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
He didn't live
long enough to see
 my mathematical vindication.


---H.S.M.Coxeter
on E.C. Escher		   Associate Professor of Mathematics 
  University of North Texas 
 
  Office: 
  General Academic Building  450 

  Mailing Address: 
  University of North Texas
  Mathematics Department
  1155 Union Circle  #311430
  Denton, Texas, USA 76203-5017 

  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 Aachen (=Aix-la-Chapelle), Germany!  Charlemagne made this old Roman spa the home of his Imperial Palace around 790 A.D.  I've joined "Lehrstuhl D für Mathematik" at RWTH Aachen University on a research sabbatical and Alexander von Humboldt Fellowship, July 2008 -- January 2010.    My permanent home is in the math department at the University of North Texas.   Watch out for the Brown Recluse!  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).  My address in Germany:
Mailing Address:

Lehrstuhl A für Mathematik
RWTH Aachen
52056 Aachen
Germany 		Physical Office:
Lehrstuhl A für Mathematik
Room 157, Hauptgebäude
Templergraben 55
D-52062 Aachen
Phone: +49-241-80-94872

MATHEMATICAL RESEARCH

My work combines ideas in Algebra, Geometry, Representation Theory, and Combinatorics.  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 (symplectic reflection algebras) with Witherspoon.  We investigate Hochschild cohomology (and Lie brackets) of skew group algebras.  I've also been working on modular invariant theory with Hartmann.  We study polynomials and forms invariant under reflection groups when the characteristic of the field may divide the group order. 

My work has been supported by several organizations:
        National Science Foundation:
                  Research Grant (DMS-0800951), 2008--2011
                  Research Grant (DMS 0402819), 2004--2008
                  Post-Doctoral Research Fellowship (Award 9971099), 1999--2002
        National Security Agency:  Young Investigators Research Grant, 2002--2004  
        Alexander von Humboldt Foundation:  Research Fellowship (at RWTH Aachen University), 2009  
        Texas Coordinating Board:  Advanced Research Program Grant ($43,469), 2008--2010.

PUBLICATIONS 
TALKS 
GRADUATE STUDENTS

Masters/Ph.D. Advisor for:
        Paisa Seelungawat
        (B.S. from MIT, M.S. from UNT, currently Ph.D. student at Univ. of South Carolina),    

         Briana Foster-Greenwood
        (B.S. from UNT, currently Ph.D. student at UNT,  needs a website,
         visiting "Lehrstuhl D für Mathematik" at RWTH Aachen University, Spring semester 2009).
ALGEBRA SEMINAR
UNDERGRADUATE STUDENTS   
Math Club Test site.  T-shirts on sale in math office, including PINK and black "Math is Sexy" shirts.
 (Not my idea, but don't let me stand in the way...)
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. 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."

Whose the boss...?