Ovidiu-Neculai Avadanei

I am currently a Gibbs Assistant Professor in the Mathematics Department at Yale University. My mentor is Professor Wilhelm Schlag. Here is my CV.

My email is ovidiuneculai.avadanei@yale.edu

My main research area is nonlinear partial differential equations. I am generally interested in nonlinear dispersive equations, such as the surface quasi-geostrophic front equations (SQG) , the Schrödinger and KdV equations, as well as in free boundary problems coming from fluid dynamics, such as the compressible Euler equations in a vacuum setting.

I received my PhD in 2025 from the Mathematics Department at the University of California at Berkeley. My advisor was Professor Daniel Tataru. My dissertation can be viewed here.

Papers and preprints

Counterexamples to Strichartz estimates and gallery waves for the irrotational compressible Euler equation in a vacuum setting arXiv:2504.17932
Low regularity well-posedness for the generalized surface quasi-geostrophic front equation, joint with Albert Ai, accepted in Pure and Applied Analysis, Volume 8, Number 2, 2026, Pages 271-329

arXiv:2311.07551

Low regularity solutions for the surface quasi-geostrophic front equation, joint with Albert Ai arXiv:2310.20143
Well-posedness for the surface quasi-geostrophic front equation, joint with Albert Ai, accepted in Nonlinearity, Volume 37, Number 5, May 2024 arXiv:2212.00117
Well-posedness for the dispersive Hunter-Saxton equation, joint with Albert Ai, accepted in International Mathematics Research Notices, Volume 2023, Issue 9, May 2023, Pages 7845-7882 arXiv:2105.01221

Conference Invited Talks

Recent Trends in Fluid Dynamics, Brin Mathematics Research Center, University of Maryland, College Park, Maryland, USA, April 9, 2026

Conference Contributed Talks

Brown-Yale Analysis/PDE Seminar, Brown University, Providence, Rhode Island, USA, October 25, 2025
Conference on Mathematics of Wave Phenomena, Karlsruhe Institute of Technology, Karlsruhe, Germany, February 24, 2025 (virtual talk)
Workshop for Young Researchers in Mathematics, "Alexandru Ioan Cuza" University of Iasi, Romania, May 23, 2024
Nonlinear Waves and Relativity Thematic Programme, Erwin Schrödinger Institute, Vienna, Austria, May 14, 2024
AMS Spring Central Sectional Meeting, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA, April 20-21, 2024
Spring School on Soliton Dynamics, Texas A&M University, College Station, Texas, USA, March 14-16, 2024
The 19th Prairie Analysis Seminar, Kansas State University, Manhattan, Kansas, USA, November 3-4, 2023
Mathematical Problems in Fluid Dynamics, part 2, Simons Laufer Mathematical Sciences Institute, Berkeley, California, USA, July 17-August 11, 2023
The Tenth Congress of Romanian Mathematicians, University of Pitesti, Pitesti, Romania, June 30-July 5, 2023
Shanks Workshop on Mathematical Aspects of Fluid Dynamics, Vanderbilt University, Nashville, Tennessee, USA, February 19-20, 2022

Poster presentations

Rivière-Fabes Symposium, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA, April 25-27, 2026

Seminar Talks

PDE Seminar, Brown University, Providence, Rhode Island, USA, March 20, 2026
PDE Seminar, Pennsylvania State University, State College, Pennsylvania, USA, February 18, 2026
Analysis Seminar, Yale University, New Haven, Connecticut, USA, April 28, 2025
Analysis and PDE Seminar, University of California at Berkeley, Berkeley, California, USA, April 21, 2025
Analysis Seminar, California Institute of Technology, Pasadena, California, USA, November 27, 2024
USC Analysis and PDE Seminar, University of Southern California, Los Angeles, California, USA, November 25, 2024
Applied and Computational Mathematics Student Seminar, University of South Carolina, Columbia, South Carolina, USA, November 11, 2024 (virtual talk)
Analysis Seminar, Columbia University, New York, New York, USA, September 20, 2024
Analysis and PDE Seminar, University of California at Los Angeles, Los Angeles, California, USA, April 30, 2024
Harmonic Analysis and PDE Student Seminar, University of California at Berkeley, Berkeley, California, USA, September 19, 2023
Harmonic Analysis and PDE Student Seminar, University of California at Berkeley, Berkeley, California, USA, March 7, 2023
PDE and Geometric Analysis Seminar, University of Wisconsin-Madison, Madison, Wisconsin, USA, February 20, 2023
Harmonic Analysis and PDE Student Seminar, UC Berkeley, Berkeley, California, USA, October 12, 2021
Graduate Student Working Group, as part of the Mathematical problems in fluid dynamics(Virtual) program, Mathematical Sciences Research Institute, Berkeley, California, May 5, 2021
Sesiunea Nationala de Comunicari Stiintifice Studentesti de Matematica, "Alexandru Ioan Cuza" University of Iasi, Romania, July 4-7, 2019

Conferences attended as participant

Nonlinear Waves and Dispersive Equations Workshop, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach-Walke, Germany, March 1-6, 2026
3rd Simons Math Summer Workshop: Partial Differential Equations of Classical Physics, Simons Center for Geometry and Physics, Stony Brook, New York, USA, July 10-18, 2025
Paris-Saclay conference in Analysis and PDE, Laboratoire de Mathématiques d'Orsay, Orsay, France, May 27-31, 2024
Recent developments in wave turbulence theory, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA, April 5-6, 2024
Advances in Nonlinear Analysis and Nonlinear Waves, IHES, Le Bois-Marie, France, May 22-26, 2023
Southern California Analysis and Partial Differential Equations, University of California at San Diego, San Diego, California, USA, November 2-3, 2019
Instruments of Algebraic Geometry, University of Bucharest, Faculty of Mathematics and Computer Science, September 17-22, 2017, Bucharest, Romania
XIIIème Colloque Franco-Roumain de Mathématiques Apliquées, ''Alexandru Ioan Cuza'' University of Iasi, Faculty of Mathematics, August 25-29, 2016

Summer Schools and Workshops

Oberwolfach Seminar: Free Boundary Problems in Fluid Dynamics, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach-Walke, Germany, October 23-29, 2022
Shanks Workshop on Mathematical Aspects of Fluid Dynamics, Vanderbilt University, Nashville, Tennessee, February 19-20, 2022<\li>
Summer Program in Partial Differential Equations(Virtual Summer Graduate School), University of Texas at Austin, Austin, May 17-21, 2021 and May 24-28, 2021
Introductory Workshop: Mathematical problems in fluid dynamics(Virtual Workshop), Mathematical Sciences Research Institute, Berkeley, January 25-February 05, 2021
Connections Workshop: Mathematical problems in fluid dynamics (Virtual Workshop), Mathematical Sciences Research Institute, Berkeley, January 20-22, 2021
Mathematical problems in fluid dynamics (Virtual Program), Mathematical Sciences Research Institute, Berkeley, January 19-May 28, 2021
Introduction to water waves (Virtual Summer Graduate School), Mathematical Sciences Research Institute, Berkeley, July 27-August 07, 2020
Sesiunea Nationala de Comunicari Stiintifice Studentesti de Matematica, "Alexandru Ioan Cuza" University of Iasi, July 4-7, 2019
Scuola Matematica Interuniversitaria, Universita degli Studi di Perugia, Department of Mathematics and Computer Science, July 23-August 17, 2018
Workshop for Young Researchers in Mathematics, ''Simion Stoilow'' Institute of Mathematics of the Romanian Academy (IMAR), May 17-18, 2018
Instruments of Algebraic Geometry, University of Bucharest, Faculty of Mathematics and Computer Science, September 11-15, 2017, Bucharest, Romania
Modern Mathematics Summer School, Jacobs University, Bremen, Germany, July 1-11, 2017

Teaching Experience

Gibbs Assistant Professor

Graduate Student Instructor

Conference and Seminar organization

Together with Allison Byars, I co-organized a Special Session called "Recent developments in the dynamics of nonlinear dispersive equations I" as part of the AMS Spring Central Sectional Meeting from April 18 to April 19, 2026.
In Fall 2023 and Spring 2024 I co-organized the UC Berkeley Harmonic Analysis and Differential Equations Student Seminar (HADES) together with Benjamin Pineau and Izak Oltman.