- Goergen Award for Excellence in Undergraduate Teaching, 2014.
- Director of Graduate Studies, U. Rochester math department, 2014-current.
- Director of Undergraduate Studies, U. Rochester math department, 2006-2010.
- Visiting Assistant Professor, U.Wisc.-Madison, 1997-2000.
- Sloan Foundation Doctoral Dissertation Fellowship, 1996.
- H. J. Ryser Scholarship, Caltech 1991.
- U. S. Air Force Mathematics and Science Award, 1988.
- NSA Mathematical Sciences Grant H98230-15-1-0319 (joint with A. Iosevich) for period 2016-2017, (Grant total $55,000 each year).
Algebraic topology, cohomology of groups and Lie Algebras. I am currently very interested in applications of topology and algebra in areas of discrete geometry and work intensively with Alex Iosevich and his students.
Courses Offered (subject to change)
- MTH 150: Discrete Mathematics
- MTH 164: Multivariable Calculus
- MTH 210: Intro to Financial Math
- MTH 440: General Topology
- MTH 248: Theory of Graphs
- MTH 448: Computational Topology
- MTH 539: Topics in Algebraic Geometry II
- On a canonical construction of tessellated surfaces from finite groups.
(With M. Herman), Topology and its Applications, Vol 228, (2017), 158-207.
- The Fuglede Conjecture holds in Z/p x Z/p.
(With A. Iosevich and A. Mayeli), Analysis and PDE 10-4, (2017), 757-764.
- Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields.
(With A. Iosevich, A. Liu and A. Mayeli), submitted, 2015.
- Tiling sets and spectral sets over finite fields.
(Paper summarizing REU work done by 14 REU students at the University of Rochester during Summer 2015 under supervision of myself, A. Iosevich and G. Petridis), to appear, Journal of Functional Analysis, 2016.
- Tiling, circle packing and exponential sums over finite fields.
(With C.D. Haessig, A. Iosevich, S. Robins and L. Vaicunas), to appear, Analysis Mathematica, 2017.
- The Square Root Law and Structure of Finite Rings.
(With B. Murphy and A. Iosevich), Moscow Journal of Combinatorics and Number Theory (2017), Vol 7, Iss. 1, 38-72.
- Group actions and Geometric combinatorics in (F_q)^d.
(With M. Bennett, D. Hart, A. Iosevich and M. Rudnev), Forum Mathematicum, Volume 29(1), (2017), 91-110.
- Long paths in the distance graph over large subsets of vector spaces over finite fields.
(With M. Bennett, J. Chapman, D. Covert, D. Hart and A. Iosevich), Journal of the Korean Mathematical Society, Volume 53, (2016), No.1, 115-126.
- On the distribution of distances in homogeneous, compact metric spaces.
(With M. Herman), Topology and its Applications, Volume 193, (2015), 97-99.
- A note on the unit distance problem for planar configurations with Q-independent direction set.
(with M. Herman), Turk. J. Math., Vol 39, (2015), 913-930.
- Kakeya Configurations in Lie groups and Homogeneous spaces.
(With B. Murphy), Topology and its Applications, Vol 180, (2015), 1-15.
- Three-point configurations determined by subsets of (F_q)^2 via the Elekes-Sharir paradigm.
(With M. Bennett and A. Iosevich), Combinatorica, Vol 34 (6), (2014), 689-706.
- Lie Algebras and Higher Torsion in p-groups.
(with N. Rogers), Journal of Algebra, 385, (2013), 192-240.
- Threshold complexes and connections to number theory.
(With T. Winfree), Turk. J. Math., 37, Issue 3, (2013), 511-539.
- Geometric Configurations in the ring of integers modulo p^L.
(With D. Covert, A. Iosevich), Indiana University Mathematics Journal 61 (2012), 1949-1969.
- Bockstein closed 2-group extensions and cohomology of quadratic maps.
(With E. Yalcin), Journal of Algebra 357, (2012), 34-60.
- Basis-conjugating automorphisms of a free group and associated Lie algebras.
(With F. Cohen, V. Vershinin, J. Wu), 146-168, Geom. Topol. Monographs, 13, Geom. Topol. Publ. Coventry, 2008.
- The stable braid group and the determinant of the Burau Representation.
(with F. Cohen), 117-129, Geom. Topol. Monographs, 10, Geom. Topol, Publ. Coventry, 2007.
- Quadratic Maps and Bockstein Closed Group Extensions.
(With E. Yalcin), Trans. Amer. Math. Soc., No. 12 (2007), 6079-6110.
- A Quillen Stratification for Hochschild cohomology of blocks.
(With S. Witherspoon), Trans. Amer. Math. Soc., 358, no. 7 (2006), 2897-2916.
- On Nilpotent Ideals in the Cohomology Ring of a Finite group.
(With E. Yalcin), Topology, 42/5 (2003), 1155-1183.
- Exponents and the Cohomology of Finite Groups,
Proc. Amer. Math. Soc., vol 128, number 7, (2000), 1893-1897.
- Cohomology of Uniformly Powerful p-groups.
(With W. Browder), Trans. Amer. Math. Soc., 352 (2000), 2659-2688.
- Nilpotent Numbers (expository).
(with K. Shankar), Amer. Math. Monthly, vol 107, number 7, (2000), 631-634.