91×ÔÅÄÂÛ̳

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 91×ÔÅÄÂÛ̳ 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, 91×ÔÅÄÂÛ̳ Department of Mathematics, 2014-2020
• Director of Undergraduate Studies, 91×ÔÅÄÂÛ̳ Department of Mathematics, 2003-2010
• Visiting Assistant Professor, 91×ÔÅÄÂÛ̳, 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)