OPEN NEIGHBORHOOD
February 5, 2020 4:30 pmImagine the universe is a periodic crystal. If gravity makes space negatively curved, the thin walls of the crystalline structure might trace out a pattern of circles in the sky, visible...
Read more
NUMBER THEORY
February 5, 2020 3:00 pmThere is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of...
Read more
DIFFERENTIAL GEOMETRY
February 4, 2020 4:15 pm**CANCELED** Most 4-manifolds do not admit symplectic forms, but most admit 2-forms that are "nearly" symplectic. Just like the Seiberg-Witten (SW) invariants, there are Gromov invariants that are compatible with...
Read more
MATHEMATICAL PICTURE LANGUAGE
February 4, 2020 3:30 pmGraph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to...
Read more
HARVARD-MIT ALGEBRAIC GEOMETRY
February 4, 2020 3:00 pmI will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system...
Read more
GAUGE-TOPOLOGY-SYMPLECTIC
January 31, 2020 3:30 pmSymplectic embedding problems are at the core of symplectic topology. Many results have been found involving balls, ellipsoids and polydisks. More recently, there has been progress on problems involving lagrangian...
Read more
MATHEMATICAL PICTURE LANGUAGE
January 7, 2020 3:30 pmIn the search for finite temperature quantum memory, people have found an exotic 3D topological model, called the fracton model. A large class of them are known to have foliation...
Read more
GAUGE-TOPOLOGY-SYMPLECTIC
December 6, 2019 3:30 pmThe Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu in 1994 to a class...
Read more
DIFFERENTIAL GEOMETRY
November 26, 2019 4:15 pmIn the last 35 years, geometric flows have proven to be a powerful tool in geometry and topology. The Mean Curvature Flow is, in many ways, the most natural flow...
Read more