Summer Graduate School

This school will present various developments in Riemannian and Kähler geometry around the notion of curvature seen as a tool to describe and understand the geometry of the objects. The school will give graduate students the opportunity to learn key ideas and techniques of the field, with an emphasis on solidifying foundations in view of potential future research. The first week will be centered around the question of the existence of Kähler metrics with special curvature properties and the famous Yau-Tian-Donaldson conjecture. The second week will focus on geometric flows in Riemannian and complex geometry. 

School Structure

Four to five courses will be running in parallel each week, with each course consisting of three to five one-hour lectures.  In addition to the lecturers, there will be problem sessions.

Prerequisites

Differential geometry: Riemannian manifolds (geodesics, Levi-Civita connections, different notions of curvature), Complex manifolds (Riemann surfaces, Kähler manifolds), differential forms, cohomology (De Rham, Dolbeault).
Basic analysis on Hilbert spaces: L^p space, Hahn-Banach theorem.

References

• Ben Andrews, Bennett Chow, Christine Guenther, Mat Langford. Extrinsic geometric flows, Graduate Studies in Mathematics. American Mathematical Society, 2020T. Aubin. Some nonlinear problems in Riemannian geometry. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 1998.
• Vincent Guedj, Ahmed Zeriahi, Degenerate Complex Monge–Ampère Equations, European Mathematical Society Press 2017.
• Jurgen Jost. Riemannian geometry and geometric analysis. Universitext. Springer, seventh edition, 2017.
• G. Székelyhidi. An introduction to extremal Kähler metrics, volume 152 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2014.
• Xi-Ping Zhu, Lectures on Mean Curvature Flows, American Mathematical Society and International Press, Boston, 2002

Application Procedure

In order to be considered for support from SLMath, students must be nominated to attend by their graduate director AND submit a separate application directly with the SMS.

SLMath is only able to support a limited number of students to attend this school.  Therefore, it is likely that only one student per institution will be funded by SLMath.

For eligibility and how to apply, see the Summer Graduate Schools homepage.