My research background so far lies between algorithms, combinatorics and optimization. This includes investigating topics in:
Mathematical Programming: linear and integer optimization, polyhedral combinatorics
Combinatorial Optimization: design and analysis of algorithms, problem formulations and complexity
Graph theory
The insightful results combining analytic arguments and the interplay between algebraic/geometric methods in the investigation of discrete structures have amazed me for me a long time. Ultimately, its beauty led me back to school, and I went through a volume of study in pure mathematics, in a self-given pre-doctoral sabbatical. (: My goal was to prepare and craft my way towards a Math PhD, while learning how to do analysis in different spaces.Â
Now that I'm retired from academia, I have a strong curiosity and an eye towards spending some free time learning more about:
Mathematical Analysis: asymptotics; linear functional analysis; convexity in topological vector spaces; operator algebras.
Combinatorics: extremal and probabilistic combinatorics; Ehrhart theory, partition functions, and lattice points in polyhedra; hyperplane arrangements.