Anne  V.  Shepler    
A mathematician 
is a blind man 
in a dark room 
searching 
for a black cat 
which isn't there.

 ---Charles R. Darwin.

   Associate Professor of Mathematics 
  University of North Texas 
  Office:  General Academic Building  450 

  Mailing Address: 
  Department of Mathematics 
  P.O. Box 311430
  University of North Texas 
  Denton, Texas, USA 76203-1430 

  Phone:  (001) 940-565-4943 
  E-mail: ashepler unt.edu

Why does the mirror reflect you left-right, and not up-down?    Coxeter, Ludwig Wittgenstein, and E.C. Escher....

GREETINGS...

from TEXAS!  Oak trees abound, no scorpions or tarantulas in sight.  I'm in the math department at the University of North Texas.  Before Texas, I spent two years at the University of California at Santa Cruz and a year at the University of Wisconsin at Madison.  I graduated from sunny University of California at San Diego  (although Doyle moved to Dartmouth: his free will). 
MATHEMATICAL RESEARCH
        My work combines ideas in Algebra, Geometry, Representation Theory, and Combinatorics and has been supported by several organizations:

I have a special interest in reflection groups. These are groups (acting on a finite dimensional vector space) generated by reflections: elements that fix a hyperplane pointwise. They include the Weyl and Coxeter groups, complex reflection groups (u.g.g.r.'s), and reflection groups over arbitrary fields.  Topics include invariant theory, arrangements of hyperplanes, regular polytopes, Hecke algebras, coinvariant algebras, Coxeter groups, Shephard Groups, and Braid groups.  (Scott Crass can explain relations with Dynamical Systems.)  

Recently, I've been working more in homological algebra.  I study deformation theory, cohomology, and Graded Hecke Algebras with Witherspoon.  We study Hochschild cohomology (and Lie brackets) of skew group algebras.  

I've also been working on modular invariant theory with Hartmann.  We investigate polynomials and forms invariant under reflection groups when the characteristic of the field may divide the group order. 

PUBLICATIONS     I use the arXiv.org e-Print server.
ALGEBRA SEMINAR     Schedule.
STUDENTS    Math Club Test site.  T-shirts on sale in math office, including PINK and black "Math is Sexy" shirts.  (Not my idea.)
RECENT INVITED TALKS
GAP  You want Chevie with linux?  No, you can't use gap4.  Yes, you must install gap3r4p4.  Doesn't compile?

PERSONAL

I grew up in Big Rapids, a small town in West Michigan.   I attended the honors college at Valparaiso University---a small liberal arts school in Indiana.  I minored in the humanities, co-founded a comedy troupe, participated in many theatre productions, and worked for the music department as a piano accompanist.   I decided to major in math after participating in an R.E.U. program at the University of Oklahoma.  I also spent a semester at Hangzhou University in China  (took Chinese language classes and also taught English at the Y.M.C.A.).   Afterwards, I moved to the West Coast to learn mathematics and scuba diving.  My brother, Kent, lives near Madison, Wisconsin.  My sister, Kathy, is working hard in Big Rapids.  I enjoy the native plant society of Texas, SCUBA diving (McAbee webcam), moray eels, mulch, yoga...  Life goal: spot wolf eel (photo: Drew Weiner) in the wild.  Dragon moray would also be nice.

 
Hyperbolic Space:          Reflection groups and modular forms:

circle limit 3:

Images by Douglas Dunham (University of Minnesota at Duluth), and Charlie Gunn with The Geometry Center (University of Minnesota).

Coxeter says of Escher's print: "He got it absolutely right to the millimetre, absolutely to the millimetre. ... Unfortunately, he didn't live long enough to see my mathematical vindication."

My Teutonic relatives....