Research Interests
Research Interests
Mathematics Education
Analysis and Partial Differential Equations (Fluid Dynamics)
Mathematics Education
Analysis and Partial Differential Equations (Fluid Dynamics)
A new type of stable shock formation in gas dynamics (with Isaac Neal, Steve Shkoller and Vlad Vicol); Communications on Pure and Applied Analysis; 23(10); 1423–1447; https://doi.org/10.3934/cpaa.2023118; 2024
Global Solutions to the Compressible Euler Equations with Heat Transport by Convection Around Dyson’s Isothermal Affine Solutions; Archive for Rational Mechanics and Analysis; 241(2); 947–1007; http://link.springer.com/article/10.1007/s00205-021-01669-w; 2021
The vacuum boundary problem for the spherically symmetric compressible Euler equations with positive density and unbounded entropy; Journal of Mathematical Physics; 62(2); 021504; https://doi.org/10.1063/5.0037656; 2021
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state (with Juhi Jang and Mahir Hadžić); Nonlinearity; 34(1); 33–91; https://dx.doi.org/10.1088/1361-6544/abb03b; 2021
Section NExT Workshop: Kinetic Mathematics Activities; Mathematical Association of America (MAA) SoCal-Nevada Section Meeting; USC; March 2026
Implementing Mastery-Based Grading in Business Calculus: Reflections and Next Steps; American Mathematical Society (AMS) Contributed Paper Session on Mathematics Teaching, Learning, and Education; 2026 Joint Mathematics Meetings; January 2026
Active Learning Activities in our Calculus I Classes Part II (with Felicia Tabing); Math Education Seminar, University of Southern California (USC); October 2024
Active Learning Activities in our Calculus I Classes Part I (with Felicia Tabing); Math Education Seminar; USC; October 2024
Vanderbilt University PDE Invited Seminar; January 2024
ICIAM 2023 Contributed Talk; August 2023
AMS 2023 Spring Western Sectional Meeting: Special Session on Nonlinear PDEs in Fluid Dynamics Invited Presentation; May 2023
University of Southern California (USC) PDE Invited Seminar; April 2023
Fluids in New Zealand (FiNZ) Workshop 2023 Contributed Talk (virtual); February 2023
UW-Madison PDE Invited Seminar; December 2022
2022 Shanks Workshop on Mathematical Aspects of Fluid Dynamics Contributed Talk; Vanderbilt University; February 2022
UC Davis PDE and Applied Math Invited Seminar (virtual); May 2021
USC Department of Mathematics Open House Poster Session (virtual); March 2021
MSRI Mathematical Problems in Fluid Dynamics Program Five Minute Research Talk (virtual); February 2021
UC Berkeley Harmonic Analysis and Differential Equations Student Seminar (HADES) Invited Talk (virtual); February 2021
UC Davis Student-Run Analysis & PDE Seminar Invited Talk (virtual); February 2021
3rd Annual Meeting of the SIAM Texas-Louisiana Section Analytical Aspect of Nonlinear Wave Equations Mini-symposium Invited Presentation (virtual); October 2020
2020 Shanks Workshop on Mathematical Aspect of Fluids Contributed Talk; Vanderbilt University; March 2020 (canceled)
SIAM Conference on Analysis of Partial Differential Equations Poster Session; Palm Springs, CA; December 2019
MSRI Summer Graduate School Recent Topics on Well-Posedness and Stability of Incompressible Fluid and Related Topics Research Talk; Berkeley, CA; July 2019
University of Michigan Conference on Nonlinear Partial Differential Equations and Applications Poster Session; July 2019
USC Summer School on Recent Advances in Mathematical Fluid Dynamics Research Talk; May 2019
USC Graduate Analysis Seminar; April 2018
USC Department of Mathematics Graduate Research Poster Session; March 2018