Jonathan Pakianathan

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

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

Personal Home Page

Awards/Lectureships/Special Positions

Director of Undergraduate Studies, U. Rochester, 2006-2010.
Visiting Assistant Professor, U.Wisc.-Madison, 1997-2000.
Sloan Foundation Doctoral Dissertation Fellowship, 1996.
E. T. Bell Mathematics Award, Caltech 1991.
U. S. Air Force Mathematics and Science Award, 1988.

Selected Publications

(dvi format available for some papers.)

Three-point configurations determined by subsets of (F_q)^2 via the Elekes-Sharir paradigm.: (With M. Bennett, A. Iosevich), submitted March 2012.

Bockstein closed 2-group extensions and cohomology of quadratic maps.: (With E. Yalcin), Journal of Algebra 357 , (2012), 34-60.

Geometric Configurations in the ring of integers modulo p^l.: (With D. Covert, A. Iosevich), to appear, Indiana University Journal of Mathematics.

Quota Complexes, Persistent Homology and the Goldbach Conjecture.: (With Troy Winfree), Submitted April 2011.

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.

Higher torsion in p-groups, Casimir operators and the classifying spectral sequence of a Lie algebra.: (With N. Rogers), Submitted July 2010.

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 interested in studying properties of the cohomology of p-groups. Specifically I am trying to describe the exponent and asymptotic exponent of the integral cohomology of a p-group directly in terms of the structure of the group. I am also interested in families of infinite dimensional semisimple Lie algebras such as the generalized Witt algebras.
I am trying to type up some 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 2010, Spring 2005, Fall 2003, Spring 2002, Fall 2001, Spring 2001.

Introduction to Topology: 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 2005 .

Graduate General Topology: 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.

Probability Theory: Fall 2004.

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 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 by other professors 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 2012:

Math 162
Calculus IIA.
Math 200
Transition to Higher Math.

Here is my schedule for Spring 2012.