Algebraic Topology: H-spaces and homotopy nilpotency, homotopy self-equivalences, fibrewise topology, Lusternik-Schnirelmann category and its variations.

Differential Topology: normal bordism, embeddings of manifolds, critical points of smooth maps between manifolds.

Geometric Topology and Geometric Group Theory: surface braid groups, mapping class groups, branched coverings, virtual knots and braids, dimension theory.

I am willing to supervise undergraduate senior projects and co-supervise graduate students in the areas of algebra, analysis, geometry and topology, and related topics in applied mathematics.

• L. Funar, C. Pintea and P. Zhang. “Examples of smooth maps with finitely many critical points in dimensions (4, 3), (8, 5) and (16, 9).” Proceedings of American Mathematical Society. (2010).
• P. Zhang. “Automorphisms of braid groups on $S^{2}, T^{2}, P^{2}$ and the Klein bottle.” Journal of Knot Theory and its Ramifications. (2008).
• P. Zhang. “Automorphisms of braid groups on closed surfaces which are not $S^{2}, T^{2}, P^{2}$ or the Klein bottle.” Journal of Knot Theory and its Ramifications. (2006).
• M. C. Crabb, W. A. Sutherland and P. Zhang. “Homotopy nilpotency.” Quarterly Journal of Mathematics. (1999).
• P. Zhang. “On embeddings of smooth covering spaces in vector bundles.” Topology and its Applications. (1995).
• P. Zhang. “On isotopy classification of embeddings of n-manifolds in $RP^{2n}$.” Topology and its Applications. (1993).