Benjamin Hayes headshot
BH

Benjamin Richard Hayes

Assistant Professor
Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
219 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
Entropy theory methods in von Neumann algebras
Source: U.S. National Science Foundation (NSF)
June 01, 2020 – May 31, 2023
ECOAS 2020 - Participant Support
Source: U.S. National Science Foundation (NSF)
October 01, 2020 – September 30, 2022
Aspects of Sofic Entropy and Algebraic Actions
Source: U.S. National Science Foundation (NSF)
September 28, 2017 – May 31, 2020
MATH 3310: Basic Real Analysis
Credits: 4
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 4330: Calculus on Manifolds
Credits: 3
Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: MATH 2310 or MATH 2315; MATH 3351 or MATH 4651 or APMA 3080; and MATH 3310 or MATH 4310
MATH 4651: Advanced Linear Algebra
Credits: 3
Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351
MATH 4900: Distinguished Major Thesis
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.
MATH 4901: Distinguished Major Thesis
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.
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 7340: Complex Analysis I
Credits: 3
Studies the fundamental theorems of analytic function theory.
MATH 8310: Operator Theory I, II
Credits: 3
Topics in the theory of operators on a Hilbert space and related areas of function theory.
MATH 8851: Group Theory
Credits: 3
Studies the basic structure theory of groups, especially finite groups.
MATH 9998: Non-Topical Research, Preparation for Doctoral Research
Credits: 1–12
For doctoral research, taken before a dissertation director has been selected.