Geometric Analysis Learning Seminar

from Friday
June 01, 2018 to Monday
December 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Friday
September 07, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Christina Sormani, CUNY
Compactness Theorems in Riemannian Geometry: Part 1

We will survey compactness theorems for sequences of Riemannian manifolds starting with the early work of Cheeger, Gromov, Anderson and moving towards more modern theorems including theorems by Cheeger-Colding, Wei-Petersen, Wenger, Sormani-Portegies, and recent graduates of the Stony Brook math department: Knox and Perales.


Friday
September 14, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Christina Sormani, CUNY
Compactness Theorems in Riemannian Geometry: Part II

A continuation of last week's talk: We will survey compactness theorems for sequences of Riemannian manifolds starting with the early work of Cheeger, Gromov, Anderson and moving towards more modern theorems including theorems by Cheeger-Colding, Wei-Petersen, Wenger, Sormani-Portegies, and recent graduates of the Stony Brook math department: Knox and Perales.


Friday
September 21, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Jingrui Cheng, Stony Brook University
Monge-Ampere equations and their generalizations

I will start with Yau's classical results on Calabi's volume conjecture and the existence of Kahler-Einstein metrics on compact Kahler manifolds when c_1 is nonpositive. These problems can be reduced to the question of solvability of Monge-Ampere type equations on compact Kahler manifolds. I will go through the apriori estimates. If time permits, I will also talk about complex Monge-Ampere equations on bounded domains as well as the existence of constant scalar curvature Kahler metrics.


Friday
September 28, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Yu Li, Stony Brook University
The structure theory of Ricci shrinking solitons

Ricci shrinking solitons, usually regarded as generalizations of positive Einstein manifolds, form an important collection of objects for our understanding of the singularities of Ricci flows. In this talk, I will introduce the classification of low dimensional Ricci shrinking solitons and a week compactness theory in higher dimensions.


Friday
October 05, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Demetre Kazaras, Stony Brook University
Positive Mass Theorem: Witten

In this talk, we will present a detailed proof of the Positive Energy Theorem in mathematical General Relativity due to Witten. The theorem states that a certain subtle geometric invariant of an asymptotically flat spin manifold (its ADM mass) is nonnegative under suitable conditions. The argument is not long so we will go over many details. The content will be widely accessible.


Friday
October 12, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Jae Ho Cho, Stony Brook University
Ricci flow and the differentiable sphere theorem

The sphere theorem has a long history beginning with the topological sphere theorem proven by M. Berger and W. Klingenberg around 1960. It states that every compact, simply connected Riemannian manifold which is strictly 1/4-pinched in the global sense should be homeomorphic to the round sphere (we can see the pinching constant 1/4 is optimal if we consider the complex projective space). And the differentiable sphere theorem asks whether we can change 'homeomorphic' to 'diffeomorphic'. We know that it is not automatically given by the previous theorem because of the existence of exotic spheres. In this talk, we will discuss about the paper of S. Brendle and R. Schoen in 2008 saying that the differentiable sphere theorem is true if it is pinched in the pointwise sense.


Friday
October 19, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Vardan Oganesyan, Stony Brook University
Differential geometry and algebraic geometry

In this talk, we are going to construct minimal Lagrangian submanifolds without any knowledge in differential geometry. We will consider applications of algebraic geometry in differential and symplectic geometry. As an example, we will describe all minimal Lagrangian tori immersed in $CP^2$ and construct some minimal submanifolds immersed in $CP^n$.


Friday
November 09, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Jean-Francois Arbour, Stony Brook University
The FIK Solitons

For all kinds of geometric structures, reducing the number of degrees of freedom by looking for highly symmetric examples as been a fruitful way to create non-trivial examples. In this talk, we will discuss the 2003 paper of Feldman-Ilmanen-Knopf in which they use Calabi's ansatz to reduce the equations for Kahler-Ricci Solitons on certain spaces to a single fourth order ODE. They successfully use this approach to construct new families of expanding, stead, and shrinking Kahler-Ricci solitons on complex line bundles over complex projective space and on higher dimensional analogues of Hirzebruch surfaces. They also give an example of an "eternal" solution to Ricci flow which flows through a singular cone at time 0.


Friday
November 30, 2018

4:00 PM - 6:00 PM
P-131 Math Tower
Jiasheng Teh, Stony Brook University
Deformation of Complex Structures

Deformation of Complex structures of Riemann surfaces was first considered by Riemann in his memoir on Abelian functions in 1857. However, the general theory for deformation of higher dimensional complex manifolds was established only much later by Kodaira and Spencer in the 1950s. In this talk, we present an overview for the basic notions and results in deformation theory. In particular, main ideas for proving the existence and completeness theorems will be given. We will end the talk with a discussion of Tian-Todorov unobstructedness theorem for Calabi-Yau manifolds.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars