ME

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

302 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

Golod-Shafarevich groups and Kazhdan's property (T)

Source: U.S. NSF - Directorate Math. & Physical Sciences

September 01, 2012 – August 31, 2016

Sloan Research Fellowship for Mikhail Ershov

Source: Sloan Foundation

September 15, 2011 – September 15, 2015

Kazhdan's property (T), Golod-Shafarevich groups and Kac-Moody groups

Source: U.S. NSF - Directorate Math. & Physical Sciences

September 15, 2009 – August 31, 2013

##### Courses

Credits: 4

A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes' and the divergence theorems/how these concepts relate to real world applications. Prerequisite: MATH 1320 or the equivalent.

Credits: 4

Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000.

Credits: 3

A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320.

Credits: 3

This course covers the basic topology of metric spaces/continuity and differentiation of functions of a single variable/Riemann-Stieltjes integration/convergence of sequences and series. Prerequisite: MATH 3310 or permission of instructor.

Credits: 3

Introduces algebraic techniques for communicating information in the presence of noise. Includes linear codes, bounds for codes, BCH codes and their decoding algorithms. May also include quadratic residue codes, Reed-Muller codes, algebraic geometry codes, and connections with groups, designs, and lattices. Prerequisite: MATH 3351 and 3354, or instructor permission.

Credits: 3

Covers the representation theory of finite groups/other interactions between linear & abstract algebra. Topics include: bilinear & sesquilinear forms & inner product spaces/important classes of linear operators on inner product spaces/the notion of group representation/complete reducibility of complex representations of finite groups/character theory/some applications of representation theory. Prerequisite: MATH 3351 (or 4651)/MATH 3354 (or 4652)

Credits: 1–3

Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.

Credits: 3

Covers the representation theory of finite groups/other interactions between linear & abstract algebra. Topics include: bilinear & sesquilinear forms & inner product spaces/important classes of linear operators on inner product spaces/the notion of group representation/complete reducibility of complex representations of finite groups/character theory/some applications of representation theory. Prerequisite: MATH 3351 or 4651/MATH 3354 or 4652.

Credits: 3

Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.

Credits: 3

Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.

Credits: 3

Algebra Seminar

Credits: 1–12

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.