ME

Mikhail V. Ershov

Professor
Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
302 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
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
MATH 2310: Calculus III
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.
MATH 3000: Transition to Higher Mathematics
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.
MATH 3310: Basic Real Analysis
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.
MATH 4310: Introduction to Real Analysis
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.
MATH 4452: Algebraic Coding Theory
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.
MATH 4657: Bilinear Forms and Group Representations
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)
MATH 4993: Independent Study
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.
MATH 5657: Bilinear Forms and Group Representations
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.
MATH 7751: Algebra I
Credits: 3
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
MATH 7752: Algebra II
Credits: 3
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
MATH 9950: Algebra Seminar
Credits: 3
Algebra Seminar
MATH 9999: Non-Topical Research
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.