Tuesday, February 20, 2018
Time  Items 

All day 

4:00pm 
02/20/2018  4:00pm to 5:00pm Symplectic duality is an equivalence between holomorphic Fukaya categories, called categories O, associated to pairs of holomorphic symplectic manifolds. All known dual pairs arise as Higgs and Coulomb branches of the moduli spaces of vacua in 3d N=4 theories and, together with Bullimore, Dimofte, and Gaiotto, I showed that category O could be identified with a certain category of boundary conditions for these theories. In recent work BravermanFinkelbergNakajima have given a rigorous mathematical definition of the Coulomb branch. I will explain how one can incorporate boundary conditions and interfaces into this construction. In particular one can show that the BFN construction is functorial with respect to holomorphic Lagrangian correspondences. The case when the Lagrangian is a cotangent fiber is joint with Joel Kamnitzer and Alex Weekes. Location: 02/20/2018  4:00pm to 5:00pm We develop from scratch a formal code that can be used to express analysis or mathematics. Such code could beused as basis for automated proof checking, or it can be used as a reference by mathematicians who want to understand or teach the basic principles of mathematics. Our design of the code serves the following goals: itaims to be minimal, it aims to be close to mathematicians' way of thinking, and it aims to be comparable to the Zermelo Fraenkel Choice system.We share some of the insights and surprises that the exercise of designing this code has triggered. https://arxiv.org/abs/1706.08905 Location: 