Ben Weinkove

About

Ben Weinkove is associated with the Northwestern University Mathematics Department, which supports research and training activities in the field of dynamics. The research group, supported by the RTG grant titled 'Dynamics: Classical, Modern, and Quantum,' aims to expose young researchers to dynamical systems in the broad sense, including the study of the time-evolution of mechanical systems and abstract models of such systems. The group emphasizes increasing research strength in dynamics both at Northwestern and across the US, with a focus on training a broad group of researchers and fostering vertically integrated mentoring. The faculty involved in this research area cover a wide range of dynamical fields and interact with various other areas of mathematics, including number theory, combinatorics, partial differential equations, quantum mechanics, group theory, and representation theory.

Research topics

• Mathematical analysis
• Mathematics
• Combinatorics
• Geometry
• Applied mathematics
• Physics
• Mathematical optimization
• Quantum mechanics
• Pure mathematics

Selected publications

• The insulated conductivity problem, effective gradient estimates and the maximum principle

  Mathematische Annalen · 2022 · 22 citations

  1st authorCorresponding
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• Weak Harnack inequalities for eigenvalues and constant rank theorems

  Communications in Partial Differential Equations · 2021 · 7 citations

  Senior authorCorresponding

  We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian and Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative version of the constant rank theorem.

  PublisherDOI

• Non-preservation of α-concavity for the porous medium equation

  Advances in Mathematics · 2024-02-12 · 5 citations

  articleSenior authorCorresponding
  PublisherDOI

• The Stefan problem and concavity

  Calculus of Variations and Partial Differential Equations · 2021-07-30 · 5 citations

  articleSenior authorCorresponding
  PublisherDOI

• Concavity of solutions to semilinear equations in dimension two

  Bulletin of the London Mathematical Society · 2022-11-05 · 4 citations

  articleOpen accessSenior author

  Abstract We consider the Dirichlet problem for a class of semilinear equations on two‐ dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.

  PublisherOA PDFDOI

Recent grants

• Elliptic and Parabolic Partial Differential Equations on Manifolds

  NSF · $207k · 2017–2020

• Parabolic flows and canonical metrics in Kahler geometry.

  NSF · $116k · 2005–2008

• PDE's in complex and symplectic geometry

  NSF · $136k · 2008–2011

Frequent coauthors

• Jian Song

  Rutgers, The State University of New Jersey

  31 shared

• Valentino Tosatti

  28 shared

• Albert Chau

  University of British Columbia

  16 shared

• Jacob Sturm

  Rutgers, The State University of New Jersey

  13 shared

• D. H. Phong

  7 shared

• Gábor Székelyhidi

  Northwestern University

  7 shared

• Morgan Sherman

  California Polytechnic State University

  7 shared

• Jianchun Chu

  Peking University

  5 shared

Labs

• RTG Dynamics: Classical, Modern and QuantumPI

Awards & honors

• Alfred P. Sloan Fellowship (2008)
• Fellow of the American Mathematical Society (2017)
• Madan Lal Puri Professor of Mathematics (2024)

Similar researchers at Northwestern University

• David Leeh-62
• Ezra Getzlerh-40
• Alexander Smithh-32