1 citations · 1 across the 6 of their papers we have counts for
6 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…
Strange Random Topology of the Circle
Uzu Lim
We characterise high-dimensional topology that arises from a random Cech complex constructed on the circle. Expected Euler characteristic curve is computed, where we observe limiti…
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…
Tangent Space and Dimension Estimation with the Wasserstein Distance
Uzu Lim, Harald Oberhauser, Vidit Nanda
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points requir…