Friday September 07, 2018 4:00 PM  6:00 PM P131 Math Tower
 Christina Sormani, CUNY
Compactness Theorems in Riemannian Geometry: Part 1We 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 CheegerColding, WeiPetersen, Wenger, SormaniPortegies, and recent graduates of the Stony Brook math department: Knox and Perales.

Friday September 14, 2018 4:00 PM  6:00 PM P131 Math Tower
 Christina Sormani, CUNY
Compactness Theorems in Riemannian Geometry: Part IIA 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 CheegerColding, WeiPetersen, Wenger, SormaniPortegies, and recent graduates of the Stony Brook math department: Knox and Perales.

Friday September 21, 2018 4:00 PM  6:00 PM P131 Math Tower
 Jingrui Cheng, Stony Brook University
MongeAmpere equations and their generalizationsI will start with Yau's classical results on Calabi's volume conjecture and the existence of KahlerEinstein metrics on compact Kahler manifolds when c_1 is nonpositive. These problems can be reduced to the question of solvability of MongeAmpere type equations on compact Kahler manifolds. I will go through the apriori estimates. If time permits, I will also talk about complex MongeAmpere 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 P131 Math Tower
 Yu Li, Stony Brook University
The structure theory of Ricci shrinking solitonsRicci 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 P131 Math Tower
 Demetre Kazaras, Stony Brook University
Positive Mass Theorem: WittenIn 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 P131 Math Tower
 Jae Ho Cho, Stony Brook University
Ricci flow and the differentiable sphere theoremThe 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 1/4pinched 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 P131 Math Tower
 Vardan Oganesyan, Stony Brook University
Differential geometry and algebraic geometryIn 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 P131 Math Tower
 JeanFrancois Arbour, Stony Brook University
The FIK SolitonsFor 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 nontrivial examples. In this talk, we will discuss the 2003 paper of FeldmanIlmanenKnopf in which they use Calabi's ansatz to reduce the equations for KahlerRicci Solitons on certain spaces to a single fourth order ODE. They successfully use this approach to construct new families of expanding, stead, and shrinking KahlerRicci 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 P131 Math Tower
 Jiasheng Teh, Stony Brook University
Deformation of Complex StructuresDeformation 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 TianTodorov unobstructedness theorem for CalabiYau manifolds.

