A Personal Roadmap

This page provides a personal mathematical roadmap: a very incomplete and subjective collection of papers in areas that I have made some effort to understand over the past decade, with a link to an online version of the paper and its mathscinet review whenever these are available. The purpose is to give the reader a better idea of where my mathematical interests lie, and to provide a guide to reading material for those new to the subject.

Such a project comes with all the obvious disclaimers: The classification into subject areas is very rough, and the order of authors within them completely arbitrary. I have by no means attempted to select the most "important" papers of any one author, but often the ones I have most benefited from reading. This includes numerous survey articles. In the case of joint papers, no judgement is intended by linking only to one author's website.

Mathematical blogs

Terry Tao | Tim Gowers | Jordan Ellenberg | Izabella Laba | Emmanuel Kowalski | Luca Trevisan | Gil Kalai | Claire Mathieu | Windows on Theory | mathbabe

Virtual seminars

Webinar in Additive Combinatorics  | Oxford Discrete Mathematics and Probability Seminar  | Virtual Combinatorics Colloquium  | Women in Combinatorics Colloquium  | Combinatorics Lectures Online  | Number Theory Web seminar  | Virtual Harmonic Analysis seminar  | Online Ergodic Theory and Analysis seminar  | TCS+

General mathematical culture

Survey articles in arithmetic combinatorics

Linear Fourier analysis

Structure in sum sets

Higher-order Fourier analysis

Model theory

Ergodic theory

Analytic number theory

Patterns in the primes

Incidence geometry and sum-product

Combinatorial geometry and geometric combinatorics

Algebraic methods

Random and pseudorandom graphs

Property testing

Other topics in theoretical computer science

Video lectures

It is increasingly common that talks at conferences and workshops are videod and archived for posterity. Again, the selection is highly subjective (the linked workshops are mostly events I attended or organised).

Igor Pak also maintains a page with links to interesting videos in combinatorics.

Other useful resources

mathscinet search | arxiv search | jstor search | AMS calendar | Cambridge LaTeX | NASA LaTeX | Terry Tao's career advice for young mathematicians

Since this page contains a large number of references, it will take some effort to maintain, so I'll be very grateful for any help you can give by notifying me of broken links.

This page was last updated 3rd February 2022.