Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
206 Kerchof Hall
141 Cabell DrCharlottesville, Virginia 22904
Diagonal harmonics and Schubert calculus
Source: The Simons Foundation, Inc.
August 15, 2021 – August 14, 2022
Collaborative Research: Catalan function and Schubert calculus
Source: U.S. National Science Foundation (NSF)
July 01, 2019 – June 30, 2022
Combinatorics of Macdonald Polynomials and Schubert Calculus
Source: U.S. NSF - Directorate Math. & Physical Sciences
October 31, 2017 – July 31, 2020
Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Credit is not given for both MATH 3350 and 3351. Prerequisite: MATH 1320.
Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 3354 or instructor permission.
Combinatorics of counting using basic tools from calculus, linear algebra, and occasionally group theory. Topics include: tableaux, symmetric polynomials, Catalan numbers, quantum binomial theorem, q-exponentials, partition and q-series identities. Bijective proofs will be emphasized when appropriate.
Covers methods of abstract algebra that can be applied to various combinatorial problems and combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra.
The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.