Room 440, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 440室)

Singularities of Special Lagrangians, I

Yohsuke Imagi (Kavli Institute for The Physics and Mathematics of The Universe)

Abstract

Special Lagrangians are involved in a large area of Geometry and String Theory concerning "counting" invariants though no definition of counting special Lagrangians is available yet because of the complicated behaviours of singular special Lagrangians (in the sense of Geometric Measure Theory). It seems much more difficult than the well-known analyses of Yang-Mills instantons (in real dimension 4) and of pseudo-holomorphic curves. On the other hand, it ought to be mirror to holomorphic Casson (Donaldson-Thomas) invariants but complex algebraic geometry does not apply (at least directly) to special Lagrangians.

I've been working on some easy singularities. In some case an analogue to the well-known cases (of Yang-Mills theory or of pseudo-holomorphic curves) holds but in other cases the more categorical approach seems important; here "categorical" means involving Fukaya categories of (not necessarily special) Lagrangians.

I will probably state my results in the 1st talk and explain part of the proofs in the 2nd talk depending upon the audience's interest.