Slava Krushkal headshot

Vyacheslav Krushkal

Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
321 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
Topology of 4-manifolds
Source: The Simons Foundation, Inc.
January 01, 2020 – December 31, 2021
AS-MATH Topology of 4-manifolds, links and Engel groups
Source: U.S. NSF - Directorate Math. & Physical Sciences
July 01, 2016 – June 30, 2019
AS-MATH Geometric and Quantum Topology in Low Dimensions
Source: U.S. NSF - Directorate Math. & Physical Sciences
October 01, 2013 – September 30, 2016
AS-MATH Geometric Topology of 4-Manifolds
Source: The Simons Foundation, Inc.
June 01, 2014 – January 09, 2015
AS-MATH Geometric Topology of 4-Manifolds
Source: William E. Simon Foundation
July 01, 2014 – July 01, 2014
Low-dimensional topology and topological methods in condensed matter physics
Source: U.S. NSF - Directorate Math. & Physical Sciences
July 01, 2010 – March 31, 2014
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 4720: Introduction to Differential Geometry
Credits: 3
Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission.
MATH 4750: Introduction to Knot Theory
Credits: 3
Examines the knotting and linking of curves in space. Studies equivalence of knots via knot diagrams and Reidemeister moves in order to define certain invariants for distinguishing among knots. Also considers knots as boundaries of surfaces and via algebraic structures arising from knots. Prerequisites: MATH 2310 and MATH 3351 and MATH 3354 or instructor permission.
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 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 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 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.