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, Germany!  Charlemagne made this old Roman spa the home of his Imperial Palace around 790 A.D.  I've joined  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.    My address in Germany:

Mailing Address: Lehrstuhl D 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

Recently, I've been working more in homological algebra, examining deformation theory, cohomology, and Graded Hecke Algebras (which include symplectic reflection algebras, Cherednik algebras, "Drinfeld Hecke algebras", etc.) with Witherspoon.  Connections with geometry abound: Physicists often regard space as a Calabi-Yau manifold endowed with symmetries.  We model this situation with the action of a finite group G acting linearily on V=C^n, complex space.  We mod out by the symmetry and regard the orbifold V/G.  The coordinate ring of V/G is the ring of invariant polynomials C[V]^G.  The orbifold V/G may have singularities and so we replace V/G with a smooth variety.  Hochschild cohomology tells us to replace the ring of invariant polynomials with the natural semi-direct product C[V]#G.  This cohomology also governs the deformation theory of C[V]#G, from which various Hecke algebras arise. 

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.

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

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GAP  You want Chevie with linux?  No, you can't use gap4.  Yes, you must install gap3r4p4.  Doesn't compile?

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PERSONAL 
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 California for grad school and scuba diving (McAbee webcam, moray eels).  Life goal: spot wolf eel (photo: Drew Weiner) in the wild.  Dragon moray would also be nice.  I religiously mulch. 

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Hyperbolic Space:          Reflection groups and modular forms:

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."

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My boss and my other boss..