RESEARCH
My research interests are convex and discrete geometry, probability and functional analysis. Topics I study include:
Geometric and functional inequalities, including isoperimetric-type inequalities and other extremal problems
Best and random approximation of convex bodies by polytopes
Partial sphere covering and optimal arrangements on the sphere
Symmetrizations of convex bodies and convex functions
My Erdős number is 3.
Publications
Preprints
Steiner symmetrization on the sphere | arXiv:2406.10614
joint with Bushra Basit, Zsolt Lángi and Jeff Ledford
An extremal problem for the convolution of logarithmically concave functions | arXiv:2401.01033
Submitted.
joint with Michael Roysdon
On Minkowski and Blaschke symmetrizations of functions and related applications | arXiv:2301.12619
Submitted.
Published Original Research
*Indicates undergraduate student co-author.
Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$ | arXiv:2212.12778
Involve, a Journal of Mathematics 17(2), 2024, 311-325.
joint with Nicolas Freeman*, Jeff Ledford and Brandon Walters*
Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas | arXiv:2202.01353
Mathematische Nachrichten 297(3), 2024, 914-931.
joint with Ben Li, Michael Roysdon and Christoph Thaele
An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$ | arXiv:2208.13927
Communications in Contemporary Mathematics 26(3), 2024 (article no. 2350006).
joint with Florian Besau
Extremal arrangements of points on the sphere for weighted cone-volume functionals | arXiv:2205.09096
Discrete Mathematics 346(12), 2023 (article no. 113595).
joint with Jeff Ledford
Extremal general affine surface areas | arXiv:2103.00294
Journal of Mathematical Analysis and Applications 505(2), 2022 (article no. 125506).
The Maximum Surface Area Polyhedron with Five Vertices Inscribed in $\mathbb{S}^2$ | arXiv:2005.13660
Acta Crystallographica Section A: Foundations and Advances 77, 2021, 67-74.
joint with Jessica Donahue* and Ben Li
Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes | arXiv:1905.08862
International Mathematics Research Notices 2021(22), 2021, 17456-17513.
joint with Florian Besau and Gil Kur
A Concentration Inequality for Random Polytopes, Dirichlet-Voronoi Tiling Numbers and the Geometric Balls and Bins Problem | arXiv:1801.00167
Discrete & Computational Geometry 65(3), 2021, 730-763.
joint with Gil Kur
The Surface Area Deviation of the Euclidean Ball and a Polytope | arXiv:1510.03881
Journal of Theoretical Probability 31, 2018, 244-267.
joint with Carsten Schuett and Elisabeth Werner
Collaborators
*Indicates undergraduate student co-author.
Jessica Donahue*
Nicolas Freeman*
Brandon Walters*
Referee/Reviewer Work
I have served as a referee or reviewer for the following venues:
American Mathematical Monthly
Bulletin of the Malaysian Mathematical Sciences Society
Illinois Journal of Mathematics
Journal of Mathematical Analysis and Applications
MathSciNet