Schedule for: 24w5260 - Conformal and CR Geometry

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

In this talk I will report my recent research on applications of potential theory in conformal geometry. I will review curvature equations in conformal geometry. Motivated from the work of Huber on the classification of open surfaces and the work of Schoen-Yau on locally conformally flat manifolds, we want to study singular behavior of solutions to curvature equations under certain curvature conditions in conformal geometry. Our approach is potential theoretic. We will demonstrate we can understand the singular behavior of the potentials outside “thin" sets. Consequently, we are able to derive geometric and topological consequences from the Hausdorff dimensions of singularities based on positivities of curvature.

Branson’s Q-curvature in conformal geometry has been one of the main objects of study for more than 20 years. Using the analogy between conformal and CR geometries, we can also define CR Q-curvature. However, it is less interesting because its integral always vanishes, so you cannot obtain a global CR invariant. It later turns out that the vanishing of CR Q-curvature allows us to define Q-prime curvature, whose integral provides a non-trivial global invariant, including the Burns-Epstein invariant in 3 dimensions. In this introductory talk, I plan to explain the origin of CR Q-curvature from the perspective of complex analysis of strictly pseudoconvex domains and its connection with Q-prime curvature. I also plan to discuss generalizations of Q-prime curvature that provide further global CR invariants, based on work by Taiji Marugame and Yuya Takeuchi.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.