Related papers: Scale Calculus and M-Polyfolds -- An Introduction
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical…
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.
Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its…
This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, Rhode Island, organized by Saugata Basu, Joseph M.…
These are notes for a graduate-level introductory course on singularity categories.
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix…
A carefully constructed explanation of my connection of the real normed division algebras to the particles, charges and fields of the Standard Model of quarks and leptons provided to an interested group of attendees of the 2nd Mile High…
R. B. Melrose's b-calculus provides a framework for dealing with problems of partial differential equations that arise in singular or degenerate geometric situations. This article is a somewhat informal short course introducing many of the…
Notes for a Course on Probability and Statistics: L1: Elements of Probability; L2: Bayesian Inference; L3: Monte Carlo Methods
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.
Using SCM higher mathematics course allows you to: more clearly understandable apply theoretical material; deprive students of routine calculations; provide multilevel learning process, and therefore enhances cognitive interest and most…
These are notes from the 2003 C.I.M.E. summer school "symplectic 4-manifolds and algebraic surfaces". They cover the same material as the author's (by now ancient) Ph.D. thesis.
In the past few years, substantial progress has been made in the understanding of the algebra of kappa classes on the moduli spaces of curves. My goal here is to provide a short introduction to the new results. Along the way, I will discuss…
These are lecture notes for five lectures given at MPI Leipzig in May 2024. We study the moduli space M_{0,n} of n distinct points on P^1 as a positive geometry and a binary geometry. We develop mathematical formalism to study…
These are the notes of my lectures at the 1996 European Congress of Mathematicians. {} Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones.…
In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…
We present an overview of techniques developed in recent years for the efficient calculation of one-loop multiparton amplitudes, in particular those relying on unitarity and collinear factorization.
We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on…
After motivating the need of a multiscale version of fractional calculus in quantum gravity, we review current proposals and the program to be carried out in order to reach a viable definition of scale-dependent fractional operators. We…