Our colleague Dennis Sullivan wins 2022 Abel Prize “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects”.

Please read the news story on SBU News website: https://news.stonybrook.edu/university/dennis-parnell-sullivan-awarded-t...

Topic:

**Geometry and Dynamics of Surfaces**

Led by: Yusheng Luo and Matthew Romney

Sponsored by the Summer Math Foundation,

the Stony Brook Department of Mathematics,

and Undergraduate Research and Creative Activities (URECA)

PhD thesis defense

Symplectic Criteria on Stratified Uniruledness of Affine Varieties

and Applications to the Miminal Model Program

by Dahye Cho

**December 6th, Monday, 1 pm-2:25 pm at P-131.**

##### August Comprehensive Exams

^{th}1pm - 5pm

Part II - August 20

^{th}1pm - 5pm

Math Tower P-131

August 4, 2021

We present a twistor correspondence for half-flat almost-Grassmannian structures on real manifolds. An almost-Grassmannian structure is (essentially) a factorization of the tangent bundle, which determines two preferred families of tangent subspaces, and this structure is said to be half-flat if one of these families is integrable. We provide global results when the underlying manifold is a Grassmannian of 2-planes, and show there exist nontrivial deformations of the standard almost-Grassmannian structure. Whereas twistor constructions typically involve moduli of closed curves in a complex manifold, we utilize and expand upon the more flexible approach pioneered by LeBrun and Mason using moduli of curves-with-boundary.

June 4, 2021

We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by linear equations. The main examples of such are affine invariant submanifolds, that is, closures of SL(2,R)-orbits. We prove that the boundary of any linear subvariety is again given by linear equations in generalized period coordinates of the boundary. Our main technical tool is an asymptotic analysis of periods near the boundary of the moduli space of multi-scale differentials which yields further techniques and results of independent interest.

May 20th, 2021

We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2\pi$, the main result being sufficient conditions for a positive function of class at least $C^2$ to be the Gaussian curvature of such a conformal conical metric on the round sphere. Our methods particularly differ from the variational approach in that they don’t rely on the Moser-Trudinger inequality. Along the way, we also prove a general precompactness theorem for compact Riemann surfaces with at least three conical singularities and angles less than $2\pi$.