Assistant Professor of Mathematics

hoehnersd@longwood.edu | |

Phone | (434) 395-2249 |

Department | Mathematics & Computer Science |

Office | Rotunda 344 |

I am an Assistant 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.

**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 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 A***77**(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)

Preprints and citations can be found in the following places:

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)