Sebastian Velazquez | Searcharxiv

arXiv2025

On moduli of foliated surfaces

We present a definition of stable family of foliations and show that the corresponding moduli functor for foliated surfaces is representable by a Deligne-Mumford stack.

math.AG↗

arXiv2024

Phase retrieval from short-time Fourier transform in LCA groups

We study the short-time Fourier transform phase retrieval problem in locally compact abelian groups. Using probabilistic methods, we show that for a large class of groups $G$ and compact subsets $K\subseteq G$ there exists a window function and a uniformly discrete set in $G\times \widehat{G}$ allowing phase retrieval in $L^2(K)$. We also study the obstructions for STFT phase retrieval on $L^2(G)$, motivating the restriction to compactly supported function spaces.

math.CA↗