​Notes

​This is a collection of my notes written at various stage of my life since I was an undergraduate student.

This is the first I wrote for the undergraduate course of Thermodynamics. It is in Japanese.Not completed. 

​Notes preparing for a brief talk at my lab.

An introductory article on quantum groups written in 2014.

A_1 Macdonald Polynomial and its duality.

Manuscript based on which I gave a talk in Australia.

How to obtain a Gaiotto state from the conformal block.

Basics of chiral algebra in 4d N=2.

Hayashi's lecture on M-theory compactified on CY3 and CY4.

My second Japanese notes. This one is on the non-relativistic scattering problem. 

This is my master thesis on W-algebra with modern insights taken. 

Short summary on fusion rules in Virasoro algebra.

Notes on a short-cut way to compute the monodromy, especially its transformation.

Towards the understanding of the Jacobi triple identity.

Several equivalent expressions of Nekrasov factor.

List of known chiral algebras dual to 4d N=2 SCFTs.

Oota's lecture on the origin of Painlevé and discrete Painlevé in 4d N=2 SU(2) gauge theories.

The second part of my notes on non-relativistic scattering problem. 

Manuscript which my talk at Seikei university is based on.

Notes on Quantum Focussing Theorem.

Short notes help understand root system.

Notes on Painleve equation.

ADHM construction from brane configuration.

Honma's lecture on N=(2,2) sigma model and F-theory.

A lecture note on topology and homology collected from my graduate course

More to be released...

List of Schur operators

General argument for open spin chain.

A review on Hope fiber.

Introduction to Heat Kernel (under construction)

S. Jeong's lecture on his work on opers (handwriting notes of mine)

Notes of two lectures given by Du Pei.

A short summary of calculations of unrefined topological vertex (under construction)

A short notes on how to derive the spherical harmonics starting from its definition.

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