Alireza Ataei

Short presentation

I am doing my PhD in mathematics. My main topic is partial differential equations (PDEs). I aim to understand the equations which are coming from natural science and develop the necessary tools for studying the solutions.

Biography

Education and Academic degrees:

• PhD in Mathematics, Uppsala University, 2021.
• MSc in mathematics, ETH Zürich, 2018-2020.
• BSc in Mathematics, Sharif University of Technology, 2014-2018

Awards:

• MSP Scholarship, ETH University, Switzerland, 2018.
• An Outstanding Student at Sharif University of Technology, 2018.
• Second Place, 18th International Mathematical Olympiad for University Students, Tehran, Iran, 2017.
• First Rank, National Scientific Student Olympiad in Mathematics, Tehran, Iran, 2017.
• Third Rank and Gold medal, Iranian Mathematics Society Competition (IMS), Tehran, Iran, 2016.
• Gold medal, University Students Contest of Mathematics, South Korea, 2016.
• Third prize, International Mathematical Competition for University Students, Bulgaria, 2016

Research

Summary of my research interests are as follows:

Partial differential equations: Harmonic analysis, Linear and non-linear elliptic and parabolic differential equations, Kato square root problem, fractional differential equations, Calculus of variations, nonlinear Schrödinger equation

Mathematical physics: Many body quantum mechanics, stability of anyons, Bose-Einstein condensate

Preprints:

• A. Ataei, M. Egert, and K. Nyström. The Kato square root problem for weighted parabolic operators. Accepted in Analysis and PDEs, (2022).
• A. Ataei and K. Nyström. The Kato square root problem for parabolic operators with an anti-symmetric part in BMO. Preprint arXiv:2210.01663, (2022).
• A. Ataei and A. Tavakoli. A comparison method for the fractional Laplacian and applications. Accepted in Advances in Mathematics (2024).
• A. Ataei and K. Nyström. On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients. Published in Potential Analysis (2024).
• A. Ataei. Boundary behavior of solutions to fractional $p$-Laplacian. Accepted in Advances in Calculus of Variations, (2023).
• A. Ataei. Existence and uniqueness of the solutions to convection-diffusion equations. Preprint arXiv:2310.20269, (2023).
• A. Ataei, D. Lundholm, D. T. Nguyen. A generalized Liouville equation and magnetic stability. Preprint arXiv:2404.09332 (2024).
• A. Ataei. A sharp condition on global well-posedness of Chern-Simons-Schrödinger equation. Preprint arXiv:2405.07315 (2024).