Youssef Hakiki
About
I am a Golomb Visiting Assistant Professor in the Department of Mathematics at Purdue University. I hold a Ph.D. in Probability Theory (July 2024) from the Faculty of Sciences at Cadi Ayyad University, Morocco, supervised by Professors Brahim Boufoussi and Mohamed Erraoui. Before that, I was a research assistant at William Marsh Rice University.
My research lies in probability theory, at the interface of rough path theory, the sample path properties of Gaussian random fields, and stochastic partial differential equations (SPDEs). I am currently developing a rigorous integration theory for “rough sheets” — functions indexed by the plane — and using it to study singular SPDEs such as the stochastic wave equation. A second line of my work studies when Gaussian random fields can hit a fixed point, with a focus on the delicate critical dimension. Read more on the research page.
News
- Jun 2026Posted the preprint “On Itô–Stratonovich formula for rough sheets” (with Samy Tindel) on arXiv.
- Jun 2026Gave a talk at the SPDEs Workshop, Ohio State University.
- Apr 2026Posted the preprint “Polarity of points for Gaussian random fields in critical dimension” (with Cheuk Yin Lee and Yimin Xiao) on arXiv.
- Apr 2026Talks at the Vanguard Seminar (UM6P, Rabat) and the Joint Moroccan & Mexican Sciences Academies Workshop on Mathematics, Rabat.
- 2026Awarded the AMS–Simons Travel Grant, 2026–2028.
- Mar 2026Poster and talk at the Seminar of Stochastic Processes (SSP 2026), Union College.
- Nov 2025Talks at the Northeast Probability Seminar (CUNY) and the Probability Seminar, Michigan State University.
Research interests
Sample path properties of random fields · rough path theory · stochastic PDEs · fractional Brownian motion & sheets · Gaussian processes · Hausdorff dimension & hitting probabilities · polarity of points · regularity structures