8/27/25 -- Ahsan Ali -- (Notes)

Abstract:  An introduction to smooth manifolds and cobordism. Examples of smooth manifolds (with boundary), (null-)cobordisms, cardinality of the set of closed n-dimensional smooth manifolds modulo cobordism. Smooth maps of manifolds, the regular value theorem, and examples.

9/3/25 -- Chris Boehlert -- (Notes)

Abstract:  The tangent space at a point in a manifold. Introduction to bundles (vector, tangent, normal), with examples. The differential of a smooth map of manifolds. The tubular neighborhood theorem.

9/10/25 -- Jenna Stitt -- (Notes)

Abstract:  Submersions of manifolds and the local submersion theorem. Regular values of smooth maps, and the regular value theorem, examples. Critical values, Sard's theorem, transversality, examples, and ideas about genericity.

9/17/25 -- Luke Tinel -- (Notes)

Abstract:  Applications and examples of regular value theorem, tubular neighborhood theorem. Maps between the set of smooth maps of spheres transverse to zero and the set of closed manifolds with trivial normal bundles, Thom collapse map, statement of equivalence of the above sets modulo homotopy and cobordism, respectively.

10/1/25 -- Hadley Wells -- (Notes)

10/8/25 -- Judah Towery -- (Notes)

10/15/25 -- Grace Stroh -- (Notes)

10/29/25 -- Alex Ballow -- (Notes)

11/5/25 -- Ziyal Jandrasi -- (Notes)