Faculty

Courses Offered (subject to change)

• MATH 150:  Discrete Mathematics
• MATH 162:  Calculus II
• MATH 164:  Multivariable Calculus
• MATH 165:  Linear Algebra and Diff. Eqns.
• MATH 200:  Transition to Higher Math
• MATH 201:  Intro to Probability
• MATH 210:  Intro to Financial Math
• MATH 215:  Fractals and Chaotic Dynamics
• MATH 217:  Math Models in Political Science
• MATH 218:  Math Models in the Life Sciences
• MATH 236H:  Honors Undergrad Algebra. (Group and Ring Theory)
• MATH 240H:  Honors Undergrad Topology
• MATH 248:  Graph Theory
• MATH 255:  Differential Geometry
• MATH 280:  Numerical Analysis
• MATH 436:  Graduate Algebra I
• MATH 437:  Graduate Algebra II
• MATH 440:  Graduate General Topology
• MATH 448:  Computational Topology
• MATH 539:  Topics in Algebraic Geometry I and II
• MATH 546:  Cohomology of Groups
• MATH 548:  Lie groups and Lie algebras
• MATH 549:  Topics in Algebraic Topology

Selected Publications

• "Random gap processes and asymptotically complete sequences." (https://arxiv.org/abs/1909.08688) (With E. Crossen and S. Mkrtchyan), arXiv:1909.08688, Journal of Theoretical Probability 35, (2022), 801-818.
• "On Gabor orthogonal bases over finite prime fields." (https://arxiv.org/abs/1712.09120) (With A. Iosevich, M. Kolountzakis, Y. Lyubarskii, A. Mayeli), arXiv:1712.09120, Bulletin of the London Math. Society, Vol. 53, Issue 2, (2021), 380-391.
• "Rigidity, graphs and Hausdorff dimension." (https://arxiv.org/abs/1708.05919) (With N. Chatzikonstantinou, A. Iosevich and S. Mkrtchyan), arXiv:1708.05919, CANT 2020: Combinatorial and Additive Number Theory IV (2021), 73-106.
• "Cayley Digraphs associated to Arithmetic Groups." (https://arxiv.org/abs/1808.06665) (With D. Covert and Y. Demiroglu), Graphs and Combinatorics, 35(no.2) (2019), 393-417.
• "Direction sets, Lipschitz graphs and density." (https://arxiv.org/abs/1703.01620) (With A. Iosevich), Bulletin of the Hellenic Mathematical Society, Vol 62 (2018), 61-65.
• "Tiling, circle packing and exponential sums over finite fields." (http://arxiv.org/pdf/1507.05861v1.pdf "PDF file") (With C.D. Haessig, A. Iosevich, S. Robins and L. Vaicunas), Analysis Mathematica ,44 no.4, (2018), 433-449.
• "On a canonical construction of tessellated surfaces from finite groups." (https://www.sciencedirect.com/science/article/pii/S0166864117302912) (With M. Herman), Topology and its Applications, Vol 228 (2017), 158-207.
• "The Fuglede Conjecture holds in Z/p x Z/p." (http://arxiv.org/pdf/1505.00883v1.pdf "PDF file") (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." (https://arxiv.org/abs/1601.03473) (With A. Iosevich, A. Liu and A. Mayeli), Bulletin of Hellenic Math Soc. 62 (2018), 80-93.
• "Tiling sets and spectral sets over finite fields." (http://arxiv.org/pdf/1509.01090v1.pdf "PDF file") (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), Journal of Functional Analysis, Vol 273, no.8, (2017), 2547-2577.
• "The Square Root Law and Structure of Finite Rings." (http://arxiv.org/pdf/1405.7657v1.pdf "PDF file") (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 $$(F q)^d$$" (http://arxiv.org/pdf/1311.4788v1.pdf) (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." (http://arxiv.org/pdf/1406.0107v1.pdf "PDF file") (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." (http://arxiv.org/pdf/1407.5607v1.pdf "PDF file") (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." (http://journals.tubitak.gov.tr/math/issues/mat-15-39-6/mat-39-6-11-1412-76.pdf "PDF file") (with M. Herman), Turk. J.  Math., Vol 39, (2015), 913-930.
• "Kakeya Configurations in Lie groups and Homogeneous spaces." (https://arxiv.org/pdf/1303.0895.pdf PDF file") (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." (http://arxiv.org/pdf/1201.5039v2.pdf "PDF file") (With M. Bennett and A. Iosevich), Combinatorica, Vol 34 (6), (2014), 689-706.
• "Lie Algebras and Higher Torsion in p-groups." (http://www.sciencedirect.com/science/article/pii/S0021869313001610) (with N. Rogers), Journal of Algebra, 385, (2013), 192-240.
• "Threshold complexes and connections to number theory." (http://journals.tubitak.gov.tr/math/issues/mat-13-37-3/mat-37-3-14-1112-14.pdf "PDF file") (With T. Winfree), Turk. J. Math., 37, Issue 3, (2013), 511-539.
• "Geometric Configurations in the ring of integers modulo $$p^L$$." (https://arxiv.org/pdf/1105.5373v1.pdf "PDF file") (With D. Covert, A. Iosevich), Indiana University Mathematics Journal 61 (2012), 1949-1969.
• "Bockstein closed 2-group extensions and cohomology of quadratic maps. (http://arxiv.org/pdf/1007.2390v2.pdf "PDF file") (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." (http://arxiv.org/pdf/math/0606374v1.pdf "PDF file") (With E.  Yalcin), Trans. Amer. Math. Soc., No. 12 (2007), 6079-6110.
• "A Quillen Stratification for Hochschild cohomology of blocks." (Hochschild.pdf) (With S. Witherspoon), Trans. Amer. Math. Soc., 358, no. 7 (2006), 2897-2916.
• "On Nilpotent Ideals in the Cohomology Ring of a Finite group." (http://dx.doi.org/10.1016/S0040-9383(02)00086-1) (With E. Yalcin), Topology, 42/5 (2003), 1155-1183.
• "Exponents and the Cohomology of Finite Groups" (http://www.ams.org/journals/proc/2000-128-07/S0002-9939-99-05214-4/S0002-9939-99-05214-4.pdf "PDF file") Proc. Amer. Math. Soc., vol 128, number 7, (2000), 1893-1897.
• "Cohomology of Uniformly Powerful p-groups." (uniform.pdf) (With W. Browder), Trans. Amer. Math. Soc., 352 (2000), 2659-2688.
• "Nilpotent Numbers (expository)." (http://www.jstor.org/stable/2589118) (with K. Shankar), Amer. Math. Monthly, vol 107, number 7, (2000), 631-634.

Awards/Lectureships/Special Positions

• Goergen Award for Excellence in Undergraduate Teaching, 2014
• Director of Graduate Studies, University of Rochester Department of Mathematics, 2014-2020
• Director of Undergraduate Studies, University of Rochester Department of Mathematics, 2003-2010
• Visiting Assistant Professor, University of Rochester, 2000-2003
• Visiting Assistant Professor, University of Wisconsin-Madison, 1997-2000
• Sloan Foundation Doctoral Dissertation Fellowship, 1996
• BS in Mathematics and Physics, Caltech, 1992
• H. J. Ryser Scholarship, Caltech 1991
• U.S. Air Force Mathematics and Science Award, 1988

Grants

• NSA Mathematical Sciences Grant H98230-15-1-0319 (joint with A. Iosevich) for period 2016-2017, (Grant total $55,000 each year)

Graduate Students Past and Present

• Donovan Snyder
  Currently co-advised with Sarada Rajeev in physics
• Charlotte Aten, PhD 2022
  University of Denver
• Charles Brittenham, PhD 2022
  Colgate University
• Semin Yoo, PhD 2021
  Korean Institute for Advanced Study
• Jacob Lichtinger, PhD 2020
  National Institute of Standards and Technology (NIST)
• Erin Brown-Crossen, PhD 2020
  Niagara University (co-advised with S. Mkrtchyan)
• Yesim Demiroglu-Karabulut, PhD 2018
  University of California, Los Angeles (UCLA) (co-advised with D. Covert)
• Brendan Murphy, PhD 2016
  Heilbronn Institute (co-advised with A. Iosevich)
• Dillon Ethier, PhD 2016
  (co-advised with A. Iosevich)
• Patrick Papadopulos, PhD 2016
  (co-advised with F. Cohen)
• Mike Bennett, PhD 2015
  (co-advised with A. Iosevich)
• Esen Aksoy, PhD 2014
  (co-advised with A. Iosevich)