About Me

Professor, Department of Mathematics, University of Wisconsin-Madison

Director of Graduate Studies, Department of Mathematics, University of Wisconsin-Madison (from July 2026)

Member of the Scientific Advisory Board, Banff International Research Station (BIRS) (from May 2026)

Research Interests

Recent and Upcoming Events

• Co-organizer with T. Duyckaerts, S. Herr, E. Lenzmann of a proposed workshop on Nonlinear Dispersive Equations, Oberwolfach, 2028 (proposal in preparation)
• Co-organizer with T. Alazard (lead), I. Bejenaru, S. Herr of the conference Waves, Dispersive Dynamics and Harmonic Analysis, in honor of Daniel Tataru, The Centre International de Rencontres Mathématiques (CIRM), Luminy, France, December 6-10, 2027
• Co-organizer of Dynamics in Geometric Dispersive Equations and the effects of Trapping, Scattering and weak Turbulence, III, Banff International Research Station (BIRS), November 29 - December 4, 2026
• Participant at Randomness, analysis and PDEs, organized in honour of Professor Nicolas Burq on the occasion of his 60th birthday, Pisa, Italy, June 8-12, 2026
• Keynote Speaker at the Fourth Annual Joint Alabama-Florida Conference on Differential Equations, Dynamical Systems and Applications, Florida International University, Miami, May 18-19, 2026
• Participant at Nonlinear Waves and Dispersive Equations Workshop, Oberwolfach, Germany, March 1-6, 2026
• Plenary Speaker at 2025 SIAM Great Lakes annual meeting, Illinois Institute of Technology, Chicago, September 27-28, 2025
• Research Visitor at IHES semester in Dispersive PDEs - organized by Frank Merle and Daniel Tataru, France, May 1 - July 1, 2025
• Speaker at Séminaire Laurent Schwartz, Institut des Hautes Études Scientifiques (IHES), Bures-sur-Yvette, May 27, 2025
• Speaker at PDE Seminar, Laboratoire Analyse, Géométrie et Applications-Paris 13, Sorbonne University, June 17, 2025
• Speaker at Workshop on Probabilistic theory and Randomness in Dispersive PDEs organized by Professor Nikolay Tzvetkov, École Normale Supérieure (ENS), Lyon, France, June 11-13, 2025
• Co-organizer with Jacek Jendrej (CNRS), Andrew Lawrie (MIT), Anne-Sophie de Suzzoni (École Polytechnique) of Nonlinear Dispersive Equations: Advances and Perspectives, Luminy, The Centre International de Rencontres Mathématiques (CIRM), France, May 12-16, 2025
• Plenary Speaker at Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, February 24-28, 2025
• Co-organizer with Daniel Tataru of the Minisymposia Recent methods in nonlinear dispersive waves, Conference on Mathematics of Wave Phenomena, Karlsruhe, February 18-24, 2025
• Speaker at Nonlinear Water Waves: Rigorous Analysis and Scientific Computing (24w5207), Banff International Research Station (BIRS), Canada, October 27 - November 1, 2024
• Speaker at Nonlinear Waves and Relativity, Workshop 1, Erwin Schrödinger International Institute for Mathematics and Physics (ESI), University of Vienna, Austria, May 13, 2024
• Speaker at the Analysis and PDE Seminar, Stanford University, March 12, 2024
• Speaker at the Harmonic Analysis and PDE Seminar, UC Berkeley, February 27, 2024

Honors and Awards

• Presidential Early Career Award for Science and Engineering (PECASE), 2025
• Vilas Associate Fellowship, UW Madison, 2025-2027
• Plenary Speaker at 2025 SIAM Great Lakes annual meeting, Illinois Institute of Technology, Chicago, September 27-28, 2025
• Plenary Speaker at Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, February 24-28, 2025
• NSF Award, DMS-2348908, 2024-2027
• 2024 DiPerna Lecture Speaker, UC Berkeley, April 12, 2024
• Invited Address at the Spring 2024 AMS Central Section Meeting, University of Wisconsin-Milwaukee, April 20-21, 2024
• Plenary Speaker at Thirteenth Ohio River Analysis Meeting (ORAM 13), University of Kentucky in Lexington, KY, March 16-17, 2024
• Simons Fellows in Mathematics, Simons Foundation, Spring 2024
• Visiting Miller Professorship Award, Miller Institute in Science, University of California Berkeley, Fall 2023
• Featured in Emissary-MSRI (page 7) in "Focus on the Scientist: Mihaela Ifrim", Spring 2021
• Hilldale Undergraduate/Faculty Research Fellowship, 2020-2021
• Sloan Research Fellowship, Alfred P. Sloan Foundation, 2019-2021
• NSF CAREER Award, DMS-1845037, 2019-2024
• UW Madison 2018 Fall Research Competition Award, deferred
• Honored Instructor Award, University of Wisconsin-Madison, Fall 2018
• Clare Boothe Luce Professorship, 2017-2022
• Clay Mathematics Institute travel award for IHES Summer School on Nonlinear Waves, Bures-sur-Yvette, France, July 18-29, 2016
• William Karl Schwarze Scholarship in Mathematics, Department of Mathematics, University of California at Davis, Spring 2010 - for research and teaching achievements
• Alice Leung Scholarship in Mathematics, Department of Mathematics, University of California at Davis, Spring 2009 - for research achievements

Research

1. Local well-posedness of spatially quasiperiodic gravity water waves in two dimensions
   M. Ifrim, J. Wilkening, X. Zhao
   arXiv, accepted in Advances in Mathematics, 2026 (34 pages)
2. Enhanced lifespan bounds for 1D quasilinear Klein-Gordon flows
   H. Huang, M. Ifrim, D. Tataru
   arXiv, submitted 2026 (65 pages)
3. Global solutions for cubic quasilinear ultrahyperbolic Schrödinger flows
   M. Ifrim, B. Pineau, D. Tataru
   arXiv, accepted in Duke Mathematical Journal, 2025 (59 pages)
4. A-priori estimates for generalized Korteweg-de Vries equations in H^-1(R)
   M. Ifrim, T. Laurens
   arXiv, accepted in Nonlinearity, 2026 (33 pages)
5. Sharp well-posedness for the free boundary MHD equations
   M. Ifrim, B. Pineau, D. Tataru, M. A. Taylor
   arXiv, submitted 2024 (136 pages)
6. Global solutions for 1D cubic defocusing dispersive equations, Part IV: general dispersion relations
   M. Ifrim, D. Tataru
   arXiv, submitted 2024 (63 pages)
7. Nonlinear interpolation and the flow map for quasilinear equations
   T. Alazard, N. Burq, M. Ifrim, D. Tataru, C. Zuily
   arXiv, accepted in Journal of the European Mathematical Society, 2026 (25 pages)
8. Modified scattering for the three dimensional Maxwell-Dirac system
   S. Herr, M. Ifrim, M. Spitz
   arXiv, accepted in Annals of PDE, 2026 (66 pages)
9. Global solutions for cubic quasilinear Schrödinger flows in two and higher dimensions
   M. Ifrim, D. Tataru
   arXiv, submitted 2024 (62 pages)
10. Book: Free Boundary Problems in Fluid Dynamics
    A. Ai, T. Alazard, M. Ifrim, D. Tataru
    Oberwolfach Seminars, vol. 54, Birkhäuser (2024), DOI (362 pages)
11. The global well-posedness conjecture for 1D cubic dispersive equations
    M. Ifrim, D. Tataru
    arXiv, Abel Symposium, 18 (2025) (23 pages)
12. Sharp Hadamard local well-posedness, enhanced uniqueness and pointwise continuation criterion for the incompressible free boundary Euler equations
    M. Ifrim, B. Pineau, D. Tataru, M. A. Taylor
    arXiv, Annals of PDE, 11 (2025), no. 1 (118 pages)
13. Global solutions for 1D cubic dispersive equations, Part III: the quasilinear Schrödinger flow
    M. Ifrim, D. Tataru
    arXiv, Inventiones mathematicae, 242 (2025), no. 1 (69 pages)
14. The lifespan of small data solutions for Intermediate Long Wave equation (ILW)
    M. Ifrim, J.-C. Saut
    arXiv, Communications in Partial Differential Equations, 50 (2025), no. 3 (42 pages)
15. Long time solutions for 1D cubic dispersive equations, Part II: the focusing case
    M. Ifrim, D. Tataru
    arXiv, Vietnam Journal of Mathematics, 52 (2024) (18 pages)
16. Global solutions for 1D cubic defocusing dispersive equations: Part I
    M. Ifrim, D. Tataru
    arXiv, Forum of Mathematics, Pi, 11 (2023) (43 pages)
17. Testing by wave packets and modified scattering in nonlinear dispersive pde's
    M. Ifrim, D. Tataru
    arXiv, Transactions of the American Mathematical Society, Series B, 11 (2024) (41 pages)
18. The time-like minimal surface equation in Minkowski space: low regularity solutions
    A. Ai, M. Ifrim, D. Tataru
    arXiv, Inventiones mathematicae, 235 (2024) (120 pages)
19. The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity
    M. Ifrim, J. Rowan, D. Tataru, L. Wan
    arXiv, Ars Inveniendi Analytica, Paper No. 3 (2022) (31 pages)
20. No pure capillary solitary waves exist in 2D finite depth
    M. Ifrim, B. Pineau, D. Tataru, M. A. Taylor
    arXiv, SIAM Journal on Mathematical Analysis, 54 (2021), no. 4 (13 pages)
21. Two dimensional gravity waves at low regularity II: Global solutions
    A. Ai, M. Ifrim, D. Tataru
    arXiv, Annales de l'Institut Henri Poincaré C Analyse non linéaire, 39 (2022), no. 4 (58 pages)
22. Local well-posedness for quasilinear problems: a primer
    M. Ifrim, D. Tataru
    arXiv, Bulletin of the American Mathematical Society, 60 (2023), no. 2 (19 pages)
23. The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
    M. Disconzi, M. Ifrim, D. Tataru
    arXiv, Archive for Rational Mechanics and Analysis, 245 (2022) (48 pages)
24. The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach
    M. Ifrim, D. Tataru
    arXiv, Annales de l'Institut Henri Poincaré C Analyse non linéaire, 41 (2024), no. 2 (79 pages)
25. Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions
    M. Ifrim, A. Stingo
    arXiv, Forum of Mathematics, Sigma, 13 (2025) (52 pages)
26. Two dimensional gravity waves at low regularity I: Energy estimates
    A. Ai, M. Ifrim, D. Tataru
    arXiv, Annales de l'Institut Henri Poincaré C Analyse non linéaire, 2025 (63 pages)
27. A Morawetz inequality for gravity-capillary water waves at low Bond number
    T. Alazard, M. Ifrim, D. Tataru
    arXiv, Water Waves, 3 (2021), no. 3 (33 pages)
28. Dispersive decay of small data solutions for the KdV equation
    M. Ifrim, H. Koch, D. Tataru
    arXiv, Annales Scientifiques de l'École Normale Supérieure, 56 (2023), no. 6 (41 pages)
29. The NLS approximation for two dimensional deep gravity waves
    M. Ifrim, D. Tataru
    arXiv, Science China Mathematics, 62 (2019), no. 6 (23 pages)
30. No solitary waves in 2-d gravity and capillary waves in deep water
    M. Ifrim, D. Tataru
    arXiv, Nonlinearity, 33 (2020), no. 10 (18 pages)
31. A Morawetz inequality for water waves
    T. Alazard, M. Ifrim, D. Tataru
    arXiv, American Journal of Mathematics, 144 (2022), no. 3 (71 pages)
32. Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
    M. Ifrim, D. Tataru
    arXiv, Annales Scientifiques de l'École Normale Supérieure, 52 (2019), no. 2 (36 pages)
33. Finite depth gravity water waves in holomorphic coordinates
    B. Harrop-Griffiths, M. Ifrim, D. Tataru
    arXiv, Annals of PDE, 3 (2017), no. 1 (82 pages)
34. Two dimensional gravity water waves with constant vorticity: I. Cubic lifespan
    M. Ifrim, D. Tataru
    arXiv, Analysis & PDE, 12 (2019), no. 4 (64 pages)
35. The lifespan of small data solutions to the KP-I
    B. Harrop-Griffiths, M. Ifrim, D. Tataru
    arXiv, International Mathematics Research Notices, 2017, no. 1 (20 pages)
36. The lifespan of small data solutions in two dimensional capillary water waves
    M. Ifrim, D. Tataru
    arXiv, Archive for Rational Mechanics and Analysis, 225 (2017), no. 3 (60 pages)
37. Two dimensional water waves in holomorphic coordinates II: global solutions
    M. Ifrim, D. Tataru
    arXiv, Bulletin de la Société Mathématique de France, 144 (2016), no. 2 (21 pages)
38. Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension
    M. Ifrim, D. Tataru
    arXiv, Nonlinearity, 28 (2015), no. 8 (15 pages)
39. Two dimensional water waves in holomorphic coordinates
    J. K. Hunter, M. Ifrim, D. Tataru
    arXiv, Communications in Mathematical Physics, 346 (2016), no. 2 (72 pages)
40. A modified energy method proving enhanced lifespan of smooth solutions of a Burgers-Hilbert equation
    J. K. Hunter, M. Ifrim, D. Tataru, D. T. Wang
    arXiv, Proceedings of the American Mathematical Society, 143 (2015), no. 8 (6 pages)
41. Enhanced lifespan of smooth solutions of a Burgers-Hilbert equation
    J. K. Hunter, M. Ifrim
    arXiv, SIAM Journal on Mathematical Analysis, 44 (2012), no. 3 (13 pages)
42. A quasilinear Schrödinger equation, large amplitude inertial oscillations in a rotating shallow fluid
    J. K. Hunter, M. Ifrim
    IMA Journal of Applied Mathematics, 78 (2013), no. 4

Proceedings, Reports and Expositions

1. Two dimensional water waves in holomorphic coordinates
   Oberwolfach Reports, Vol 41 (2013), pp 2344-2346
2. Well-posedness and dispersive decay of small data solutions for the Benjamin-Ono equation
   Oberwolfach Reports (Nonlinear Evolution Equations: Analysis and Numerics, 2019 - Oberwolfach report)
3. Long time dynamics for two dimensional water waves
   Oberwolfach Reports (Mathematical Theory of Water Waves, 2019 - Oberwolfach report)
4. Morawetz inequalities for water waves
   T. Alazard, M. Ifrim, D. Tataru
   (13 pages), Proceedings Volume of Conference on Mathematics of Wave Phenomena, Karlsruhe, Germany, 2018

Teaching

Mentoring

Postdoctoral Fellows

• Thierry Laurens, Van Vleck Postdoc, University of Wisconsin-Madison, August 2023 - August 2026
• Albert Ai, Henry Luce and RTG Postdoctoral Fellow, University of Wisconsin-Madison, August 2019 - 2024
• Albert Ai, Simons Mentor (Postdoctoral Mentor), University of California, Davis, June 2023 - June 2025
• Annalaura Stingo, Simons Mentor (Postdoctoral Mentor), University of California, Davis, June 2019 - June 2021

Graduate Students

• Allison Byars, Ph.D. 2026; incoming Postdoctoral Fellow, University of North Carolina at Chapel Hill (Fall 2026)
• Hongjing (Noah) Huang, Ph.D. Student (fifth year), University of Wisconsin-Madison
• Cecily Bartsch, Ph.D. Student, University of Wisconsin-Madison
• Lizhe Wan, former Ph.D. Student, now Postdoctoral Fellow in Beijing

Professional Activities

Service

• Director of Graduate Studies (DGS), Department of Mathematics, University of Wisconsin-Madison, July 2026 - present
• Member of the Scientific Advisory Board of the Banff International Research Station (BIRS), three-year term, May 2026 - 2029

Conference and Workshop Organization

• Co-organizer with T. Duyckaerts, S. Herr, E. Lenzmann of a proposed workshop on Nonlinear Dispersive Equations, Oberwolfach, 2028 (proposal in preparation)
• Co-organizer with T. Alazard (lead), I. Bejenaru, S. Herr of the conference Waves, Dispersive Dynamics and Harmonic Analysis, in honor of Daniel Tataru, The Centre International de Rencontres Mathématiques (CIRM), Luminy, France, December 6-10, 2027
• Co-organizer with D. Tataru, J. Marzuola, A. Ai of the BIRS workshop Dynamics in Geometric Dispersive Equations and the effects of Trapping, Scattering and weak Turbulence, III (26w5556), November 29 - December 4, 2026
• Member of the AWM Research Symposium Organizing Committee
• Member of the 2024 NSF Committee of Visitor (CoV)
• Co-organizer with Jacek Jendrej (CNRS), Andrew Lawrie (MIT), Anne-Sophie de Suzzoni (École Polytechnique) of Nonlinear Dispersive Equations: Advances and Perspectives, Luminy, The Centre International de Rencontres Mathématiques (CIRM), France, May 12-16, 2025
• Co-organizer with Daniel Tataru of the Special Session on Nonlinear waves at the AMS Sectional Meeting, University of Wisconsin-Milwaukee, April 20-21, 2024
• Co-organizer with Daniel Tataru of the Minisymposia Recent methods in nonlinear dispersive waves, Conference on Mathematics of Wave Phenomena, Karlsruhe, February 18-24, 2025
• Co-organizer of the one month research gathering: MSRI program 'Mathematical problems in fluid dynamics' during Summer 2023, July 17 - August 11, 2023
• Chair of Hilldale/Holstrom Physical Sciences Award Committee, University of Wisconsin-Madison, 2024-2025, 2025-2026
• OVCRGE Research Committee member (served as a member of the award committee for the Fall competition, and Villas research awards), UW Madison, 2020-2023
• Co-organizer of the Oberwolfach Seminar: Free Boundary Problems in Fluid Dynamics, October 23-30, 2022
• Co-organizer of the BIRS workshop Women in nonlinear dispersive PDEs, February 5-10, 2023
• Co-organizer of the PDE Geometric Analysis seminar, Madison, 2021-2023
• Co-organizer of the PDE VIRTUAL research seminar, UC Berkeley - UW Madison, 2020-2023
• Co-organizer of the Water waves and other interface problems seminar during the MSRI program, January - May 2021
• Co-organizer of the MSRI program 'Mathematical problems in fluid dynamics' during Spring 2021
• Co-organizer of the MSRI conference 'Introductory Workshop: Mathematical problems in fluid dynamics' during Spring 2021
• Co-organizer of the MSRI conference 'Recent Developments in Fluid Dynamics' during Spring 2021
• Co-organizer of the Celebration of Women in Mathematics at MSRI, May 2021
• Co-organizer of the graduate summer school at MSRI: Introduction to water waves, 2020
• Co-organizer of the AMS Sectional: 'Nonlinear Dispersive Equations and Water Waves', University of Wisconsin, Madison, September 14-15, 2019
• Association for Women in Mathematics Mentor for the Joint Mathematics Meetings, San Diego, CA, January 10-13, 2018

Educational Outreach

• Co-organizer Putnam Club since 2017-2022. Chair of the Putnam Club in 2018-2019 when we ranked 14th nationwide - best UW Madison result in the last 12 years
• Coach for Jefferson Middle School MathCounts team, 2017-2019
• Madison Math Circle Instructor, Fall 2017-2020