Jonathan Pakianathan

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

Office: (585) 275-2216
Home: (585) 359-1797
jonpak@math.rochester.edu

Personal Home Page

Awards/Lectureships

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.

Curriculum Vitae

Here is a dvi copy of my curriculum vitae.
Here is a pdf copy of my curriculum vitae.

Selected Publications

(dvi format available for some papers.)

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.

On Generalized Witt Algebras in One Variable: (with N. Kawamoto and K. Nam), preprint.

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 (dvi).
Courses taught at University of Rochester
(With links to the course websites if still available.)

Undergraduate analysis: Functions of a Real Variable I Fall 2002 , Fall 2001 .

Introduction to Discrete Mathematics Spring 2002 , Fall 2001 , Spring 2001 .

Introduction to Topology Spring 2002 .

Introduction to P-adic Analysis Fall 2006 .

Fractals and Computer Graphics Spring 2003 .

Graduate Algebra I
Here are the homeworks from that course: HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9 HW10 Fall 2003 .

Graduate Algebra II
Here are the homeworks from that course: HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 HW9 HW10 Spring 2004 .

Linear Algebra and Differential Equations Fall 2002 , Spring 2003 , Fall 2007 .

Linear Algebra and its Applications Fall 2000 .

Calculus II Spring 2001 .

Calculus II (advanced sequence) Fall 2000 (homepage no longer available).

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 being used by Prof. McMurdy 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). (German, French, Spanish, Italian and Portuguese only.)
Topology Seminar
Click here to go to the topology seminar homepage.
Teaching Spring 2008:

Math 215
Fractals and Computer Graphics.

Here is my schedule for Spring 2008.