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Vlassis Mastrantonis

Postdoctoral Researcher
Cornell University
vm429 (at) cornell.edu


About

Welcome to my webpage! I am an H.C. Wang Assistant Professor at Cornell University. I am interested in geometric analysis, convex geometry, several complex variables, and geometric flows.

I completed my PhD in 2025 at the University of Maryland, College Park under the supervision of Yanir A. Rubinstein. Prior to that, I completed Part III of the Mathematical Tripos at Cambridge University in 2018, and received my undergraduate degree in Mathematics from the University of Athens in 2017.

Books

    An invitation to convex, complex, and differential geoemtry via the Mahler conjectures (with Y.A. Rubinstein),
    solicited by the Amer. Math. Soc.

Publications and Preprints

    \(L^p\)-Legendre transforms and Mahler integrals\(:\) Asymptotics and the Fokker-Planck heat flow
    preprint, 2024, arxiv: 2411:10439.
    Two-dimensional Błocki, \(L^p\)-Mahler, and Bourgain conjectures (with Y.A. Rubinstein),
    preprint, 2024, arxiv: 2401:10992, to appear in Indiana Univ. Math. J.
    A Santaló inquality for the \(L^p\)-polar body
    Contemp. Math. 810 (2025), 31-52.
    \(L^p\)-polarity, Mahler volumes, and the isotropic constant (with B. Berndtsson and Y.A. Rubinstein),
    Analysis & PDE 17-6 (2024), 2179-2245.
    The Nazarov proof of the non-symmetric Bourgain-Milman inequality (with Y.A. Rubinstein),
    Indiana Univ. Math. J. 73 (2024), 911-953.
    Relations of the spaces \(A^p(\Omega)\) and \(C^p(\partial\Omega)\) (with N. Georgakopoulos and V. Nestoridis),
    Results Math. 73, 86 (2018).
    Nowhere differentiable functions of analytic type on products of finitely connected planar domains (with C. Panagiotis),
    Monatsh. Math. 187 (2018), 327-341.

Invited Conference Talks

    Midwestern Workshop on Asymptotic Analysis, Indiana University Bloomington, 11-13 October 2024.
    Gothenburg Complex Geometry Conference, Gothenburg, Sweeden, 26-30 August 2024.
    Recent Developments in Geometric Analysis, AMS Spring Eastern Sectional Meeting, Howard University, 6-7 April 2024.
    Convex and Complex: Perspectives on Positivity in Geometry, Cetraro, Italy, October 2022.
    (You can watch the talk here)

Invited Seminar Talks

    Geometric and Functional Inequalities and Applications, May 26, 2025.
    Analysis Seminar, Cornell University, May 5, 2025.
    Analysis Seminar SAMPS, NTUA, Athens, Greece, January 13, 2025.
    Measure Theory Seminar, Kent State University, March 6, 2024.

Outreach

Over the past three years, I have mentored five undergraduate projects for the Directed Reading Program at the University of Maryland:

I also gave a talk at the Interaction between Convex Geometry and Complex Geometry REU at the University of Maryland on July 1, 2024.

Code

magicMahler is a Python library designed for geometric computations involving polytopes in the plane. Key features include calculating essential notions from my research:

Here is an example of a Graham scan implementation:

Graham Scan