|Selected Faculty Research
|| Research Areas: Combinatorics, Representation Theory, Lie Theory, Mathematical/Theoretical Physics
- T. Friedmann, P Hanlon, R. Stanley, M. Wachs, “On a generalization of Lie(k): a CataLAnKe theorem,” Advances in Mathematics 380 (2021) 1075700
- T. Friedmann, P. Hanlon, R. Stanley and M. Wachs, “Action of the symmetric group on the free LAnKe: a CataLAnKe theorem,” Séminaire Lotharingien de Combinatoire 80B(2018), Article #63(FPSAC2018).
- T. Friedmann, “On the derivation of the Wallis Formula for π in the 17th and 21st centuries,” in V. Dobrev (ed.), Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, Springer Proceedings in Mathematics and Statistics 263 (2018).
- T. Friedmann and J. Harper, “On H-spaces and a Congruence of Catalan numbers,” Homology, Homotopy, and Applications 19 (2017) 1.
|| 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.