Home page: coming soon
Researh interests: Algebraic topology, category theory, morse theory, optimization, networks, sensing & compression
I am a second year PhD student interested in cellular & topological sheaves, signal processing, and optimization.
Before coming to Penn I earned undergraduate degrees in Mathematics and Classical Studies from Willamette University, and an MSc in Mathematics from the University of Oregon. My early research interests concentrated in the disparate fields of representation theory and computational linguistics. Today they span topics in geometry, geometric topology, category theory, sheaf theory, and optimization.
My recent interests lie in sheaf-theoretic tools for network modeling and computation. Ghrist et al. demonstrate the utility of flow sheaves for efficient computation in the domain of network coding. Recent work by S. Krishnan points to natural applications for monoidal sheaves in strengthening the celebrated max flow min cut theorem, and its expansive consequences across disciplines in engineering. Motivated by problems in non-convex optimization, I currently explore topological theories of alternatives to generalize and hopefully deepen our understanding of the linear and convex theories of alternatives key to modern methods of optimization.