Paula Burkhardt-Guim
My last name is pronounced: BURK-hahrt GHIM

My contant information and office hours are available on my math department webcard.

I am an assistant professor of mathematics at Stony Brook University. From 2021 - 2024 I was a Post-Doctoral Associate and NSF Postdoctoral Fellow at NYU Courant, where my mentor was 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 Fall 2024 I am teaching MAT 310 Linear Algebra. I am also a co-organizer for the Stony Brook Geometry / Topology Seminar and the Stony Brook Mathematics Colloquium.

CV

Here is a pdf of my CV.

Papers and Preprints

Smoothing L^\infty Riemannian metrics with nonnegative scalar curvature outside of a singular set, 2024, submitted. [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.

Teaching

Fall 2024: MAT 310 Linear Algebra (at SBU)
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)