Related papers: Tricky Arithmetic
This is the transcript of a lecture given at UMass-Lowell in which I compare and contrast the work of Godel and of Turing and my own work on incompleteness. I also discuss randomness in physics vs randomness in pure mathematics.
Another introduction to perverse sheaves with some exercises. Expanded version of five lectures at the 2015 PCMI.
This survey is based on a series of talks I gave at the conference "Dynamical systems and diophantine approximation" at l'Instut Henri Poincar\'e in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for…
This text highlights issues present in the proof of Lemma 6.10 of the Baumgartner (1943 -- 2011) article "Almost disjoint sets, the dense set problem and the partition calculus" of 1976, and intends to present a correction at the same time…
This text is an appendix to our work "On the growth of Kronecker coefficients", arXiv:1607.02887. Here, we provide some complementary theorems, remarks, and calculations that for the sake of space are not going to appear into the final…
This article has been withdrown by the author.
These exercises complement my notes "Derived categories, resolutions, and Brown representability".
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
A method of estimating sums of multiplicative functions braided with Dirichlet characters is demonstrated, leading to a taxonomy of the characters for which such sums are large.
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive…
This is a review of recent results on conformal (super)algebras. It may be viewed as an amplification of my Wigner medal acceptance speech (given in July 1996 in Goslar, Germany) reproduced in the introduction.
We give polynomial-time dynamic-programming algorithms finding the areas of words in the presentations $\langle a, b \mid a, b \rangle$ and $\langle a, b \mid a^k, b^k; \ k \in \mathbb{N} \rangle$ of the trivial group. In the first of these…
This article is based on a talk given at a one-day meeting in NUI, Maynooth on the Fourth of April, 2008, held to honour David Walsh and Richard Watson. It surveys joint work with the author.
When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison gave it an enthusiastic review in the Scientific American and Martin Gardner was kind enough to say in his Mathematical Games column that "every recreational…
These notes attempt to give a short survey of the approach to support theory and the study of lattices of triangulated subcategories through the machinery of tensor triangular geometry. One main aim is to introduce the material necessary to…
These are corrections to the second edition of the book ``Vertex algebras for beginners'', University Lecture Series, 10, American Mathematical Society, Providence, RI, 1998.
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…