All lectures on Saturday will be held at Natural Science Building Auditorium
| Saturday morning, 04/13/2024 | |
| 9:00am-9:45am | If you need a ride please wait at the lobby or inform us ahead of time. If you can offer a ride, please provide it to the people waiting at the lobby. |
| 10:00am-10:50am | Registration. Coffee and snacks served |
| 10:50am-11:00am | Welcome and a brief introduction |
| 11:00am-11:50am | Minicozzi Eigenvalue monotonicity and almost splitting in Ricci flow. |
| Saturday afternoon, 13/14/2024 | |
| 1:30pm-2:20pm | Kleiner Mean curvature flow in R^3 and the Multiplicity One Conjecture. |
| 2:20pm-2:50pm | Break, refreshments served |
| 2:50pm-3:40pm | Lai Riemannian and Kaehler flying wing steady Ricci solitons |
| 3:40pm-4:10pm | Break, refreshments served |
| 4:10pm-5:00pm | Sun Bubbling in Kahler geometry |
| 5:30pm | If you can offer a ride or need a ride to dinner please meet at NSB |
| 6:15pm | Due to the high costs there is no organized conference dinner. Please refer the Hotel and Travel page from the main page for a list of restaurants. |
| Sunday morning, 04/14/2024 | |
| 8:15am-8:30am | If you need a ride please wait at the lobby or inform us ahead of time. If you can offer a ride, please provide it to the people waiting at the lobby |
| 8:40am-9:10am | Coffee and snacks |
| 9:10am-10:00am | De Philippis Monge Ampere equation and unique continuation for differential inclusions. |
| 10:00am-10:25am | Break, refreshments served |
| 10:25am-11:15am | Wei Fundamental Gap of Convex Domains in Space Forms and Surface |
| 11:15am-11:40am | Break, refreshments served |
| 11:40am-12:30pm | Zhou Existence of four minimal spheres in S^3 with a bumpy metric |
Monge Ampere equation and unique continuation for differential inclusions. (De Philippis).
Abstract:The Monge Ampere equation is a prototypical non linear equation arising in several questions concerning Geometry, Optimal Design, Optimal transport.... I will review some of the applications and some of the known results, in particular concerning Sobolev regularity of the solutions. I will then show how, in 2 dimension, these results have an equivalent formulation in terms of a unique continuation property for solution of a differential inclusions and use this link to reprove the Sobolev regularity result for planar solutions of the MA equation obtained by Figalli Savin and myself in 2013. This is a joint work with Andre Guerra and Riccardo Tione.
Mean curvature flow in R^3 and the Multiplicity One Conjecture. (Kleiner).
Abstract:An evolving surface is a mean curvature flow if the normal component of its velocity field is given by the mean curvature. First introduced in the physics literature in the 1950s, the mean curvature flow equation has been studied intensely by mathematicians since the 1970s with the aim of understanding singularity formation and developing a rigorous mathematical treatment of flow through singularities. I will discuss progress in the last few years which has led to the solution of several longstanding conjectures, including the Multiplicity One Conjecture. This is joint work with Richard Bamler.
Riemannian and Kaehler flying wing steady Ricci solitons (Yi Lai ).
Abstract: Steady Ricci solitons are fundamental objects in the study of Ricci flow, as they are self-similar solutions and often arise as singularity models. Classical examples of steady solitons are the most symmetric ones, such as the 2D cigar soliton, the O(n)-invariant Bryant solitons, and Cao’s U(n)-invariant Kahler steady solitons. Recently we constructed a family of flying wing steady solitons in any real dimension n≥3, which confirmed a conjecture by Hamilton in n=3. In dimension 3, we showed all steady gradient solitons are O(2)-symmetric. In the Kahler case, we also construct a family of Kahler flying wing steady gradient solitons with positive curvature for any complex dimension n≥2, which answers a conjecture by H.-D. Cao in the negative. This is partly collaborated with Pak-Yeung Chan and Ronan Conlon.
Eigenvalue monotonicity and almost splitting in Ricci flow. (W. Minicozzi).
Abstract: I will talk about some joint work with Toby Colding on the monotonicity of eigenvalues for certain operators in Ricci flow and what it tells us about lower bounds for eigenvalues, when it forces the flow to split as a product with a line, and how it relates to the strong rigidity of cylinders.
Bubbling in Kahler geometry (Sun).
Abstract:It is a common phenomenon in geometric analysis that when a singularity forms one may see a bubbling phenomenon from a rescaling process. I will discuss this in the context of Kahler geometry and present some results concerning the singularity formation of Kahler-Einstein metrics. I will also discuss new questions in Riemannian geometry and algebraic geometry that arise out of this study.
Fundamental Gap of Convex Domains in Space Forms and Surface (Wei).
Abstract: The fundamental (or mass) gap refers to the difference between the first two eigenvalues of the Laplacian or more generally for Schr\"{o}dinger operators. It is a very interesting quantity both in mathematics and physics as the eigenvalues are possible allowed energy values in quantum physics. We will review many results for convex domains in $\mathbb R^n, \mathbb S^n, \mathbb H^n$ with Dirichlet boundary conditions, starting with the breakthrough of Andrews-Clutterbuck. Then we will present a recent estimate for the convex domain in surfaces with positive curvature. The last result is joint with G. Khan, H. Nguyen, M. Tuerkoen.
Existence of four minimal spheres in S^3 with a bumpy metric (Zhou).
Abstract:In 1982, S. T. Yau conjectured that there exists at least four embedded minimal 2-spheres in the 3-sphere with an arbitrary metric. In this talk, we will show that this conjecture holds true for bumpy metrics and metrics with positive Ricci curvature. This is a joint work with Zhichao Wang (Fudan University).