Mihaela Ifrim

Mihaela Ifrim is a Professor of Mathematics at the University of Wisconsin-Madison, specializing in nonlinear dispersive partial differential equations and fluid mechanics. Her research focuses on well-posedness, global solutions, and asymptotic behavior of equations modeling water waves, free boundary problems, and geometric PDEs, with significant contributions to quasilinear dispersive systems and harmonic analysis techniques.

Her research program centers on nonlinear dispersive equations, fluid mechanics, and harmonic analysis, particularly investigating cubic dispersive equations in one dimension, quasilinear Schrödinger flows, and water wave models. She develops innovative methods including wave packet testing, modified scattering theory, and low-regularity analysis to address long-time dynamics and global existence problems. Her work bridges pure analysis with physical applications in fluid dynamics.

Recent publications reveal a concentrated effort on global well-posedness for cubic dispersive equations across multiple dimensions, with systematic studies of defocusing and focusing cases. Her collaborations, primarily with Daniel Tataru, have produced breakthroughs in free boundary Euler equations, compressible fluids with physical vacuum, and relativistic systems, establishing connections between geometric PDEs and dispersive phenomena.

Professor Ifrim's awards reflect exceptional recognition in mathematical analysis:

• Sloan Research Fellowship (2019-2022)
• NSF CAREER award DMS-1845037 (2019-2024)
• Simons Fellowship in Mathematics (2023-2024)
• NSF Award DMS-2348908 (2024-2027)
• Clare Luce Boothe Professorship (2017-2022)

She actively mentors through the Madison Math Circle, Putnam Club (achieving national ranking #14 in 2019), and Jefferson Middle School MathCounts. Her current NSF grants support fundamental research in dispersive PDEs while her service includes co-organizing major workshops like Women in Nonlinear Dispersive PDEs and MSRI programs on fluid dynamics, demonstrating leadership in fostering collaborative research environments.

Professor Ifrim co-leads the PDE Geometric Analysis seminar at UW Madison and the PDE Virtual Research Seminar with UC Berkeley, creating platforms for international collaboration. Her involvement in organizing the MSRI program 'Mathematical Problems in Fluid Dynamics' and the Oberwolfach Seminar on Free Boundary Problems highlights her role in shaping research directions for the next generation of analysts.