Algebraic Topology. Currently, I am most interested in using methods of algebraic topology to capture rigorously the concept of conformal field theory and modular functors via lax algebras over 2-theories, and in resulting connections with elliptic cohomology. Recently, I also became interested in D-brane categories (where some of the same formalism applies) and in fundamental string theory, in particular the N=2-string and supergravity.
J.M.Gomez, P.Hu and I.Kriz: Stringy bundles and infinite loop space theory
P.Hu, I.Kriz and K.Ormsby: Some remarks on motivic homotopy theory over algebraically closed fields
P.Hu and I.Kriz: On modulXSar functors and the ideal Teichmueller tower
P.Hu and I.Kriz: Conformal field theory and elliptic cohomology
I.Kriz: On spin and modularity in conformal field theory
P.Hu, I.Kriz and A.A.Voronov: On Kontsevich's Hochschild cohomology conjecture
P.Hu and I.Kriz: Closed and open conformal field theories and their anomalies
I.Kriz: The BRST cohomology of the N=2-string
I.Kriz: On the N-superconformal algebra
I.Kriz: Conway number games for multiple players
Here is a link to the Hopf Topology Archive at Purdue.
Here is a link to Bob Bruner's Midwest Topology Seminar web page and an old Midwest Topology Seminar which was held in Ann Arbor.
Summer 08: Math 215 Winter 08: Math 696. Fall 07: Currently, Math 695 and Math 285. Last semester, I was teaching Math 797 (Conformal field theory).
Handout 1:Two basic substitutions.
Handout 2:Existence and uniqueness for a first order LDE .
Handout 3:Some basic theory for systems of ODE's. .
Handout 4:Separation of variables for autonomous systems of two ODE's. .
Handout 5:The determinant.
Handout 6:From integrating factors to variation of constants.
Here is a link to some of my old teaching. Recently, I taught Math 285, Math 286, Math 695 and Math 696 (Algebraic Topology).
Now featured in the Scientific American.
If you ever tried the 15-puzzle or Rubik's cube, you may be interested in the following three puzzles, which were programmed by Paul Siegel, a Michigan undergraduate, as a part of an REU project. The puzzles should run on any Windows32 machine.
For instructions, or to find out how solving these puzzles will help you learn about Sporadic simple groups without taking a course in advanced algebra, click here: README
Here is a picture of a prototype of the Number Planet, a mechanical puzzle designed by Oskar Van Deventer and myself, and based on M12. For more questions, please email me.
An interesting J.S.Bach webpage
Listen to my home recording of Ricercar by J.S. Bach, the Etude in C major, Op. 10, no. 1 by F.Chopin or the Nocturne in F minor, Op. 55, no.1 by F.Chopin. For more complex music, try the Sonata in B flat major, Op.106, ("Hammerklavier"), 4th movement by L.van Beethoven. For explanation of this prelude and fugue, see this link. Here is my rendition of the Beethoven sonata Op. 109, 1st and 2nd movement and 3rd movement , and my brief essay on the piece. For jazz, try my rendition of Sehnsucht by Brad Mehldau. Here is Beethoven's sonata Op. 111, 1st movement and 2nd movement.
If you like pop music, here is my rendition of Lucky by Jason Mraz.
Here is me playing my own pieces Prelude , Serenade and Sad Song. Here is a brief explanation of the pieces.