I'm Lily, a second-year Ph.D. student in mathematics at the University of Pittsburgh studying geometry, topology, and functional analysis. My current research focuses on finite element exterior calculus and the construction of finite element spaces of double forms, with broader interests in geometric analysis, fixed point theory, optimization, combinatorics, and graph/network theory. I'm also interested in public policy, computer networks, urban geography, hardware, procedural generation, music production, speed-typing, and competitive rhythm games. I'm always happy to hear from people interested in collaborating.
— The best time to plant a tree was 20 years ago. The second-best time is now.
Geometric measure theory; metric geometry; Sobolev mappings between manifolds; geometry of Heisenberg groups; Lipschitz mappings into metric spaces; area and co-area formulas; geometric flows; finite element exterior calculus; differential forms and double forms.
Algebraic topology; degree theory for Sobolev and Orlicz-Sobolev mappings; Lipschitz and Hölder homotopy groups; homotopy and approximation of low-rank mappings; topology of manifolds; topology of metric spaces; combinatorial and discrete geometry.
Sobolev spaces; Sobolev spaces on metric spaces; Poincaré inequalities; maximal functions; Whitney extension problems; convex analysis; fixed-point theory; nonlinear functional analysis; mappings of finite distortion; harmonic analysis methods.
Finite element exterior calculus; compatible finite element spaces; discrete differential forms and double forms; de Rham complexes; mixed finite element methods; structure-preserving discretizations for geometry and PDEs.
Y. Berchenko-Kogan, L. DiPauloPDFarXiv:2511.19297
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