Related papers: Lectures on Minimal Surface Theory
These lectures are a brief introduction to supersymmetry.
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
Let $a: I\to \mathbb{R}^3 $ be a real analytic curve satisfying some conditions. In this article, we show that for any real analytic curve $l:I\to \mathbb R^3$ close to $a$ (in a sense which is precisely defined in the paper) there exists a…
Three lectures on effective field theory given at the Seventh Summer School in Nuclear Physics, Seattle June 19-30 1995.
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…
We discuss the relative log minimal model theory for log surfaces in the analytic setting. More precisely, we show that the minimal model program, the abundance theorem, and the finite generation of log canonical rings hold for log pairs of…
These notes follow a lecture series at the "Singularities and low dimensional topology" winter school at the R\'enyi Institute in January 2023, with a target audience of graduate students in singularity theory and low-dimensional topology.…
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational complex projective surfaces.
These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is…
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author…
This is a written-up version of eight introductory lectures to the Hodge theory of projective manifolds. The table of contents should be self-explanatory. The only exception is section 8 where I discuss, in a simple example, a technique for…
These notes have been prepared as reading material for the mini-course that the author gave at IMS, National University of Singapore, as part of the "Summer school on the moduli space of Higgs bundles".
This is a set of four lectures presented at the Theoretical Advanced Study Institute (TASI-09) in June 2009. The goal of the lectures is to introduce students to some of the basic ideas and tools required for theoretical analysis of…
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
This is an introductory article to the theory of multiple gaps.
This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on…
We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we develop existence and regularity theory for free…
These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.
These four lectures, given at the British Universities Summer School in Theoretical Elementary Particle Physics (BUSSTEPP), held in 2014 in Southampton, are a brief introduction to a selection of current topics in physics Beyond the…