Steven Hoehner
Associate Professor of Mathematics

I am an Associate Professor in the Department of Mathematics & Computer Science. I earned a Ph.D. in Mathematics from Case Western Reserve University in 2016, an M.S. in Mathematics from the Ohio State University in 2012, and a B.S. in Applied Mathematics from Columbia University in 2008. I am a first-generation college student and Pell grant recipient.

TEACHING

Courses I have taught at Longwood:

• MATH 135 Mathematical Modeling of Finances
• MATH 164 Precalculus
• MATH 171 Statistical Decision Making
• MATH 175 Discrete Mathematics
• MATH 261 Calculus I
• MATH 280 Linear Algebra
• MATH 307 Game Theory
• MATH 362 Differential Equations
• MATH 372 Mathematical Probability and Statistics I
• MATH 390/490 Directed Independent Study 
• CTZN 410 Critical Reasoning and the Numbers Game in Civil Discourse. An examination of the uses of logic, critical reasoning, mathematics and statistics in civil discourse, focusing on an attempt to get to the bottom of what we and others believe.
• MATH 462 Advanced Calculus (introductory real analysis)

RESEARCH

My research interests lie in Convex and Discrete Geometry, Functional Analysis, Probability, Information Theory and other areas that appeal to convexity. 

Publication list: (* indicates undergraduate student co-author)

• Steven Hoehner and Michael Roysdon. An extremal problem for the convolution of logarithmically concave functions. Submitted. (arXiv:2401.01033)
• Steven Hoehner and Julia Novaes*. An extremal property of the symmetric decreasing rearrangement. Submitted. (arXiv:2305.10501)
• Steven Hoehner. On Minkowski and Blaschke symmetrizations of functions and related applications. Submitted. (arXiv:2301.12619)
• Nick Freeman*, Steven Hoehner, Jeff Ledford, David Pack* and Brandon Walters*. Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$. To appear in Involve, a Journal of Mathematics. (arXiv:2212.12778)
• Florian Besau and Steven Hoehner. An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$. To appear in Communications in Contemporary Mathematics, https://doi.org/10.1142/S0219199723500062. (arXiv:2208.13927)
• Steven Hoehner and Jeff Ledford. Extremal arrangements of points on a sphere for weighted cone-volume functionals. Discrete Mathematics 346(12) (Dec. 2023), https://doi.org/10.1016/j.disc.2023.113595. (arXiv:2205.09096)
• Steven Hoehner, Ben Li, Michael Roysdon and Christoph Thaele. Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas. Mathematische Nachrichten (to appear). DOI: doi/10.1002/mana.202200495 (open access) (arXiv:2202.01353)
• Steven Hoehner. Extremal general affine surface areas. Journal of Mathematical Analysis and Applications 505(2) (2022), article no. 125506. DOI: 10.1016/j.jmaa.2021.125506. (arXiv:2103.00294)
• Jessica Donahue*, Steven Hoehner and Ben Li. The Maximum Surface Area Polyhedron with Five Vertices Inscribed in the Sphere $\mathbb{S}^2$. Acta Crystallographica A77 (2021), 67--74. DOI: 10.1107/S2053273320015089. (arXiv:2005.13660)
• Steven Hoehner and Gil Kur. A Concentration Inequality for Random Polytopes, Dirichlet-Voronoi Tiling Numbers and the Geometric Balls and Bins Problem. Discrete & Computational Geometry 65(3) (2021), 730--763. DOI: 10.1007/s00454-020-00174-3. (arXiv:1801.00167)
• Florian Besau, Steven Hoehner and Gil Kur. Intrinsic and dual volume deviations of convex bodies and polytopes. International Mathematics Research Notices 2021(22) (2021), 17456--17513. DOI: 10.1093/imrn/rnz277. (arXiv:1905.08862)
• Steven Hoehner, Carsten Schuett and Elisabeth Werner. The Surface Area Deviation of the Euclidean Ball and a Polytope. Journal of Theoretical Probability 31 (2018), 244--267. DOI: https://doi.org/10.1007/s10959-016-0701-9. (arXiv:1510.03881)

Some recent or upcoming talks:

• (Upcoming February 22, 2024) A New Geometric Definition of Euler's Number with an Application to Random Polytopes. Online Asymptotic Geometric Analysis Seminar.
• (October 15, 2023) Extremal arrangements of points on the sphere for weighted cone-volume functionals. American Mathematical Society 2023 Fall Southeastern Sectional Meeting, special session on Discrete Geometry and Geometric Optimization, University of South Alabama.
• (August 19, 2023) An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$. Poster presentation at the Informal Analysis Seminar, Kent State University. 
• (June 1, 2023) On Minkowski and Blaschke symmetrizations of functions and related applications. Geometry Seminar at Friedrich-Schiller-Universitat Jena. (online)
• (January 26, 2023) An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$. Online Asymptotic Geometric Analysis Seminar.
• (June 16, 2022) Extremal properties of the sphere for weighted cone-volume functionals. SIAM Conference on Discrete Mathematics (DM22) held at Carnegie Mellon University.
• (June 4, 2022) Asymptotic expected T-functionals of random polytopes with applications to Lp surface areas, Canadian Mathematical Society Summer 2022 meeting (hybrid), special session "Convex geometry and partial differential equations". (online)
• (October 18, 2021) The geometric balls and bins problem. Blackwell Talks Colloquium at Longwood University.
• (June 8, 2021) Extremal general affine surface areas, Canadian Mathematical Society 75th+1 Summer 2021 Meeting (online), special session "New Perspectives on the Brunn-Minkowski Theory". 
• (September 27, 2019) Intrinsic and dual volume deviations of convex bodies and polytopes, New York University/Courant Geometry Seminar.

AWARDS

• 2023 Faculty Excellence in Mentoring Award at Longwood University
• SIAM Early Career Travel Award (June 2022)