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Hedrick Assistant Adjunct Professor

UCLA Department of Mathematics

perlmutter@ucla.edu

I am a Hedrick Assistant Adjunct Professor in the math department at UCLA working under the supervision of Deanna Needell. Here are my CV and google scholar profile.

My current research is focused on the Mathematics of Data Science and Applied Harmonic Analysis. More specifically, in recent years my two primary areas of research have been:

1. Geometric Deep Learning: I work on developing, analyzing, and applying deep learning methods for graph- and manifold-structured data. This includes both (a) work on the geometric scattering transform, a predesigned, wavelet-based model of neural networks, and (b) work constructing high-performing networks for signed and/or directed graphs. In the past year, I have become increasingly interested in using these methods in biomedical applications such as AI-aided drug discovery, analyzing metabolic networks, and predicting patient outcomes from single-cell data.

2. Phase Retrieval: My work in phase retrieval focuses on problems arising in ptychographic imaging. In particular, it focuses on developing computationally efficient, noise-robust algorithms with provable recovery guarantees for inverse problems arising from structured, locally supported, phaseless measurements.

Additionally, I have also worked on problems related to applied probability, audio denoising, data-set benchmarking, and tensor compression.

From Fall 2017-Summer 2020, I was a postdoc in the Department of Computational Mathematics, Science and Engineering at Michigan State University working on problems related to Phase Retrieval and the Mathematics of Deep learning under the supervision of Matt Hirn and Mark Iwen. From Fall 2016-Summer 2017, I was a postdoc in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill, working on problems in high-dimensional probability under the supervision of Amarjit Budhiraja. I did my graduate work at Purdue University working on problems on the interface of probability and harmonic analysis under the supervision of Rodrigo Bañuelos.