Eric Rowell
- Courses1
- Reviews2
- School: Texas A&M University
- Campus: College Station
- Department: Mathematics
- Email address: Join to see
- Phone: Join to see
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Location:
College Station, TX - Dates at Texas A&M University: April 2007 - April 2018
- Office Hours: Join to see
Biography
Texas A&M University College Station - Mathematics
Professor Of Mathematics at Texas A&M Univ., Consultant at Microsoft Research, Visiting Professor at Peking Univ.
Higher Education
Eric
Rowell
Bryan/College Station, Texas Area
Two of my passions are topological quantum computation and international travel. I take joy in explaining mathematics to academics and the broader public, so when I can combine these passions I am at my happiest!
Experience
Texas A&M University
Assoc. Prof. of Mathematics
Eric worked at Texas A&M University as a Assoc. Prof. of Mathematics
Texas A&M University
Professor Of Mathematics
Eric worked at Texas A&M University as a Professor Of Mathematics
Texas A&M University
Assistant Professor
Eric worked at Texas A&M University as a Assistant Professor
Indiana University
Postdoctoral Fellow, Mathematics
Eric worked at Indiana University as a Postdoctoral Fellow, Mathematics
Microsoft
Consultant
Consulting at Station Q, researching the computational power of anyons.
Peking University, Beijing International Center For Mathematical Research
Distinguished Visiting Professor
Eric worked at Peking University, Beijing International Center For Mathematical Research as a Distinguished Visiting Professor
University of California
Research Assistant
Eric worked at University of California as a Research Assistant
Education
University of California, San Diego
Ph.D; M.A; B.A
Mathematics; Mathematics
Advisor: Hans Wenzl Thesis Title: Tensor categories arising from quantum groups and BM W -algebras
Publications
Modular categories, integrality and Egyptian fractions
Proceedings of the American Mathematical Society
Abstract: It is a well-known result of Etingof, Nikshych and Ostrik that there are finitely many inequivalent integral modular categories of any fixed rank . This follows from a double-exponential bound on the maximal denominator in an Egyptian fraction representation of . A naïve computer search approach to the classification of rank integral modular categories using this bound quickly overwhelms the computer's memory (for ). We use a modified strategy: find general conditions on modular categories that imply integrality and study the classification problem in these limited settings. The first such condition is that the order of the twist matrix is or , and we obtain a fairly complete description of these classes of modular categories. The second condition is that the unit object is the only simple non-self-dual object, which is equivalent to odd-dimensionality. In this case we obtain a (linear) improvement on the bounds and employ number-theoretic techniques to obtain a classification for rank at most for odd-dimensional modular categories.
