4 papers
Universal topological statistics on triangulated singular spaces
Uzu Lim, Omer Bobrowski, Primoz Skraba
We prove a universality theorem for random persistent homology over a class of triangulable spaces. More precisely, let be a compact -triangulable spa…
Cohomology of p-adic fields and Local class field theory
Uzu Lim
In this expository article, we outline a basic theory of group (co)homology and prove a cohomological formulation of the Local Reciprocity Law: $${\rm Gal}(L/K)^{\rm ab} \cong H_T^…
HADES: Fast Singularity Detection with Local Measure Comparison
Uzu Lim, Harald Oberhauser, Vidit Nanda
We introduce Hades, an unsupervised algorithm to detect singularities in data. This algorithm employs a kernel goodness-of-fit test, and as a consequence it is much faster and far…
Harmonic Forms, Hodge Theory and the Kodaira Embedding Theorem
Uzu Lim
In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differ…