Related papers: Notes on Motivic Periods
These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. They are based on introductory lectures given at Stony Brook…
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values…
These notes grew out of several introductory talks I gave during the years 2003--2005 on motivic integration. They give a short but thorough introduction to the flavor of motivic integration which nowadays goes by the name of geometric…
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
We demonstrate the existence of noise-induced periodicity (coherence resonance) in both a discrete-time model and a continuous-time model of an excitable neuron. In particular, we show that the effects of noise added to the fast and slow…
Notes from a series of 13 one hour (or more) lectures on Plasma Physics given to Ramesh Narayan' research group at the Harvard-Smithsonian Center for Astrophysics, between January and July 2012. Lectures 1 to 5 cover various key Plasma…
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.
In these lectures we review the motivation, principles of and (circumstantial) evidence for the program of unification of the fundamental forces. In an appendix, we review the group theory pertinent to the program.
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
The motive associated to the second Symanzik polynomial of the double-box two-loop Feynman graph with generic masses and momenta is shown to be an elliptic curve.
Brief lecture notes for a course about random matrices given at the University of Cambridge.
These notes are based on a lecture course by L. Chekhov held at the University of Manchester in May 2006 and February-March 2007. They are divulgative in character, and instead of containing rigorous mathematical proofs, they illustrate…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.
This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…
These lecture notes cover the theory of convex optimization, with a particular emphasis on first-order methods.
This is a slightly extended version of a seminar given the 8th of June at the TASI 99 at Colorado University in Boulder. The motivations behind two time theory are explained and the theory is introduced via one of the theory's easier gauges…
These are extended notes of a lecture about the papers 1207.1883 by Esnault-Levine-Wittenberg and 1308.3024 by Wittenberg. The aim is to define the Esnault-Levine-Wittenberg indices, establish their basic properties amd to pose several…
I review the motivation for the early-time cosmic acceleration stage in expanding universe and discuss simple inflationary scenarios. Preheating and reheating are considered in great detail. This is a sample chapter from my book "Physical…