Asst Prof, 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 under the direction of Elisabeth Werner. Prior to that, I earned an M.S. in Mathematics from the Ohio State University in 2012, and a B.S. in Applied Mathematics from Columbia University in 2008.

**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 and other areas that appeal to convexity.

Publication list:

- Hoehner, S. On Minkowski and Blaschke symmetrizations of functions and related applications. arXiv: 2301.12619
- Freeman, N., Hoehner, S., Ledford, J., Pack, D. and Walters, B. Surface areas of equifacetal polytopes inscribed in the unit sphere $\mathbb{S}^2$. (Submitted) arXiv: 2212.12778
- Besau, F. and Hoehner, S. An intrinsic volume metric for the class of convex bodies in $\mathbb{R}^n$. (To appear in
*Communications in Contemporary Mathematics*) arXiv: 2208.13927 - Hoehner, S. and Ledford, J. Extremal arrangements of points on a sphere for weighted cone-volume functionals. (Submitted) arXiv: 2205.09096
- Hoehner, S., Li, B., Roysdon, M. and Thaele, C. Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas. (Submitted) arXiv: 2202.01353v2
- Hoehner, S. Extremal general affine surface areas.
*Journal of Mathematical Analysis and Applications***505**(2) (2022), article no. 125506. DOI: 10.1016/j.jmaa.2021.125506 - Donahue, J., Hoehner, S. and Li, B. 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 - Hoehner, S. and Kur, G. 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 - Besau, F., Hoehner, S. and Kur, G. Intrinsic and dual volume deviations of convex bodies and polytopes.
*International Mathematics Research Notices***2021**(22) (2021), 17456--17513. DOI: 10.1093/imrn/rnz277 - Hoehner, S., Schuett, C. and Werner, E. 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

Preprints and citations can be found in the following places:

Some recent talks:

- (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 talk via Zoom) - (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". (online talk via Zoom) - (September 27, 2019)
*Intrinsic and dual volume deviations of convex bodies and polytopes*, New York University/Courant Geometry Seminar.