reflect you left-right, and not up-down?
Ludwig Wittgenstein, and
BEFORE YOU EMAIL ME:
UNT students: put the course name and main idea on the subject line!
UNT students: is the answer to your question in the syllabus?
I don't respond to emails about private tutoring (non UNT students), web development, or coding.
Graduate students: nagging is allowed, sometimes encouraged.
Letters of recommendation: best ask 2-6 weeks before due date, more time is required if over a break.
I don't respond to emails asking about research/lab positions;
these go to PhD students in math at UNT.
Post-doc positions are another story.
Saying mathematics is about numbers is like saying literature is
about letters. Likewise, manipulating equations in theoretical
mathematics can be
about as important as manipulating grammar in literature.
Mathematics often has more in common with arts and music than other
scientific fields: We imagine what could be possible. Indeed,
choose theoretical mathematics because it requires more imagination than any other field
they have encountered. Math is also #1 in job satisfication according to JobRated.com. Undergrads: see Tom Forde's page. ALGEBRA
I'm on the steering committee and
organizer for conference
TORA = Texas-Oklahoma
Representations and Automorphic forms
supported by the National Science Foundation and Oklahoma State University, University of Oklahoma, and University
of North Texas (UNT). Next meeting: TORA IX will take place Apr 7-8, 2018 at the University of Oklahoma.
meeting: September 17--18, 2011, UNT. (Plenary speakers: Nils Skoruppa, Sol
Friedberg, Martin Raum.)
meeting: March 23--24, 2013, UNT. (Plenary speakers: Ken Ribet, Nolan
Wallach, Susie Kimport.)
VII meeting: April 8--10, 2016, UNT. (Plenary speakers: Vyjayanthi Chari,
Kon Ono, Nickolas Andersen.)
TORA X meeting: April 5--5, 2019, UNT. (Plenary speakers: Ozlem Imamoglu, David Vogan, Olivia Beckwith.)
work in pure mathematics at intersections of algebra, geometry,
invariant theory, representation theory, and combinatorics.
Recent interests include homological algebra,
deformation theory, cohomology, and Drinfeld orbifold algebras (which
include symplectic reflection algebras, rational
Cherednik algebras, graded Hecke algebras, Drinfeld Hecke algebras,
Weyl algebras, universal enveloping algebras, and twists by a group
action or quantum parameters). I'm also interested in group
codes, i.e., codes in computer science
build on isometry groups and
Physicists often regard space as a Calabi-Yau manifold endowed
with symmetry. We model the local setting with a finite group G acting
linearily on a finite dimensional vector space V. We
mod out by symmetry to obtain the orbifold V/G which
may have singularities. Geometrically, we might replace V/G with a smooth
variety, but Hochschild cohomology recommends an algebraic approach:
replace the ring of invariant polynomials S^G with the
natural semi-direct product algebra S#G.
cohomology governs the deformation theory and
predicts various algebras important in representation theory,
combinatorics, and the geometry of orbifolds.
I also work with reflection
groups. These are groups (acting on a finite dimensional vector
space) generated by reflections: elements that fix a hyperplane
(or "mirror") pointwise. They include the Weyl and Coxeter groups,
complex reflection groups (u.g.g.r.'s), and reflection groups over
arbitrary fields. Their
study intertwines invariant theory and
arrangements of hyperplanes. (Scott
Crass can explain relations with
My work has been supported by
Collaboration Grant for Mathematicians, Award Number 429539, 2016--2021 National Science Foundation:
Standard Research Grant
(DMS-1101177), Principal Investigator (100% credit), 2011--2014
Standard Research Grant (DMS-0800951), Principal Investigator (100% credit), 2008--2011
Standard Research Grant (DMS 0402819), Principal Investigator (100% credit), 2004--2008
Fellowship (Award 9971099), Principal
Investigator (100% credit), 1999--2002
TORA Conference Grant
Conference Grant (DMS-1302770), Co-Principal Investigator, 2013--2014
Conference Grant (DMS-1600642), Co-Principal Investigator, 2013--2014 National Security
Agency: Research Grant, Principal Investigator (100% credit), 2002--2004 Simons
Collaboration Research Grant for Mathematicians, Principal Investigator (100% credit), Award Number 429539. Alexander von
: Research Fellowship (at RWTH Aachen
University), Principal Investigator (100% credit), 2009 Texas
Coordinating Board: Advanced Research Program Grant, Principal Investigator (100% credit),
AWM The American Women for
Mathematics (AWM) organizes a workshop at the joint American Mathematical Society and Mathematical Association of America meetings each January, currently supported by an NSF AWM ADVANCE grant. Sarah Witherspoon and I organized the poster session Jan 2017 and the workshop Jan 2018 on Noncommutative Algebra and Representation Theorywith speakers: Chelsea Walton, Sian Fryer, Van Nguyen, Gordana Todorov, Elizabeth Drellich, Khrystyna Serhiyenko, Ellen Kirkman, Vyjayanthi Chari, Julia Plavnik, Natasha Rozhkovskaya, Pamela Harris, Monica Vazirani, Julia Pevtsova
Outside of office hours and giving lectures, your math instructor is likely advising graduate
students, refereeing papers, writing grant proposals, preparing
manuscripts for publication, doing editorial work for journals,
reviewing budgets, writing talks, skyping or phoning with
collaborators, reviewing university programs, writing reports,
designing new courses, grading papers, evaluating grant applications,
preparing lectures and exams, organizing conferences, reviewing
graduate and job applications, revising articles, writing
letters of recommendation, reviewing PhD theses, proof
reading manuscripts, attending department meetings, updating webpages,
writing computer code, completing mathematical computations, and
proving new theorems. That is why many instructors ask you to make an appointment instead of just dropping by.
I attended the 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 a Research Experience
for Undergraduates 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. Moray eels
provide nice examples for constructing orbifolds.
Maybe not the wolf
eel. And, in case you were wondering, the Mason and Hamlin BB is 212 cm long. And, yeah, it does sound really "fat". Especially with custom Isaac hammers (swoon). Especially Pixies acoustic "Where Is My Mind".
Reflection groups and modular forms:
Images by Douglas Dunham (University
of Minnesota at Duluth), and Charlie Gunn with The Geometry Center
(Univ 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