Nicholas Kuhn headshot

Nicholas J. Kuhn

Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
318 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
Problems in equivariant and chromatic homotopy theory
Source: The Simons Foundation, Inc.
September 01, 2020 – August 31, 2025
FRG: Collaborative Research: The Calculus of Functors & the Theory of Operads
Source: U.S. NSF - Directorate Math. & Physical Sciences
June 01, 2010 – November 30, 2014
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 4770: General Topology
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, MATH 3310 and MATH 3351 or equivalent.
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 5700: Introduction to Geometry
Credits: 3
Topics selected from analytic, affine, projective, hyperbolic, and non-Euclidean geometry. Prerequisite: MATH 2310, 3351, or instructor permission.
MATH 5896: Supervised Study in Mathematics
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.
MATH 7600: Homological Algebra
Credits: 3
Examines categories, functors, abelian catqegories, limits and colimits, chain complexes, homology and cohomology, homological dimension, derived functors, Tor and Ext, group homology, Lie algebra homology, spectral sequences, and calculations. Prerequisite: MATH 5770.
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 7810: Algebraic Topology II
Credits: 3
Devoted to chomology theory: cohomology groups, the universal coefficient theorem, the Kunneth formula, cup products, the cohomology ring of manifolds, Poincare duality, and other topics if time permits. Prerequisite: MATH 7800.
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 7840: Homotopy Theory
Credits: 3
Definition of homotopy groups, homotopy theory of CW complexes, Huriewich theorem and Whitehead's theorem, Eilenberg-Maclane spaces, fibration and cofibration sequences, Postnikov towers, and obstruction theory. Prerequisite: MATH 7800.
MATH 8850: Topics in Algebraic Topology
Credits: 3
Selected advanced topics in algebraic topology.
MATH 9800: Topology Seminar
Credits: 3
Topology 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.