TK

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

304 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

AS-MATH Sloan Research Fellowship - Koberda

Source: Sloan Foundation

September 15, 2017 – September 14, 2021

Homeomorphism Groups of One-manifords: Rigidity and Regularity

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

September 01, 2017 – August 31, 2021

GAGTA 2018: Geometric and Asymptotic Group Theory with Applications

Source: U.S. National Science Foundation (NSF)

June 01, 2018 – May 31, 2019

AS-MATH Virginia Topology Conference 2016: Mapping class groups and low dimensional topology

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

November 01, 2016 – October 31, 2017

AS-MATH Right-angled Artin subgroups of real algebraic groups

Source: The Simons Foundation, Inc.

September 01, 2016 – August 31, 2017

##### 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 the material from Math 2310 (multivariable calculus) plus topics from complex numbers, set theory, and linear algebra. Prepares students for taking advanced mathematics classes at an early stage. Credit is not given for both Math 2310 and Math 2315.

Credits: 4

This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B- or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315.

Credits: 3

Topics include abstract topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., the fundamental group. Prerequisites: MATH 2310 or 2315 or APMA 2120 and MATH 3315 or MATH 3351 or MATH 4651 or APMA 3080

Credits: 3

This course provides a framework for the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides a student through the beginning phases of the process of research and writing. Prerequisite: Acceptance into the Distinguished Major Program.

Credits: 3

This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee. Prerequisite: MATH 4900.

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

A rigorous program of supervised study designed to expose the student to a particular area of mathematics. Prerequisite: Instructor permission and graduate standing.

Credits: 3

Covers topics in first order logic and model theory.

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

Topics include the fundamental group, covering spaces, covering transformations, the universal covering spaces, graphs and subgroups of free groups, and the fundamental groups of surfaces. Additional topics will be from homology, including chain complexes, simplicial and singular homology, exact sequences and excision, cellular homology, and classical applications. Prerequisite: MATH 5352, 5770, or equivalent.

Credits: 3

Studies the basic structure theory of groups, especially finite groups.

Credits: 3–9

Independent 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.