Teaching

Math 4750: Introduction to Knot Theory

Semester
Spring
Year offered
2021

This class gives an overview of both classical and modern results in Knot theory: the Kauffman bracket and the Jones polynomial; the Alexander polynomial; Khovanov homology; Seifert surfaces; examples...

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Math 7830: Fiber bundles

Semester
Spring
Year offered
2021

Course material: Vector bundles, principal bundles, characteristic classes (Stiefel-Whiteney, Chern, Pontryagin). Orientability, Euler class. Classifying spaces (for vector bundles and principal...

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MATH 8750: Topology of Manifolds

Semester
Fall
Year offered
2019
Topics include the Whitney trick and its failure in 4 dimensions; its analogues in 3-dimensions: the Dehn lemma and the loop theorem; Milnor's invariants for classical links; various special 2...
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MATH 8750: Topology of Manifolds

Semester
Fall
Year offered
2018
The main goal of the class is to give an introduction to geometric and quantum topology in low (2, 3, 4) dimensions. Specific topics that will be discussed include the (colored) Jones polynomial of...
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MATH 4720: Introduction to Differential Geometry

Semester
Spring
Year offered
2017
Topics include: manifolds, the Gauss map, parallel transport, curvature of curves and surfaces, the first and second fundamental forms, surface area and volume, geodesics, the exponential map, the...
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MATH 3340: Complex Variables

Semester
Fall
Year offered
2016
Topics covered in this class include analytic functions, complex integration, Cauchy formulas, power series, residue theory, conformal mappings, and Laplace transforms.