Bi-annual Algebraic and Tropical
Brown and YaLE
Spring 2017 @ Brown
April 4, 2017
The BATMOBYLE is a vehicle for bringing together the algebraic and
tropical geometry groups of Brown and Yale for a biannual day of talks
alternating between the two universities.
Alicia Harper (Brown) -- The boundary complex of a Deligne-Mumford stack |
Boundary complexes of algebraic varieties are an intriguing invariant that, at first sight, seem to reflect rather coarse information about a divisor D inside of X. It is an amazing fact - emerging from the works of Danilov, Stepanov, and Payne – that the simple homotopy type of the boundary complex of D depends only on the complement of D inside X. Using recent advances including destackification and the weak factorization theorem for stacks, we show that this result is also true for Deligne-Mumford stacks.
Tony Yue Yu (IAS/Clay) -- Gluing holomorphic cylinders
I will talk about a gluing formula for counting holomorphic cylinders in log Calabi-Yau surfaces. The formula roughly says that cylinders can be glued together to form longer cylinders, and the number of longer cylinders is equal to the product of the numbers of shorter cylinders. Our approach uses Berkovich geometry, deformation theory and several ideas from Gromov-Witten theory.
Diane Maclagan (Warwick) -- Tropical Schemes
Tropical geometry allows varieties, and their
compactifications and degenerations, to be studied using combinatorial
and polyhedral techniques. While this idea has proved surprisingly
effective over the last decade, it has so far been restricted to the
study of varieties and algebraic cycles. I will discuss joint work
with Felipe Rincon that gives a definition for of a subscheme of a
tropical toric variety. This builds on work of Jeff and Noah
Giansiracusa on tropicalizing subschemes.