Rajeev Walia, Ph.D.

Faculty, CLI
Specialty: Mathematics
Phone: 507-258-8239
Fax: 507-258-8066
Office: 318 Commons
Email: rwalia@umn.edu

Just ASK Hours

Education

Ph.D., Mathematics, Michigan State University, 2007
M.A., Mathematics, Indian Institute of Technology, Kharagpur, 1998
B.A., Mathematics, Indian Institute of Technology, Kharagpur, 1996

Background

I have always been fascinated by mathematics, whether it involves research or teaching. After receiving my masters in India, I came to the U.S. to pursue a Ph.D. at Michigan State University. Following that, I taught for a few years at the University of California, Riverside before coming to UMR. Altogether, in my many years of teaching, I have taught everything from basic algebra, to calculus, trigonometry, differential equations, linear algebra, discreet mathematics, and so on. In spite of teaching mathematics for so long, my experience at UMR has been exceptionally unique and rewarding. This is primarily because students are highly motivated to learn and excel in connection with UMR’s integrated academic approach across disciplines.

Teaching

For me, mathematics was one of those things (maybe the only thing) that came naturally. Therefore, I am intrigued by the number of students, especially undergraduates, who struggle with mathematical concepts. I find myself continually asking “What is the confusion? Where is the disconnect? What is the best way for me to explain these concepts?” I often believe the growing epidemic of students with a math handicap lies not in an actual lack of ability, but in a wrongful perception that gets reinforced over time. Another explanation for students’ math struggles is an overwhelming anxiety which stems from a failure to differentiate between a systematic approach to problem solving and mass memorization of facts and formulae. Thus continues my passion for teaching. During my years as an instructor, I am glad that I have been able to find answers to some of my questions, but the quest is ongoing, and probably, never ending.

Research

My area of research is in pure math in the field of representation theory of Lie algebras and combinatorics. More specifically, I study tensor factorization and the spin functor for Kac-Moody algebras. A “factorization phenomenon” occurs when a representation of a Lie algebra is restricted to a subalgebra, and the result factors into a tensor product of smaller representations of the subalgebra. This phenomenon can be analyzed for symmetrizable Kac-Moody algebras (including finite-dimensional, semi-simple Lie algebras). I have obtained a few factorization results for a general embedding of a symmetrizable Kac-Moody algebra into another and provided an algebraic explanation for such a phenomenon using Spin construction.

I extended the notion of the Spin functor from finite-dimensional to symmetrizable Kac-Moody algebras, which requires a very delicate treatment. I introduced a certain category of orthogonal g-representations for which, surprisingly, the Spin functor gives a g-representation in Bernstein-Gelfand-Gelfand category. I derived the formula for the character of Spin representation for the above category and worked out the factorization results for an embedding of a finite-dimensional, semi-simple Lie algebra into its untwisted affine Lie algebra.

Select Publication

Walia, Rajeev. “Tensor factorization and Spin construction for Kac-Moody algebras.” Advances in Mathematics 222 (2009), no. 5, 1649–1686.