Jonathan Pakianathan

Professor of Mathematics

Ph.D. in Mathematics, Princeton University, 1997.

B.S. in Mathematics and Physics, Caltech, 1992.

809 Hylan Hall
(585) 275-2216

jonathan dot pakianathan at rochester period ed u

Fall 2024 Office Hours in Hylan 809:
MATH440: Wednesday 1:55-3PM and Thursday 11AM-noon.

Awards/Lectureships/Special Positions

• Goergen Award for Excellence in Undergraduate Teaching, 2014.
• Director of Graduate Studies, U. Rochester math department, 2014-2020.
• Director of Undergraduate Studies, U. Rochester math department, 2003-2010.
• Visiting Assistant Professor, U. Rochester, 2000-2003.
• 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.

Grants

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

Research Overview

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.

Graduate Students Past and Present

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

Some past courses taught

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

Selected Publications

• “A quantitative version of the Steinhaus theorem.”
  (With A. Iosevich), arXiv:2401.12112, submitted (2024).

• “Random walks and the Euclidean association scheme in finite vector spaces.”
  (With C. Brittenham), arXiv:2401.04814v2, to appear, Canadian Journal of Mathematics (2024).

• “Random gap processes and asymptotically complete sequences.”
  (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.”
  (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.”
  (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.”
  (With D. Covert and Y. Demiroglu), Graphs and Combinatorics, 35(no.2) (2019), 393-417.

• “Direction sets, Lipschitz graphs and density.”
  (With A. Iosevich), Bulletin of the Hellenic Mathematical Society, Vol 62 (2018), 61-65.

• “Tiling, circle packing and exponential sums over finite fields.”
  (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.”
  (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), Bulletin of Hellenic Math Soc. 62 (2018), 80-93.

• “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), Journal of Functional Analysis, Vol 273, no.8, (2017), 2547-2577.

• “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.