# Perspectives in Mathematical Science I (2017 Summer, Part 3 -- Hamanaka)

News

• I am sorry that I seemed to forget to write ``Tr'' in Exercise 1. (Without Tr, the formula NEVER holds in general!) This is due to my mistake and hence I have decided that 15pt. (for the Ex.1) is added to all students in the class. (2017/09/06)
• The lecture is finished. Thank you very much. (2017/07/25)
• This homepage is open. (2017/05/30)

Syllabus of Part 3 (For total one, see here.)

• Title of Part 3: ADHM construction of Instantons
• Instructor: Masashi Hamanaka
• Date: Tuesday, 14:45--16:15 (during June 27th -- July 25th)
• Room: School of Science Building 1 (Mathematics), Room 109
• Language: English
• Course contents: I would like to discuss the Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction of instantons and related topics. Instantons are finite-action (global) solutions to the Anti-Self-Dual Yang-Mills equations in four dimension. They play crucial roles in geometry and physics. The ADHM construction is based on a beautiful duality (one-to-one correspondence) between a moduli space of the instantons and a moduli space of the ADHM data. While the former is specified by a non-linear partial differential equation in four dimension, the latter is specified by a matrix equation which is much easier to treat.
The purpose of my part is to give an elementary proof of the duality in the ADHM construction in four dimensional Euclidean space, together with a brief introduction to instantons in geometry and physics. There would be no need to know manifolds, vector bundles, connections and so on in advance. I would also like to mention the D-brane interpretations of them, generalization to noncommutative spaces, and application to monopoles in three dimension. More detailed syllabus will be distributed at the beginning of part 3 (on June 27th).
• References (7/18):
• Grading: Attendance and Report (Details will be announced on June 27th.)

Plan --- ADHM construction of Instantons (Update: 7/25)

• 6/27：Overview (Slide), Instantons [Material1]