Pak.jpg
Jonathan Pakianathan


Ph.D. in Mathematics, 1997, Princeton University
B.S. in Physics and Mathematics, 1992, Caltech
Professor
Department of Mathematics
University of Rochester
Rochester, NY 14627.

Office: (585) 275-2216
jonpak@math.rochester.edu

Awards/Lectureships/Special Positions

Goergen Award for Excellence in Undergraduate Teaching, 2014.
Director of Undergraduate Studies, U. Rochester, 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.

Grants

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

Selected Publications

(dvi format available for some papers.)
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), submitted, 2015.
Tiling, circle packing and exponential sums over finite fields.
(With C.D. Haessig, A. Iosevich, S. Robins and L. Vaicunas), submitted, 2015.
The Square Root Law and Structure of Finite Rings.
(With B. Murphy and A. Iosevich), submitted, 2015.
On a canonical construction of tessellated surfaces via finite group theory, Part I.
(With M. Herman, E. Yalcin), submitted, 2014.
On a canonical construction of tessellated surfaces via finite group theory, Part II.
(With M. Herman), submitted, 2014.
The Fuglede Conjecture holds in Z/p x Z/p.
(With A. Iosevich and A. Mayeli), to appear, Analysis and PDE, (2016).
Group actions and Geometric combinatorics in (F_q)^d.
(With M. Bennett, D. Hart, A. Iosevich and M. Rudnev), to appear, Forum Mathematicum, (2016).
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), to appear, Journal of the Korean Mathematical Society, (2015).
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, Volume 180, (2015), 1-15.
Three-point configurations determined by subsets of (F_q)^2 via the Elekes-Sharir paradigm.
(With M. Bennett, 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 Troy 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.
On generalized Witt algebras in one variable.
(With Ki Bong Nam), Turk. J. Math., 35, Issue 3, (2011), 405-436.
Sets of directions determined by subsets of vector spaces over finite fields,
(With A. Iosevich, H. Morgan), Integers, Volume 11, Issue 6, (2011) 815-825.
Correlation Angles and Inner Products: Application to a Problem from Physics.
(With Adam Towsley and David Douglass), ISRN Applied Mathematics, vol. 2011, Article ID 323864, 2011.
Basis-conjugating automorphisms of a free group and associated lie algebras.
(With Fred Cohen, V. Vershinin, J. Wu), 147-168, Geom. Topol. Mongr., 13 , Geom. Topol. Publ. Conventry, 2008.
The stable braid group and the determinant of the Burau Representation.
(With Fred Cohen), 117-129, Geom. Topol. Mongr., 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.
Hochschild Cohomology and Linckelmann Cohomology for Blocks of Finite Groups.
(With S. Witherspoon), J. Pure Appl Algebra, 178 (2003), 87-100.
On Commuting and Non-Commuting Complexes
(with E. Yalcin), Journal of Algebra, 236 (2001) 396-418.
Cohomology of Universal Frattini Extensions
(with A. Adem), J. Pure Appl. Algebra, 159 (2001) 1-14.
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.
Lifting Lie Algebras over the Residue Field of a Discrete Valuation Ring
(with W. Browder), J. Pure Appl Algebra, 142 (1999) 239-247.
Separation of Foreground Radiation from Cosmic Microwave Background Anisotropy Using Multifrequency Measurements
(with W. Brandt, C. Lawrence, A. Readhead and T. Fiola), Astrophysical Journal, vol 424, (1994) 1-21.

Research Interests

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.
I have partial notes with Fred Cohen on the braid groups of surfaces and their relation to mapping class groups and arithmetic groups like SL(2,Z). These notes are based on a seminar Fred gave at the University of Wisconsin, Madison.

If you are interested, here are a few sections of the latest version (last updated: 2 November, 1999)

Braid groups (pdf).

Courses taught at University of Rochester

(Links to course websites have been removed as they are not accessible outside the university intranet. Some notes and HW is posted here but if you would like to see any course materials, just ask me for them by email.)
Undergraduate analysis: Functions of a Real Variable I: Fall 2002, Fall 2001.
Introduction to Discrete Mathematics: Fall 2014, Fall 2010, Spring 2005, Fall 2003, Spring 2002, Fall 2001, Spring 2001.
Graph Theory: Spring 2015.
Introduction to Topology: Spring 2013 (Honors version), Spring 2007, Spring 2002.
Introduction to Differential Geometry: Fall 2010.
Introduction to P-adic Analysis (Graduate Course): Fall 2004 .
Cohomology of Groups (Graduate Course): Fall 2011, Fall 2005 .
Computational Topology: Fall 2015 .
Differential Topology and Intersection Theory with an eye toward Algebraic Geometry (Grad Course): Fall 2013 .
Graduate General Topology: Fall 2014, Fall 2006 .
Vector Bundles, Characteristic Classes and Spectral Sequences (Grad course): Fall 2009, Spring 2010.
Lie Groups, Lie Algebras and their Representations (Grad course): Fall 2010, Spring 2011 .
Fractals and Computer Graphics: Spring 2008, Spring 2006, Spring 2003.
Graduate Algebra I
Here are the homeworks from that course: HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9 HW10 Taught: Fall 2005, Fall 2003.
Here are the coursenotes from that course: N1 , N2 , N3 , N4 , N5 , N6 , N7 , N8 , N9 , N10 , N11 , N12 , N13 , N14 , N15 .
Graduate Algebra II
Here are the homeworks from that course: HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9 HW10 Taught: Spring 2006, Spring 2004.
Mathematical Models in Political Science: Fall 2008.
Mathematical Models in the Life Sciences: Fall 2009, Spring 2011.
Introduction to Financial Mathematics (Honors version): Fall 2013, Fall 2015.
Numerical Analysis: Fall 2012.
Probability Theory: Fall 2004, Fall 2012.
Transition to Higher Mathematics: Spring 2012.
Linear Algebra and Differential Equations: Fall 2002, Spring 2003, Fall 2007.
Linear Algebra and its Applications: Fall 2000.
Calculus II: Spring 2010, Spring 2005, Spring 2001.
Calculus IIA (advanced sequence): Spring 2012, Spring 2004, Fall 2000.
Multivariable Calculus: Spring 2009.
WebWorK for M150 (discrete math), Spring 2002:
While the original WebWorK page has been taken down, the problems I wrote to use WebWorK in M150 are still being used this semester and can be accessed here. You may login to check out the WebWorK sets by following the instructions on the webpage for "practice" users.

Other Work Experience

Summer Undergraduate Research Fellowship in Astronomy, Caltech, Summer 1991.
Summer Intern at L.S.I. Logic, Silicon Valley, Summer 1990.
Summer position making database of power supplies used at Stanford Linear Accelerator Center, Summer 1989.

Famous Quotes and Misc.

Click here for some of my favorite math quotes and propaganda.

Click here for some quotes on rationalism versus dogma.

Click here for some quotes on freedom and liberty. (Page under construction)

Click here if you are interested in showing your support for various petitions and causes.

Click here if you need to translate a short English passage into another language (or vice versa).

Topology Seminar

Click here to go to the topology seminar homepage.

Teaching Spring 2016:

Math 164
Multivariable Calculus.

Here is my schedule for Spring 2016.