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 few years, 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 rather 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  Luca Trevisan  Emmanuel Kowalski  Gil Kalai Claire Mathieu
Arithmetic combinatorics
Tim Gowers
A new proof of Szemeredi's Theorem for arithmetic progressions of length 4 
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Quasirandomness, counting and regularity for 3uniform hypergraphs 
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Lower bounds of towertype for Szemeredi's uniformity lemma 
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Mathematics: A very short Introduction 
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Ben Green
The primes contain arbitrarily long arithmetic progressions (with T. Tao) 
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An inverse theorem for the Gowers U^3 norm, with applications (with T. Tao) 
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Finite field models in additive combinatorics 
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Montreal lecture notes on quadratic Fourier analysis 
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Terry Tao
A sumproduct estimate in finite fields, and applications (with J. Bourgain and N. Katz) 
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A quantitative ergodic theory proof of Szemeredi's Theorem 
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The dichotomy between structure and randomness, arithmetic progressions and the primes 
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Imre Ruzsa
Tom Sanders
Ergodic theory
Sasha Leibman
Polynomial extensions of van der Waerden's and Szemeredi's Theorems (with V. Bergelson) 
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Convergence of multiple ergodic averages along polynomials of several variables 
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Intersective polynomials and the polynomial Szemeredi Theorem (with V. Bergelson and E. Lesigne) 
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Bryna Kra
Nonconventional ergodic averages and nilmanifolds (with B. Host) 
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Montreal lecture notes on ergodic methods in additive combinatorics 
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Multiple recurrence and nilsequences (with V. Bergelson, B. Host and an appendix by I. Ruzsa) 
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Nikos Frantzikinakis
Ergodic averages for independent polynomials and applications (with B. Kra) 
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A Hardy field extension of Szemeredi's Theorem (with M. Wierdl) 
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Multiple ergodic averages for three polynomials and applications 
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Tamar Ziegler
The primes contain arbitrarily long polynomial progressions (with T. Tao) 
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Universal characteristic factors and Furstenberg averages 
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Combinatorics
Noga Alon
Benny Sudakov
Jozsef Solymosi
Janos Pach
Thirteen problems on crossing numbers (with G. Toth) 
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Crossing families (with B. Aronov, P. Erdos, W. Goddard, D.J. Kleitman, M. Klugerman, L.J. Schulman) 
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Classical harmonic analysis
Jean Bourgain
On triples in arithmetic progression 
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On arithmetic progressions in sums of sets of integers 
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Lambda_psets in analysis: results, problems and related aspects 
mathscinet 

Izabella Laba
From harmonic analysis to arithmetic combinatorics 
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An improved bound on the Minkowski dimension of Besicovitch sets in R^3 (with N. Katz and T. Tao) 
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Number theory
Alex Gamburd
Sieving and expanders (with J. Bourgain and P. Sarnak) 
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Akshay Venkatesh
The work of Einsiedler, Katok and Lindenstrauss on the Littlewood Conjecture 
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Equidistribution, Lfunctions and ergodic theory: on some problems of Yu.V. Linnik (with P. Michel) 
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Elon Lindenstrauss
Invariant measures and arithmetic quantum unique ergodicity 
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Invariant measures and the set of exceptions to Littlewood's conjecture (with M. Einsiedler and A. Katok) 
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Peter Sarnak
Harald Helfgott
Improving Roth's theorem in the primes (with A. de Roton) 
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How small must illdistributed sets be? (with A. Venkatesh) 
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Trevor Wooley
Diophantine problems in many variables: the role of additive number theory 
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Waring's problem: a survey (with R.C. Vaughan) 
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Kannan Soundararajan
Small gaps between prime numbers: The work of GoldstonPintzYildirim 
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Theoretical computer science
Assaf Naor
The two possible values of the chromatic number of a random graph (with D. Achlioptas) 
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Euclidean distortion and the sparsest cut (with S. Arora and J.R. Lee) 
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Avi Wigderson
Expander graphs and their applications (with S. Hoory and N. Linial) 
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P, NP and mathematics  a computational complexity perspective 
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Alex Samorodnitsky
Low degree tests at large distances 
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Inverse conjecture for the Gowers norm is false (with S. Lovett and R. Meshulam) 
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Luca Trevisan
Gowers uniformity, influence of variables, and PCPs (with A. Samorodnitsky) 
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Additive combinatorics and theoretical computer science 

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Upandcoming
Neil Lyall
Polynomial configurations in difference sets (with A. Magyar) 
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A new proof of Sárközy's theorem 

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Thai Hoang Le
Pablo Candela
On the structure of steps of threeterm arithmetic progressions in a dense set of integers 
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Olof Sisask
On the maximal number of threeterm arithmetic progressions in subsets of Z_p (with B.J. Green) 
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A probabilistic technique for finding almost periods of convolutions (with E. Croot) 
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Hoi Nguyen
Derrick Hart
Sum product estimates in finite fields via Kloosterman sums (with A. Iosevich and J. Solymosi) 
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Boris Bukh
No nontrivial solutions to a linear equation in integers 
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Other websites
mathscinet search  arxiv search  jstor search  AMS calendar  Cambridge LaTeX  NASA LaTeX  Jahr der Mathematik
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.
