I am a Heilbronn Reader in Combinatorics and Number Theory at the University of Bristol, and the Associate Chair of the Heilbronn Institute for Mathematical Research.

Publications | Talks | CV | Pseudorandomness Simons Institute 2017 | google+

My research focuses on identifying and quantifying arithmetic structure in dense sets of integers and combines Fourier-analytic, combinatorial and probabilistic methods. It forms part of a thriving area called arithmetic combinatorics, a subject that includes many beautiful results such as the Green-Tao Theorem on long arithmetic progressions in the primes. Some of my work has close connections with ergodic theory and applications to theoretical computer science.


School of Mathematics
University of Bristol
University Walk
Bristol BS8 1TW
United Kingdom
Email: julia dot wolf at bristol dot ac dot uk
Office: 2.06 Howard House
Office hours: by appointment
Phone: +44 (0)117 331 1663
Fax: +44 (0)117 331 5264


7th July 2016

Our biannual Bristol-Oxford 1-day meeting in additive combinatorics will henceforth be known as "BrOx". We look forward to an exciting programme today!

9th May 2016

My paper with Alex Saad, entitled "Ramsey multiplicity of linear patterns in certain finite abelian groups", is finally out. The journal link is now available on my publications page.

25th March 2016

A massive thank you to all our speakers at the BMC Special Session in Combinatorics, who over the last couple of days painted an exciting and inspiring picture of the current combinatorial research landscape!

1st March 2016

Discrete Analysis, a new arXiv overlay journal, was officially launched today. The first seven articles to be published include a solution of the Erdos discrepancy problem, as well as a finite-field version of a well known Ramsey-theoretic problem on monochromatic sums and products. Take a look! For more details on the background and philosophy of the journal see Tim Gowers's blog post.

20th November 2015

In spring 2017 we are bringing together mathematicians and theoretical computer scientists for a semester-long research programme on Pseudorandomness at the Simons Institute in Berkeley. Activities will include three workshops, focusing on constructing expanders and extractors, leveraging weak pseudorandomness properties and exploiting the structure-randomness dichotomy. Applications for junior research fellowships close on 15th December.

3rd November 2015

The third instalment of our Bristol-Oxford 1-day meeting in additive combinatorics is happening today! Please click here for the programme.

15th September 2015

We are launching a brand new arXiv overlay journal called Discrete Analysis, which is an open-access mathematical journal with an emphasis on areas of mathematics that are broadly related to additive combinatorics, including harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and parts of theoretical computer science. While Discrete Analysis has a conventional editorial board and refereeing process, it does not host the articles it accepts and instead simply links to preprints that are posted on the arXiv. For a more comprehensive explanation of what the journal is trying to achieve, see Tim Gowers's blog post. The journal is now soliciting submissions and hopes to publish its first issue in early 2016.

1st September 2015

After many years I've finally got round to updating my personal roadmap. New features include links to blogs and videod conference talks which may be of interest to visitors of this site.

23rd March 2015

Following on from our inaugural event in September 2014, we are pleased to announce that we will be holding a second 1-day meeting in additive combinatorics on Thursday, 23rd April 2015, this time hosted by the University of Oxford.

18th August 2014

A new survey article entitled 'Finite field models in arithmetic combinatorics--ten years on' is now online. It attempts to follow in the footsteps of Ben Green's influential expository piece from almost a decade ago, and covers some more recent results including the elegant proof of Plünnecke's inequality by Petridis, Croot-Sisask almost-periodicity, Sanders's log-bound for Bogolyubov's lemma as well as the latest developments in higher-order Fourier analysis.

13th August 2014

This autumn I will be teaching a graduate course on the 'Analysis of points and lines' through the Taught Course Centre, a platform Bristol shares with Bath, Imperial, Oxford and Warwick. Lectures take place 2-4pm on Friday afternoons starting 17th October. A tentative syllabus and further information are now available from the course website.

13th May 2014

This ad is for locals only. On Saturday, 14th June 2014 I will be playing in a concert with the Brunel Sinfonia, starting at 7:30pm at Victoria Rooms. The programme is sure to please.

Mussorgsky - Pictures at an Exhibition
Barber - Symphony No. 1
Tchaikovsky - Romeo & Juliet Overture

23rd March 2014

I am pleased to announce that we will be holding a 1-day additive combinatorics meeting at Bristol on Thursday, 18th September 2014. The main speakers are Juanjo Rue, Tom Sanders, Mark Walters and Thomas Bloom. The first talk starts at 11am and there will be a reception followed by a conference dinner in the evening. The event is made possible by a grant from the LMS and the generous support of the Heilbronn Institute. Further details are available on the conference website.

12th December 2013

Video recordings of the many excellent talks at last week's Simons Institute workshop on 'Neo-classical methods in discrete analysis' are now available from the workshop website.

8th October 2013

Due to technical issues in more than one participating node, the start of my graduate course 'Introduction to additive combinatorics' in the Taught Course Centre has been delayed by one week. The first session will now take place at 9am on Tuesday, 15th October. Apologies for the late notice.

6th September 2013

There are still a few free spaces left at the Simons Institute workshop 'Neo-classical methods in discrete analysis', which will be held at the brand new Simons Institute for the Theory of Computing in Berkeley from 2nd to 6th December 2013. Those interested in participating are asked to register on the workshop webpage as soon as possible. My co-organiser Luca Trevisan and I are very excited about how the programme is shaping up!

30th August 2013

As of this weekend I am officially back in the UK, as a Heilbronn reader in combinatorics and number theory at the University of Bristol. My French and Cambridge email accounts remain operational, but I should prefer it if you used my new Bristol account for work-related purposes.

11th May 2013

Together with Emmanuel Breuillard, Ben Green, Jozsef Solymosi and Terence Tao, I am organising one of the workshops during IPAM's semester-long programme 'Algebraic techniques for combinatorial and computational geometry'. The workshop's topic is 'Finding algebraic structures in extremal combinatorial configurations', and it will be held in Los Angeles from 19th to 23rd May 2014. A preliminary (and incomplete) list of speakers is now available, and applications for funding to attend the workshop, targeted especially at early-career researchers, are now open. For details see the workshop website.

3rd December 2012

At 2pm I'll be defending my habilitation thesis at the University Paris-Sud (Orsay), room 113-115 in building 425. The committee consists of Emmanuel Breuillard, Etienne Fouvry, Ben Green, Harald Helfgott, Bernard Host and Alain Plagne, and the thesis itself is available from my publications page.

25th October 2012

On the arXiv this week is joint work with Eli Ben-Sasson, Noga Ron-Zewi and Madhur Tulsiani. We give a new sampling-based and L^p norm-free proof of Croot and Sisask's almost-periodicity lemma. As an application we prove an algorithmic version of Sanders's quasipolynomial Boglyubov lemma. This allows us to improve the running time of our previous "quadratic Goldreich-Levin algorithm" (joint work with Madhur Tulsiani from last year), which computes the large quadratic Fourier coefficients of a function with high probability.

17th October 2012

As of this evening a new preprint on an extension of the Tao-Ziegler theorem on polynomial progressions in the primes will be available on the arXiv. Together with Thái Hoàng Lê, we prove that any subset of the primes of relative positive density contains a polynomial configuration x+P_1(p-1), . . ., x+P_k(p-1), where x is an integer, p is a prime and P_1, . . . , P_k are polynomials with integer coefficients and zero constant term.

Also, if you are a regular visitor you will have noticed that the website has had a facelift, having stuck with the same design for almost a decade. While some of the pages have been updated, the content hasn't changed much, and I hope you'll find everything in its usual place.

10th June 2012

In order to take full advantage of all those excellent mathematicians who will be visiting Paris at the start of July on the occasion of the conference Additive Combinatorics in Paris 2012, Bernadette Charron-Bost and I are organizing a one-day colloquium on discrete mathematics and computer science. The event will take place at Ecole polytechnique on July 4th, and speakers include Noga Alon, Prasad Tetali and Jacob Fox. More information is available from this page.

25th May 2012

Our additive combinatorics group has been awarded a major 3-year grant by the French Agence Nationale de la Recherche under the ANR Blanc scheme. The project runs under the name "Combinatoire Additive: Ensembles, Séquences et Applications Remarquables" (CAESAR) and includes amongst others Eric Balandraud, Emmanuel Breuillard, Benjamin Girard, Andrew Granville (as member of the CNRS international unit at Montréal), Harald Helfgott and Wolfgang Schmid. It is led by Alain Plagne.

24th March 2012

The text for the Bourbaki seminar on polynomial configurations in the primes, which I will be giving later today, is now available on my preprints page. A related popular mathematics article which I have written can be found on the beautiful French website Images des mathématiques.

21st March 2012

Endre Szemerédi has been awarded the Abel Prize 2012. Congratulations!

2nd November 2011

I am organizing a study group on arithmetic combinatorics (GTCA), open to all interested mathematicians in the Paris area. It will be held every other Tuesday at 4pm. For more information, see this new page.

14th July 2011

Together with Alain Plagne, Eric Balandraud, Benjamin Girard and Wolfgang Schmid I am organizing a week-long conference entitled Additive Combinatorics in Paris 2012, to be held in memory of Yahya ould Hamidoune at the Institut Henri Poincaré during the second week of July next year. We have an amazing list of keynote speakers lined up, and hope that many of you will be able to participate. An official announcement will be sent out a few weeks from now. For more information, including a registration form, please visit our website.

24th May 2011

Madhur Tulsiani and I have uploaded our paper "Quadratic Goldreich-Levin Theorems" to the arXiv. We give an algorithmic version of the U^3 inverse theorem and various refinements thereof, allowing us to compute for the fist time the large "quadratic Fourier coefficients" of a given bounded function. For an extended abstract and further links see my preprints page.

24th November 2010

From personal experience I know that the French academic system can seem rather intransparent and impenetrable from the outside. I have therefore listed some opportunities for young mathematicians to spend some time in France to pursue their research interests on this new page.

28th July 2010

As of the start of the academic year, I will be a Hadamard Associate Professor at Ecole Polytechnique in Paris. As a result this website will probably soon experience a linguistic transformation.
I intend to return to the US periodically in the near future. If you are interested in my travel schedule you can take an educated guess on the basis of my talk and conference announcements, or simply email me.

10th February 2010

Three new joint papers with Tim Gowers have found their way onto the arXiv today. We give a strong quadratic decomposition theorem in both vector spaces over finite fields (arXiv:1002.2209) and the cyclic group modulo a prime (arXiv:1002.2210), as well as a general regularity-type decomposition into polynomial phases in the former setting (arXiv:1002.2208). As a consequence we are able to prove the general case of an earlier conjecture of ours regarding the true complexity of a system of linear forms. For more details please see Papers and Preprints.

8th January 2010

I'll be teaching a graduate course entitled 592: Topics in Probability and Ergodic Theory this semester, with emphasis on arithmetic structures in subsets of the integers and the primes.

The course is suitable for any graduate student with an interest in number theory, harmonic analysis or combinatorics. We shall explore various approaches to establishing the existence of arithmetic structure in arbitrary subsets of the integers and the primes. These approaches include purely combinatorial methods, analytic techniques as well as a thorough discussion from a dynamical systems point of view.

A preliminary list of topics is available from the course webpage, which will be expanded in due course.

2nd November 2009

On Thursday, November 5 I'll be giving a lecture in the series 'Mathematical Careers and Ideas' for undergraduates at Rutgers. My title will be Calculus against the swine flu: modelling the spread of infectious disease. Epidemiology is certainly not my speciality, but it doesn't take much calculus to draw some interesting and sometimes counterintuitive conclusions about the spread of influenza (and similar diseases). There is free pizza after the talk! Please click on the link above for further details.

1st July 2009

My teaching pages have been updated. In particular, there is a new section entitled Student Resources, which contains what I believe to be useful links and information for mathematically inclined students at Rutgers and elsewhere. Also, I have made some preliminary information available on 477: Mathematical Theory of Probability and 152: Calculus II for the Mathematical and Physical Sciences, which I will be teaching at Rutgers in the fall.

28th June 2009

Having neglected my violin for a few months, I am excited to announce that I'll be part of the Mercury Orchestra's second summer season.

Mercury Orchestra
Channing Yu, conductor
Saturday, 18th July at 8pm
Harvard Sanders Theatre in Cambridge, Massachusetts
Strauss - Don Juan
Mahler - Symphonie No. 5

Tickets are now on sale online at the Harvard Box Office.

20th May 2009

For experimental purposes I have installed jsMath on my Preprints page, which may now display a font warning when you visit for the first time. The idea is that jsMath displays mathematical symbols flexibly and much better than ordinary html, so I thought I'd give this a go. Feedback is always welcome.

5th March 2009

A long overdue overhaul of this website has taken place in order to create room for more mathematics. My private pages are temporarily unavailable.

3rd February 2009

The Discrete Math Seminar at Rutgers has its own webpage this semester. The program is now finalised and includes speakers and abstracts through the end of April.

5th October 2008

Ben Green and I have submitted a short note on Elkin's improvement of Behrend's construction to the arXiv:0810.0732.

26th September 2008

I do not get to vote in this country. Please do it for me.

1st August 2008

This summer I have been involved as a mentor in the Summer Program for Undergraduate Research SPUR at MIT. Both my students Cordelia Link and Yuncheng Lin won a Rogers Family Award for their projects, details of which will be made available in the near future. Watch this space.

30th June 2008

A program of 20th century French classics with pianist Albert Kim and the Mercury Orchestra in the heart of Harvard Square.

Mercury Orchestra
Saturday, 19th July at 8pm
Harvard Sanders Theatre in Cambridge, Massachusetts
Ravel - La Valse
Ravel - Piano Concerto in G Major
Debussy - La Mer

Tickets are now on sale online at the Harvard Box Office. Out of all orchestras I've ever played with, this one has by far the largest and best viola section. (I expect that especially musical readers from Cambridge, UK, will appreciate the content of this statement!)

24th June 2008

This coming weekend I'll be performing with the Cambridge Symphony Orchestra in a summer pops concert hosted by Harvard's JFK School of Government.

Cambridge Symphony Orchestra
Sunday, 29th June at 3pm
JFK Lawn in Cambridge, Massachusetts
In case of rain: The Greater Boston Vineyard Church, 170 Rindge Ave. (near Davis Sq.)

The program includes Copland's 'Lincoln Portrait', 'Harry Potter and the Goblet of Fire', 'StarWars', 'The Washington Post March' and 'The Ride of the Valkyries' amongst many other popular classics. Admission is free. Come along!

20th June 2008

This summer I am teaching Advanced Calculus at MIT as part of the MITES 2008 program. Further details are available from my teaching page.

13th February 2008

My fate for the coming academic year has been decided: During the fall I will be a postdoctoral fellow attending the program Ergodic Theory and Additive Combinatorics at MSRI in Berkeley. In January I'll be taking up an assistant professorship at Rutgers University. Some might simply call it a postdoc.

8th February 2008

I am co-organizing a series of seminars at the IAS this term, mainly of an ergodic theory/analysis flavour. A preliminary list of speakers and abstracts can be found under Mathematics - IAS Analysis Seminar.

1st November 2007

My joint paper with Tim Gowers on 'The true complexity of a system of linear equations' appeared on the arXiv today. The abstract is available in the section Mathematics - Preprints, which also contains a link to the arXiv download for the paper.

5th September 2007

My new contact details can be found in the section About Me - Contact. I have completed my move to Princeton, NJ, where I will be a member of the Institute for Advanced Study until May 2008.

10th June 2007

I have signed up to run 5K in this year's 'Race for Life' in Cambridge on Sunday, 8th July. OK, it's not a marathon. If you'd still like to sponsor me (in aid of 'Cancer Research UK'), you can do so at www.raceforlifesponsorme.org/juliawolf until 22nd July 2007.

3rd June 2007

My website is back after lying dormant for over a year. To provide a certain amount of continuity, many news items from the previous incarnation of this website have remained on this page. The layout has changed very little, although you will find that a number of sections are now password-protected.

27th June 2005

Yet another one, but possibly my last one for quite some time:

Cambridge Graduate Orchestra
Sunday 10th July
7:30pm in Trinity College Chapel
Sarasate - Zigeunerweisen
Montsalvatge - Cinco Canciones Negras
Saint-Saens - Symphony No. 3

Come. Tickets available on the door or online. For more details see the website www.cambridgegraduateorchestra.com or have a look at the poster!

13th February 2005

I had given up advertising concerts that I am playing in, but the following event marks an exception:

Cambridge Graduate Orchestra
Monday 7th March
8pm at West Road Concert Hall
Schnittke - (K)ein Sommernachtstraum
Rachmaninoff - Rhapsody on a Theme of Paganini
Rimsky-Korsakov - Scheherazade

This is a truly wonderful programme, and it would be great to have a good audience! For more details, or to purchase tickets online, visit www.cambridgegraduateorchestra.com.

On a slightly different (and more scientific) note, it has been brought to my attention that the Department of Experimental Psychology at Cambridge is currently running a project entitled Is there a maths gene?. Whatever your level of mathematical ability, click on the link above to participate in the high-profile survey (you may have seen parts of it in The Guardian). You will be entered into a draw to win tickets to Trinity May Ball, it's fun and they even tell you your score and promise to inform you of the overall result of the experiment - go on!

19th October 2004

New stuff!

I've added pictures from the AIM workshop in San Francisco (Photographs - San Francisco) and my trip to Chile (Photographs - Chile). There is also a new page with links to some of my friends' pages (About Me - Friends). If you are supervised by me, you might like to check out the updated section Mathematics - For Supervisees. And finally, tickets for the Clare College Music Society Michaelmas Term Concert are on sale now! For more details click here.

3rd May 2004

I shall abuse this space to advertise two concerts that I will be playing in over the next few weeks.

Orchestra on the Hill
Saturday 8th May
8pm in the New Hall Dome
Elgar - Pomp and Circumstance Marches No. 1 - 5
Haydn - Nelson Mass


Clare College Music Society May Week Concert
Sunday 13th June
7pm in Clare College, Dining Hall
Schumann - Genoveva Overture
Mozart - Sinfonia Concertante
Strauss - Der Abend
Britten - A Young Person's Guide to the Orchestra
More details at CCMS May Week Concert - tickets usually sell out phenomenally fast!

10th April 2004

Many pages have been updated over the past few days, take a look!

26th January 2004

On Monday, 2nd February I will be giving a joint talk (with Sir Nicholas Barrington) on 'The Fascination of Numbers'.
It will take place in the Thirkill Room in Clare Old Court, starting at 8:30pm.
If you plan to attend, you are kindly requested to email the President of the Dilettante Society, Richard West.

I will also be singing in Clare's Lent Term concert:

Mozart's Requiem
Friday 13th February
8pm at West Road Concert Hall

26th September 2003

The big news is that (after many attempts and compromises) I have finally managed to set up this website!
If nothing else, I hope it provides some useful links to other people's pages on the web. I would also like to apologise for the fact that some places of this website are still under construction - more content will be added soon.
Comments of any kind are always appreciated, so please don't hesitate to get in touch.


PS: If you can't see a menu on the left but would like to see one, please enable JavaScript.
If the page does not display properly, you are probably using an ancient version of Netscape. Please notify me of this occurrence.

This page was last updated 15th July 2016.