My last name is pronounced:

**Office:** 906 Warren Weaver Hall

**Email:** pb2682@nyu.edu

I am a Post-Doctoral Associate and NSF Postdoctoral Fellow at NYU Courant, where my supervisor is Bruce Kleiner. I received my Ph.D. in 2021 from UC Berkeley, where I was advised by Richard Bamler. I work on problems in geometric analysis, particularly those related to Ricci flow and scalar curvature.

In Spring 2024 I am teaching MATH-UA 325 010 Analysis. I am also a co-organizer for the Courant Geometric Analysis and Topology Seminar.

*Smoothing L^\infty Riemannian metrics with nonnegative scalar curvature outside of a singular set*, 2024.
[arXiv: 2406.04564]

*ADM mass for C^0 metrics and distortion under Ricci-DeTurck
flow*, 2022, Journal für die reine und angewandte Mathematik
(Crelle's Journal) (2023) **2024**, 806, 187 - 245, doi: 10.1515/crelle-2023-0085.
[arXiv:
2208.145506][article]

*Defining pointwise lower scalar curvature bounds for C^0 metrics
with regularization by Ricci flow*, SIGMA (2020) **16**,
128, 10 pages, doi: 10.3842/SIGMA.2020.128. [arXiv: 2007.14967][article]
(this is a survey of "Pointwise lower scalar...", below)

*Pointwise lower scalar curvature bounds for C^0 metrics via
regularizing Ricci flow*, Geometric and Functional Analysis
(2019) **29**, 1703 - 1772, doi: 10.1007/s00039-019-00514-3.
[arXiv:
1907.13116][article]
(see
above for a survey of this work)

*One-level density for holomorphic cusp forms of arbitrary level*
(with O. Barrett, J. DeWitt, R. Dorward, S. J. Miller),
Research in Number Theory (2017) **3**, doi: 10.1007/s40993-017-0091-9.
[arXiv: 1604.03224]

*Random matrix ensembles with split limiting behavior*
(with P. Cohen, J. Dewitt, M. Hlavacek, S.J. Miller, C. Sprunger,
Y. N. Truong Vu, R. Van Peski, K. Yang,
and an appendix joint with M. Fernandez and N. Sieger), Random
Matrices: Theory and Applications (2018) **7** No. 3.
[arXiv:1609.03120]

*Visual properties of generalized Kloosterman sums* (with
A. Z.-Y. Chan, G. Currier, S. R. Garcia, F. Luca, H. Suh),
Journal of Number Theory (2016) **160**, 237-253.
[arXiv:1505.00018]

*An exhibition of exponential sums: visualizing supercharacters*
(with G. Currier, S. R. Garcia, M. de Langis, B. Lutz, H. Suh),
Proceedings of Bridges 2015: Mathematics, Music, Art,
Architecture, Culture (2015), 475-478.

**Spring 2024:** MATH-UA 325 010 Analysis (at NYU)

**Fall 2023:** MATH-GY 7033-1 Graduate
Linear Algebra I (at NYU Tandon)

**Spring 2023:** MATH-GA 2120 Graduate
Linear Algebra II (at NYU)

**Fall 2022:** MATH-UA.0122-005
Calculus II (at NYU)

**Spring 2018:** Graduate Student Instructor (GSI) for Math 16B
Analytic Geometry and Calculus (at UC Berkeley)

**Fall 2017:** GSI for Math 16A Analytic Geometry and Calculus (at UC Berkeley)

**Spring 2017:** GSI for Math 1B Calculus (at UC Berkeley)

**Fall 2016:** GSI for Math 1A Calculus (at UC
Berkeley)