My research interests lie in convex and discrete geometry, functional analysis, probability and information theory. Topics I've studied 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;
Affine surface areas and applications.
My Erdős number is 3.
*Indicates undergraduate student co-author.
New fiber and graph combinations of convex bodies | arXiv:2503.05392
To appear in Mathematika.
joint with Sudan Xing
On the Optimality of Random Partial Sphere Coverings in High Dimensions | arXiv:2501.10607
Submitted 12/30/2024.
joint with Gil Kur
On a partial covering problem for the sphere
Submitted 10/9/2024.
joint with Anna Jackson* and Reese Vincent*
On maximal intersection position for logarithmically concave functions and measures | arXiv:2401.01033
Submitted 3/18/2025.
joint with Michael Roysdon
Steiner symmetrization on the sphere | arXiv:2406.10614
To appear in the Indiana University Mathematics Journal.
joint with Bushra Basit, Zsolt Lángi and Jeff Ledford
On Minkowski symmetrizations of $\alpha$-concave functions and related applications | arXiv:2301.12619
Submitted 12/10/2024.
An extremal property of the symmetric decreasing rearrangement | arXiv:2305.10501
joint with Júlia Novaes*
*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, David Pack* 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 Schütt and Elisabeth Werner
I have been blessed to work with many talented people, including the following coauthors:
(*Indicates undergraduate student co-author.)
Jessica Donahue*
Nicolas Freeman*
Anna Jackson*
Júlia Novaes*
David Pack*
Reese Vincent*
Brandon Walters*
Sudan Xing, June 2024
Ben Li, January 2022
Florian Besau, March 2020
Gil Kur, November 2019
I have served as a referee or reviewer for the following:
American Mathematical Monthly
Bulletin of the Malaysian Mathematical Sciences Society
Illinois Journal of Mathematics
Incite: The Journal of Undergraduate Scholarship (Longwood University)
Journal of Mathematical Analysis and Applications
MathSciNet