|Selected Faculty Research
|| Research Areas: Combinatorics, Representation Theory, Lie Theory, Mathematical/Theoretical Physics
|| Research Areas: Number Theory, Algebraic Geometry, History of Mathematics, Expository Writing in Mathematics
- Math through the Ages, expanded second edition, with William P. Berlinghoff. Oxton House and Mathematical Association of America, 2015.
- “Was Cantor Surprised?” The American Mathematical Monthly, 118 (March, 2011), 198–209. Reprinted in Best Writing in Mathematics 2012, ed. Mircea Pitici, Princeton University Press, 2012.
- “Quadratic Twists of Rigid Calabi-Yau Threefolds over ℚ,” in Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds, ed. Radu Laza, Matthias Schütt and Noriko Yui, Fields Institute Communications, 67, Springer, 2013, 517–533.
|| Research Areas: Mathematical Neuroscience, Logic, Algebra
- Jan E. Holly, M. Arjumand Masood, Chiran S. Bhandari. “Asymmetries and Three-Dimensional Features of Vestibular Cross-Coupled Stimuli Illuminated through Modeling” Journal of Vestibular Research 16 (2016) 343-358.
- Jan E. Holly, Scott J. Wood, Gin McCollum. “Phase-Linking and the Perceived Motion during Off-Vertical Axis Rotation” Biological Cybernetics 102 (2010) 9-29.
- Jan E. Holly. “Pictures of Ultrametric Spaces, the p-adic Numbers, and Valued Fields” The American Mathematical Monthly 108 (2001) 721-728.
|| Research Areas: Matrix Analysis, Linear Algebra, Operator Theory
- Livshits, L. ; MacDonald, G. W. ; Marcoux, L. W. ; Radjavi, H. “A spatial version of Wedderburn’s principal theorem.” Linear Multilinear Algebra 63 (2015), no. 6, 1216–1241.
- Livshits, L. ; MacDonald, G. ; Marcoux, L. W. ; Radjavi, H. “Paratransitive algebras of linear operators II.” Linear Algebra Appl. 439 (2013), no. 7, 1974–1989.
- Livshits, L. ; MacDonald, G. ; Marcoux, L. W. ; Radjavi, H. “Paratransitive algebras of linear operators.” Linear Algebra Appl. 439 (2013), no. 7, 1955–1973.
|| Research Areas: Functional Analysis, Operator Theory, Linear Algebra
- Hawkins, K.; Hebert-Johnson, U.; Mathes, B. “The Fibonacci identities of orthogonality” to appear in Linear Algebra and Its Applications.
- Mathes, B. ; Xu, Y. “Rings of Uniformly Continuous Functions” Int. J. Contemp. Math. Sciences (2014), pp. 309 – 312
- Dixon, J.; Goldenberg, M. ; Mathes, B. ; Sukiennik, J. Linear Algebra and Its Applications (2014), pp. 177-187
|| Research Areas: Analysis, Probability, PDEs, Mathematical Physics
- On the Convolution Powers of Complex Functions on Z (with Laurent Saloff-Coste), Journal of Fourier Analysis and Applications (2015)
- Convolution Powers of Complex Functions on Zd (with Laurent Saloff-Coste), Revista Matemática Iberoamericana, (2017)
- Positive-homogeneous operators, heat kernel estimates and the Legendre-Fenchel transform (with Laurent Saloff-Coste), Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos. Progress in Probability. (2017)
||Research Areas: Knot Theory, Geometric Topology
- Additive invariants for knots, links and graphs in 3-manifolds (with Tomova) Geometry & Topology (2018)
- Dehn filling and the Thurston norm (with Baker) Journal of Differential Geometry (2019)
- Distortion and the bridge distance of knots (with Blair, Campisi, Tomova) Journal of Topology (2020).
||Research Areas: Applied Algebraic Geometry and Mathematical Neuroscience
- E. Gross, N. Kazi Obatake, and N. Youngs, Neural ideals and stimulus space visualization 2017, Advances in Applied Mathematics, to appear.
- C. Curto, E. Gross, J. Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, and N. Youngs, What makes a neural code convex?, SIAM Journal of Applied Algebra and Geometry, Vol 1 (2017) 222-238.
- C. Curto, V. Itskov, A. Veliz-Cuba, and N. Youngs. The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bull. Math. Biol., 75 (2013) no. 9, 1571–1611.