Tristan Buckmaster

About

Tristan Buckmaster is a Professor of Mathematics currently at New York University, a position he has held since 2022. Prior to this, he was a Professor of Mathematics at the University of Maryland from 2022 to 2023, and an Assistant Professor of Mathematics at Princeton University from 2017 to 2022. He began his academic career as a Courant Instructor at New York University from 2014 to 2017. Buckmaster holds a PhD from the University of Leipzig and the Max Planck Institute for Mathematics in the Sciences, awarded in 2014. His research has been recognized with several prestigious honors, including the 2019 Clay Research Award, the 2020 Hadamard Lectures at the Institut des Hautes Études Scientifiques, and the 2014 Leipzig Promotionspreis (PhD Prize). He has also been a member of the Institute for Advanced Study during 2021-2022, participating in the program on H-Principle and Flexibility in Geometry and PDEs. Buckmaster holds dual Australian and British citizenship and is a US permanent resident.

Research topics

• Mathematics
• Physics
• Mathematical analysis
• Mechanics

Selected publications

• Smooth imploding solutions for 3D compressible fluids

  Forum of Mathematics Pi · 2025-01-01 · 10 citations

  articleOpen access1st authorCorresponding

  Abstract Building upon the pioneering work of Merle, Raphaël, Rodnianski and Szeftel [67, 68, 69], we construct exact, smooth self-similar imploding solutions to the 3D isentropic compressible Euler equations for ideal gases for all adiabatic exponents $\gamma>1$ . For the particular case $\gamma =\frac 75$ (corresponding to a diatomic gas – for example, oxygen, hydrogen, nitrogen), akin to the result [68], we show the existence of a sequence of smooth, self-similar imploding solutions. In ad…

  PublisherDOI

• Intermittent Convex Integration for the 3D Euler Equations

  Princeton University Press eBooks · 2023-07-11 · 7 citations

  book1st authorCorresponding

  A new threshold for the existence of weak solutions to the incompressible Euler equations To gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solutions to these PDEs that exhibit turbulent properties. This book belongs to such a program, one that has brought convex integration techniques into hydrodynamics. Convex integration techniques have been…

  PublisherDOI

• Smooth imploding solutions for 3D compressible fluids

  arXiv (Cornell University) · 2022-08-19 · 6 citations

  preprintOpen access1st authorCorresponding

  Building upon the pioneering work [Merle, Raphaël, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413, 2022] we construct exact, smooth self-similar imploding solutions to the 3D isentropic compressible Euler equations for ideal gases for all adiabatic exponents $γ>1$. For the particular case $γ=\frac75$ (corresponding to a diatomic gas, e.g. oxygen, hydrogen, nitrogen), akin to the previous result, we show the exis…

  PublisherOA PDFDOI

• Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks

  arXiv (Cornell University) · 2022-01-18 · 2 citations

  preprintOpen accessSenior author

  Whether there exist finite time blow-up solutions for the 2-D Boussinesq and the 3-D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new numerical framework, employing physics-informed neural networks (PINNs), that discover, for the first time, a smooth self-similar blow-up profile for both equations. The solution itself could form the basis of a future computer-assisted proof of blow-up for both equations. In addition, we demonstrate PINNs could be su…

  PublisherOA PDFDOI

• Discovery of Unstable Singularities

  ArXiv.org · 2025-09-17

  preprintOpen access

  Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial conditions. Historically, numerical approaches have primarily identified stable singularities. However, these are not expected to exist for key open problems, such as the boundary-free Euler and Navier-Stokes cases, where unstable singularities are hypothesiz…

  PublisherOA PDFDOI

Recent grants

• Analytic Methods in Hydrodynamic and Wave Turbulence

  NSF · $201k · 2019–2022

• CAREER: Singularities in fluids

  NSF · $234k · 2022–2024

• Analytic Methods in Hydrodynamic and Wave Turbulence

  NSF · $117k · 2016–2018

Frequent coauthors

• Vlad Vicol

  60 shared

• Maria Colombo

  18 shared

• Jalal Shatah

  New York University

  17 shared

• Steve Shkoller

  University of California, Davis

  14 shared

• Javier Gómez-Serrano

  Brown University

  13 shared

• Pierre Germain

  11 shared

• Camillo De Lellis

  9 shared

• László Székelyhidi

  8 shared

Awards & honors

• 2019 Clay Research Award (joint with Vlad Vicol and Philip I…

Similar researchers at New York University

• Jiawei Zhangh-76
• Foster Provosth-60
• Panagiotis Ipeirotish-50