Each semester one or more geometry/topology faculty or postdocs organize a seminar-style reading course for graduate students. Usually these courses center around a book or collection of articles, which students study on their own and present in course meetings. Current courses are listed below; more information can be found by contacting the organizer.

Students are encouraged to suggest topics for future reading courses!

**Stable Homotopy and Low-dimensional Topology** For some time now, there have been increasing interactions between low-dimensional
topology and stable homotopy theory. Smooth topology in low dimensions is in some sense the opposite of the “stable regime”, so this
interaction is somewhat indirect. This seminar will focus on the path between the two fields that passes through gauge theory, particularly
Seiberg-Witten theory, which involves the study of vector bundles, connections, and curvature. Roughly, one uses the differential geometry
\to construct a homotopy-theoretic object associated to a given smooth 3- or 4-dimensional manifold, such as an element of a stable homotopy
group, or a spectrum in the sense of homotopy theory, whose properties reflect subtle aspects of the differential topology of the original
manifold.

As this involves ideas from a wide swath of topology and geometry, a goal of the seminar will be to introduce participants to topics they are not familiar with; it is not anticipated that anyone will be expert, or even conversant, with everything mentioned above.

As a starting point, we will study the paper of Bauer and Furuta that introduces the stable homotopy refinement of the Seiberg-Witten
invariant for 4-manifolds; then progress to the work of Manolescu constructing a ``Seiberg-Witten-Floer homotopy type’’ for 3-manifolds.

Options abound for further reading, including a variety of quite recent results and applications.

Organizer: Tom Mark

**Moduli spaces of Higgs bundles and the Kobayashi-Hitchin correspondence** Followed
lecture notes by Guichard. Organizers: Sara Maloni and Tom Mark

**Invariants of 4-manifolds from Khovanov homology** Studied a new invariant, informally known as the “skein lasagne module,” giving rise to invariants
of smooth 4-dimensional manifolds. Organizer: Slava Krushkal

**Anosov representations** Organizer: Sara Maloni

**The Z-hat invariant and quantum modular forms** Studied the invariants of 3-manifolds recently introduced by Gukov-Pei-Putrov-Vafa based on
ideas of supersymmetry in physics, and their relation to quantum invariants of 3-manifolds and to quantum modular forms. Organizer: Slava Krushkal

**Teichmueller geometry and Nielsen-Thurston Classification** Organizer: Sara Maloni

**Heegaard Floer homology** Organizer: Thomas Mark

**Floer Theory**
Organizer: Tom Mark.

**Lie Algebras in Homotopy Theory**
Organizers: Nick Kuhn and Julie Bergner

**The mapping class group, Teichmueller space and the space of measured foliations** Organizer: Sara Maloni

**An overview of Thurston geometrization** Organizers: Sara Maloni and Tom Mark