Thomas Mark headshot
TM

Thomas E. Mark

Professor
Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
327 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
RTG: Research Training in Topology and Geometry at the University of Virginia
Source: U.S. National Science Foundation (NSF)
July 01, 2019 – June 30, 2024
AS-MATH Low-dimensional contact and symplectic topology
Source: The Simons Foundation, Inc.
September 01, 2017 – August 31, 2022
Virginia Topology Conference 2018
Source: U.S. National Science Foundation (NSF)
September 01, 2018 – August 31, 2019
AS-MATH Low DImensional Contact and Symplectic Topology
Source: U.S. NSF - Directorate Math. & Physical Sciences
August 15, 2013 – July 31, 2017
Fibrations and the topology of low-dimensional manifolds
Source: U.S. NSF - Directorate Math. & Physical Sciences
July 15, 2009 – June 30, 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 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 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 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 7010: Seminar on Research in Mathematics
Credits: 1–3
This seminar discusses the issues related to research in Mathematics. There are speakers from the different areas of mathematics represented at the University of Virginia. Credit may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7800: Algebraic Topology I
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.
MATH 7820: Differential Topology
Credits: 3
Topics include smooth manifolds and functions, tangent bundles and vector fields, embeddings, immersions, transversality, regular values, critical points, degree of maps, differential forms, de Rham cohomology, and connections. Prerequisite: MATH 5310, 5770, or equivalent.
MATH 7830: Fiber Bundles
Credits: 3
Examines fiber bundles; induced bundles, principal bundles, classifying spaces, vector bundles, and characteristic classes, and introduces K-theory and Bott periodicity. Prerequisite: MATH 7800.
MATH 8750: Topology of Manifolds
Credits: 3
Studies regular and critical values, gradient flow, handle decompositions, Morse theory, h-cobordism theorem, Dehn's lemma in dimension 3, and disk theorem in dimension 4. Prerequisite: Math 5770.
MATH 9820: Geometry and Topology Seminar
Credits: 1–3
Discusses subjects from geometry and topology.
MATH 9995: Independent Research
Credits: 3–9
Independent Research
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.