My research focuses on understanding how to estimate and compute geometric, topological and dynamical invariants given samples of a topological space or the dynamics. I'm particularly interested in understanding and developing statistical methods to estimate these invariants, and adapting tools from algebraic topology to the study of spaces of samples. The techniques I use to treat this problem are broad, drawing from homotopy theory, homological algebra, sheaf theory, probability and statistics, operator theory, and spectral geometry.

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