Jonathan Pakianathan

**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.

- (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.

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

**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.

**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.

**Math**164*Multivariable Calculus.*