# Seminar by Hidehiko Shimada "Membrane interaction and a three-dimensional analog of Riemann surfaces"

### Date

### Location

### Description

Mathematical and Theoretical Physics Unit would like to invite you to a seminar:

- Speaker: Hidehiko Shimada, High Energy Accelerator Research Organization(KEK)
- Date/Time: February 3rd / 14:00-15:00
- Venue: C016, Lab1

Title: Membrane interaction and a three-dimensional analog of Riemann surfaces

Abstract: It is an important problem to understand whether the matrix model of M-theory contains the splitting(-joining) interactions of membranes.

In the talk, I will discuss the splitting processes in the pp-wavematrix model, which are certain tunnelling processes.

After a brief discussion of the relation to the ABJM theory via the AdS/CFT correspondence, I will show that the BPS instanton equations governing such processes are equivalent to the three-dimensional Laplace equation, under an approximation which is valid when the matrix size is large. I will further show that the solution which corresponds to a splitting process is not defined on R^3, but rather on a space which is constructed by stitching two R^3's, in a manner analogues to the construction of Riemann surfaces.

I will also show plots, constructed using explicit solutions to the Laplace equation, which capture explicitly the behaviours of membranes in the splitting processes.

The talk will be based on arxiv:1508.03367, done in collaboration with Stefano Kovacs (Dublin IAS) and Yuki Sato (Chulalongkorn Univ., Bangkok).

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