Lectures on the topological recursion for Higgs bundles and quantum curves
by Olivia Dumitrescu, Motohico Mulase
Publisher: arXiv 2015
Number of pages: 69
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves associated with Higgs bundles.
Home page url
Download or read it online for free here:
by Donu Arapura - Purdue University
Algebraic geometry is the geometric study of sets of solutions to polynomial equations over a field (or ring). In this book the author maintains a reasonable balance between rigor and intuition; so it retains the informal quality of lecture notes.
by J.M. Landsberg - arXiv
This is survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory. The article is written to be accessible to graduate students. Numerous open questions are presented.
by J. S. Milne
This is an introduction to the arithmetic theory of modular functions and modular forms, with an emphasis on the geometry. Prerequisites are the algebra and complex analysis usually covered in advanced undergraduate or first-year graduate courses.
by Igor V. Dolgachev - Cambridge University Press
The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times.