# Yue Sheng

• AMCS PhD Student

## Contact Information

427 Jon M. Huntsman Hall,
3730 Walnut Street,

## Past Courses

• ### MATH460 - TOPOLOGY

Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Fundamental groups and covering spaces, and related topics.

• ### MATH465 - DIFFERENTIAL GEOMETRY

Differential geometry of curves in the plane and in 3-space;n gauge theories Surfaces in 3-space; The geometry of the Gauss map;ons. The language of Intrinsic geometry of surfaces; Geodesics; Moving frames; of vector bundles, The Gauss-Bonnet Theorem; Assorted additional topics.

• ### MATH500 - TOPOLOGY

Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Fundamental groups and covering spaces, and related topics.

• ### MATH501 - DIFFERENTIAL GEOMETRY

The course moves from a study of extrinsic geometry (curves and surfaces in n-space) to the intrinsic geometry of manifolds. After a review of vector calculus and a section on tensor algebra, we study manifolds and their intrinsic geometry, including metrics, connections, geodesics, and the Riemann curvature tensor. Topics include Eulerian curvature and Euler's theorems, the Gauss map and first/second fundamental forms, the Theorema Egregium, minimal surfaces in n-space; other topics as time permits.

## Knowledge@Wharton

The Problem with Heroes

For any leader, the ongoing presence of heroes is both a cause for celebration and a reason for deep concern, because it indicates a failure of the wider system, writes Whartonâ€™s Gregory P. Shea in this opinion piece.

Knowledge @ Wharton - 2020/05/29
The Politics of Pandemics: Why Some Countries Respond Better Than Others

Strong state capacity and low economic inequality are more important than being a democracy when it comes to dealing with health emergencies like pandemics, Wharton research shows.

Knowledge @ Wharton - 2020/05/26
Pulling Through the Pandemic: Advice for Entrepreneurs

Whartonâ€™s Karl Ulrich offers guidance for entrepreneurs trying to make it to the other side of the coronavirus pandemic.

Knowledge @ Wharton - 2020/05/26