoffman, supervised by Professor James Orlin.
- [PDF]: Designed an integer program to find proper colorings of randomly constructed non-planar graphs
Combinatorics
- Expander Graphs and their Construction, May 2022, P. Hoffman.
- [PDF]: Proved the existence of expander graphs using randomized constructions and proved the unique neighbor expansion
- Polygon Dynamics Under Reflection Operations, December 2022, P. Hoffman with O. Lores & C. Yung.
- [PDF]: Studied the dynamics of a polygon as its vertices are iteratively reflected across the perpendicular bisector of their neighbors
Machine Learning
- Random Matrix Initialization Methods in Machine Learning, May 2021
- [PDF]: Used randomized initialization methods to improve performance of 2-layer feed forward neural networks
Bayesian inference
- An Overview of the Nested Sampling Algorithm, May 2023, P. Hoffman, supervised by
Professor Peter Kempthorne.
- [PDF]: Studied the Nested Sampling algorithm and its application to calculating the normalizing factor in Bayesian statistics