My last name is pronounced:

**Office:** 906 Warren Weaver Hall

**Email:** pbguim@cims.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.

In Spring 2023 I am teaching MATH-GA 2120 Graduate Linear Algebra II. I am also a co-organizer for the Courant Geometric Analysis and Topology Seminar.

*ADM mass for C^0 metrics and distortion under Ricci-DeTurck
flow*, 2022, submitted.
[arXiv:
2208.145506]

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

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

**Spring 2018:** GSI, Math 16B with Professor Yuan (at UC Berkeley)

**Fall 2017:** GSI, Math 16A with Professor Paulin (at UC Berkeley)

**Spring 2017:** GSI, Math 1B with Professor Stankova (at UC Berkeley)

**Fall 2016:** GSI, Math 1A with Professor Paulin (at UC
Berkeley)