Talks
4th6th July 2023, Trinity 200, Trinity College, Cambridge.
21st June 2023, Heilbronn Colloquium, University of Manchester.
6th May 2023, Minisymposium of the Roman Number Theory Association, Università Roma Tre, Rome.
'Higherorder generalisations of stability and arithmetic regularity'
19th October 2022, Ergodic Theory and Analysis Seminar, Rutgers The State University of New Jersey.
'Three questionsno answers'
17th August 2022, Extremal combinatorics and geometry, Workshop, Banff International Research Station.
'The structure of stable sets'
3rd August 2022, Unimod 2022, EMS Summer School, University of Leeds.
'Efficient regularity lemmas in higherorder Fourier analysis'
28th June 2022, Fourier analysis @200, ICMS Edinburgh.
'Irregular triads in 3uniform hypergraphs'
15th June 2022, SIAM Conference on Discrete Mathematics, plenary talk, Pittsburgh, PA.
'Irregular triads in 3uniform hypergraphs'
1st June 2022, Oxford 1day Meeting in Combinatorics, University of Oxford.
'Irregular triads in 3uniform hypergraphs'
23rd May 2022, DIMAP Seminar, Centre for Discrete Mathematics and its Applications, University of Warwick.
'Higherorder generalisations of stability and arithmetic regularity'
30th March 2022, Logic Seminar, The Hebrew University of Jerusalem.
'Irregular triads in 3uniform hypergraphs'
15th March 2022, MITHarvardMSR Combinatorics Seminar, Massachusetts Institute of Technology, Cambridge, MA.
'Irregular triads in 3uniform hypergraphs'
8th March 2022, Combinatorics and TCS Seminar, University of Chicago, IL.
'Higherorder generalisations of stability and arithmetic regularity'
17th February 2022, Logic Seminar, University of Oxford.
'Higherorder generalisations of stability and arithmetic regularity'
26th January 2022, Virtual Harmonic Analysis Seminar.
'Higherorder generalisations of stability and arithmetic regularity'
30th November 2021, Workshop on Model Theory and Combinatorics, Fields Institute, Toronto.
'Efficient structurerandomness decompositions'
26th November 2021, DIAMANT Symposium, University of Utrecht.
'Arithmetic combinatorics through the modeltheoretic lens'
24th June 2021, Association for Symbolic Logic North American Annual Meeting, plenary talk, Notre Dame University.
'Efficient structurerandomness decompositions'
6th February 2020, Analysis seminar, University of Kent.
'The structure of stable sets'
12th September 2019, Heilbronn Annual Conference, University of Bristol.
'Efficient regularity lemmas'
8th May 2019, London 2day colloquium in combinatorics, Queen Mary, University of London.
'The structure of stable sets in finite abelian groups'
19th December 2018, Logic Seminar, University of Freiburg.
'The structure of stable sets in finite abelian groups'
1st December 2018, Lancashire Yorkshire Model Theory Seminar, University of Leeds.
'The structure of stable sets'
26th September 2018, BOWL 8, University of Oxford.
'Recent developments in graph and arithmetic regularity'
27th June 2018, Discrete Mathematics Days/JMDA18, plenary talk, Seville, Spain.
'The structure of stable sets in finite abelian groups'
26th March 2018, Model theory and applications, Institut Henri Poincaré, Paris.
'Some Applications of Relative Entropy in Additive Combinatorics'
12th December 2017, 10th Anniversary of the Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick.
'Stable arithmetic regularity'
5th October 2017, Additive Combinatorics and Applications, Center of Mathematical Sciences and Application, Harvard University, Cambridge, MA.
'Szemeredi's theorem in the primes'
22nd September 2017, The Music of Numbers: in honour of Javier Cilleruelo, ICMAT, Madrid, Spain.
'Some applications of relative entropy in additive combinatorics'
5th July 2017, British Combinatorial Conference, plenary talk, University of Strathclyde.
'Arithmetic regularity lemmas'
30th June 2017, Interactions with Combinatorics, University of Birmingham.
'Counting monochromatic structures in finite abelian groups'
14th June 2017, Canadam 2017, plenary talk, Ryerson University, Canada.
'Additive combinatorics over finite fields: recent progress and open problems'
6th June 2017, 13th International Conference on Finite Fields and their Applications, plenary talk, Gaeta, Italy.
'Counting monochromatic structures in finite abelian groups'
24th April 2017, Combinatorics seminar, University of California Berkeley.
'Some thoughts on solutions to linear systems in the primes'
12th September 2016, Rencontre de théorie analytique et élémentaire des nombres à la mémoire de Kevin Henriot, IHP, Paris.
'Ramsey multiplicity of patterns in finite abelian groups'
30th October 2015, New York Number Theory Seminar, CUNY Graduate Center.
'Current challenges in quadratic Fourier analysis'
19th September 2015, Joint LMS/EMS Mathematical Weekend, University of Birmingham.
'Counting monochromatic structures in finite abelian groups'
15th September 2015, Noncombinatorial combinatorics, University of Warwick.
'Ramsey multiplicity of patterns in finite abelian groups'
8th July 2015, Journées Arithmétiques 2015, Debrecen, Hungary.
'El análisis armónico cuadrático y sus aplicaciones'
1st July 2015, Sextas Jornadas de Teoría de Números, Valladolid, Spain.
'Ramsey multiplicity'
13th April 2015, Postgraduate Combinatorics Conference, Queen Mary, London.
'Ramsey multiplicity of patterns in abelian groups'
30th March 2015, British Mathematical Colloquium, University of Cambridge.
'Ramsey multiplicity of patterns in abelian groups'
25th November 2014, Arithmetic and allied subjects on the banks of the Neva, Euler International Mathematical Institute, St Petersburg.
'Ramsey multiplicity of patterns in abelian groups'
11th November 2014, DIMAP Seminar, Centre for Discrete Mathematics and its Applications, University of Warwick.
'Ramsey multiplicity of patterns in abelian groups'
18th September 2014, Additive Combinatorics @ Bristol, University of Bristol.
'Towards a BurrRosta conjecture for sets'
18th June 2014, Second Joint International Meeting of the Israel Mathematical Union and the American Mathematical Society, Tel Aviv.
'Beyond the Gowers norms'
11th March 2014, Simons Symposium on Discrete Analysis: Beyond the Boolean cube, Puerto Rico.
'Sousgroupes approximatifs et applications'
17th January 2014, Séminaire Géométrie, Institut de Mathématiques de Bordeaux.
'Finitefield models in additive combinatorics'
10th December 2013, Workshop on Emerging applications of finite fields, Linz, Austria.
'Current challenges in higherorder Fourier analysis'
20th November 2013, Harmonic analysis meeting, University of Birmingham.
'Polynomial configurations in the primes'
14th November 2013, Number theory seminar, University of Oxford.
'A quadratic GoldreichLevin theorem'
28th June 2013, Séminaire Codage, Cryptologie, Algorithmes, INRIA Saclay.
'A quadratic GoldreichLevin theorem'
18th June 2013, Algorithms and Complexity Seminar, LIAFA, Université Paris 7.
'Sumsets, sampling and almost periodicity'
16th May 2013, London 2day colloquium in combinatorics, London School of Economics, UK.
'Polynomial configurations in the primes'
16th March 2013, Number theory days 2013, EPFL, Lausanne.
'Polynomial configurations in the primes'
5th March 2013, Linfoot Seminar, University of Bristol, UK.
'Polynomial configurations in the primes'
30th January 2013, Discrete analysis seminar, University of Cambridge, UK.
'Sousgroupes approximatifs et applications'
12th  14th November 2012, Forum des jeunes mathématiciennes, plenary lecture, Institut Henri Poincaré, Paris.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur'
24th May 2012, IMJ Colloquium, Institut de Mathématiques de Jussieu, Paris.
'Colouring graphs and elements of Z_n: analogies and differences'
11th April 2012, Oberwolfach miniworkshop on Hypergraph Turan Problems, Germany.
'From additive combinatorics to number theory: adding the squares'
2nd April 2012, Young Researchers in Mathematics 2012, keynote lecture, University of Bristol, UK.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur'
30th January 2012, Séminaire d'analyse harmonique, Université Orsay, Paris.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur'
29th November 2011, Séminaire Dynamique, Arithmétique, Combinatoire
ERNEST, Institut de Mathématiques de Luminy, France.
'Ergodic, analytic and combinatorial approaches to decomposition theorems for bounded functions'
21st November 2011, LondonParis Number Theory Seminar, Institut Henri Poincaré, Paris.
'Large sets with little structure'
16th November 2011, Discrete Mathematics Group, Freie Universität Berlin, Germany.
'Finite field models in additive number theory'
27th October 2011, Integers 2011, Plenary Lecture, University of West Georgia, Carollton, GA.
'Quadratic pseudorandomness and decomposition theorems for bounded functions'
20th October 2011, Theory Seminar, University of Chicago, IL.
'Counting arithmetic progressions'
18th October 2011, Combinatorics and Probability Seminar, University of Pennsylvania, Philadelphia, PA.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur'
10th June 2011, Journeé de Théorie Analytique des Nombres, Nancy Université, France.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur'
8th June 2011, Séminaire tournant de Théorie Analytique des Nombres et d'Approximation Diophantienne, Université Claude Bernard, Lyon, France.
'Le principe de transfert'
13th and 19th May 2011, Number Theory Study Group, Chevaleret, Paris.
'Counting solutions to linear systems in uniform sets'
6th April 2011, Heilbronn seminar, University of Bristol.
'Facteurs caractéristiques en combinatoire additive'
22nd March 2011, Séminaire de Théorie Ergodique, Jussieu, Paris.
'Recent improvements on the cap set problem (due to Bateman and Katz)'
11th March 2011, Number Theory Student Seminar, CUNY Graduate Center, New York, NY.
'Counting solutions to linear systems in uniform sets'
22th November 2010, Rencontres de théorie analytique et élémentaire des nombres, Institut Henri Poincaré, Paris.
'Exponential sums over locally defined quadratics'
4th November 2010, Conference "Exponential sums over finite fields and applications", ETH, Zurich.
'Decomposition theorems for bounded functions'
28th October 2010, Séminaire d'Analyse Fonctionelle, Jussieu, Paris.
'Structure and randomness in the integers: harmonic analysis and beyond'
4th June 2010, ETH, Zurich.
'What Fourier analysis can and cannot tell us about the integers'
20th May 2010, Ecole Polytechnique, Paris.
'Large sets with little structure'
19th May 2010, Séminaire de combinatoire additive, Universite Paris 6, France.
'What Fourier analysis can and cannot tell us about the integers'
7th May 2010, Symposium "New Directions in Mathematics", University of Zurich.
'What Fourier analysis can and cannot tell us about the integers'
25th February 2010, Algebra, Number Theory and Combinatorics Seminar, University of Texas at Austin, Austin, TX.
'Interpreting polynomial structure analytically'
8th February 2010, Discrete Math and Computer Science Seminar, IAS, Princeton, NJ.
'Introduction to additive combinatorics'
5th February 2010, Number Theory Student Seminar, CUNY Graduate Center, New York, NY.
'Interpreting polynomial structure analytically'
2nd December 2009, Workshop on Analytical Methods in Combinatorics, Additive Number Theory and Computer Science, IPAM, Los Angeles, CA.
'Highrank polynomial phase decompositions, with numbertheoretic applications'
7th November 2009, AMS Sectional Meeting, Special Session on Arithmetic Combinatorics, UC Riverside, CA.
'The minimum number of monochromatic 4term progressions'
29th October 2009, Discrete Math Seminar, Princeton University, Princeton, NJ.
'Counting solutions to linear systems modulo N  an introduction to local quadratic Fourier analysis'
24th October 2009, AMS Sectional Meeting, Special Session on Analytic Number Theory, Penn State University, PA.
'The minimum number of monochromatic 4term progressions'
6th October 2009, Discrete Math Seminar, Columbia University, New York, NY.
'The minimum number of monochromatic 4term progressions' [Slides]
28th May 2009, Combinatorial and Additive Number Theory conference, CUNY Graduate Center, New York, NY.
'Minimal characteristic factors for linear systems  a quantitative approach' [Slides]
13th May 2009, Conference on Dynamical Systems and Randomness, Institut Henri Poincare, Paris, France.
'The minimum number of monochromatic 4term progressions'
4th March 2009, Discrete Math Seminar, University of Delaware, Newark, DE.
'Monochromatic structures in the integers'
10th February 2009, Discrete Math Seminar, Rutgers University, New Brunswick, NJ.
'What Fourier analysis can and cannot tell us about the integers'
15th December 2008, Number Theory Seminar, University of Edinburgh, Edinburgh, UK.
'Decompositions into polynomial phase functions'
7th November 2008, Discrete Rigidity Phenomena in Additive Combinatorics Workshop, Mathematical Sciences Research Institute, Berkeley, CA.
'The structure of popular difference sets'
25th September 2008, Number Theory Seminar, CUNY, New York, NY.
'Minimal characteristic factors for linear systems'
19th September 2008, Mathematical Sciences Research Institute, Berkeley, CA.
'The true complexity of a system of linear equations'
15th July 2008, Canadian Number Theory Association Meeting X, Waterloo, ON.
'Linear configurations in uniform sets'
27th March 2008, Joint ColumbiaNYUCUNY Number Theory Seminar, New York, NY.
'Counting solutions to linear systems in uniform sets'
21st March 2008, Number Theory Seminar, Stanford/AIM, Palo Alto, CA.
'Uniformity norms and the complexity of linear systems'
11th January 2008, Analysis and PDE Seminar, University of California, Los Angeles, CA.
'Decompositions into quadratic phase functions'
14th November 2007, Arithmetic Combinatorics Seminar, Institute for Advanced Study, Princeton, NJ.
'Minimal characteristic factors in arithmetic combinatorics'
30th October 2007, Dynamical Systems Seminar, Northwestern University, Evanston, IL.
'Linear configurations in uniform sets'
3rd October 2007, Short Talk, Institute for Advanced Study, Princeton, NJ.
'Linear configurations in uniform sets'
14th May 2007, Discrete Analysis Seminar, Cambridge, UK.
'Long arithmetic progressions in the primes: constructing a pseudorandom majorant for the vonMangoldt function'
28th April 2006, Number theory study group, Massachusetts Institute of Technology, Cambridge, MA.
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'When is a mathematical object wellbehaved?'
13th December 2022, Zurich Colloquium in Mathematics, Zurich.
'When is a mathematical object wellbehaved?'
17th May 2022, Mathematical Colloquium, King's College London.
'When is a mathematical object wellbehaved?'
2nd March 2022, Department Colloquium, University of Chicago, IL.
'The structure of stable sets'
19th March 2019, Pure Colloquium, Open University.
'The structure of stable sets'
8th February 2019, Department Colloquium, Imperial College London.
'The structure of stable sets: from additive number theory to model theory'
16th October 2018, Department Colloquium, University College London.
'The structure of stable sets: from additive number theory to model theory'
30th April 2018, LMS Women in Maths Days 2018, Newton Institute, Cambridge.
'The structure of stable sets: from additive number theory to model theory'
24th November 2017, Pure Colloquium, University of Manchester.
'The structure of stable sets: from additive number theory to model theory'
23rd November 2017, School Colloquium, University of Leeds.
'The rise (and decline?) of the structure/randomness dichotomy'
17th April 2017, Colloquium, Center for Communications Research, La Jolla.
'In pursuit of structure: why a little randomness (almost) always helps'
3rd April 2017, Open Lecture, Simons Institute, University of California Berkeley.
'Quadratic Fourier analysis: why and when linear phases are not enough'
5th February 2016, Mathematics Department Colloquium, Warwick University.
'Quadratic Fourier analysis'
11th December 2015, Sofia Kovalevskaya Colloquium, Berlin Mathematical School.
'From combinatorics to group theory (and back again)'
18th November 2015, Pure Mathematics Colloquium, University of Sheffield.
'Approximate groups'
28th February 2014, Landscapes in Mathematical Sciences, University of Bath.
'Polynomial progressions in the primes, d'après Green, Tao et Ziegler'
24th March 2012, Séminaire Bourbaki, École Normale Supérieure, Paris.
'An Introduction to Quadratic Fourier Analysis'
14th January 2010, Mathematics Department Colloquium, University of Georgia, Athens, GA.
'What the Fourier transform can and cannot tell us about the integers'
22nd October 2009, Women in Mathematics Lecture Series, Massachusetts Institute of Technology, Cambridge, MA.
'Quadratic Fourier Analysis'
21st October 2008, Mathematics Department Colloquium, University of California Santa Cruz, Santa Cruz, CA.
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'Combinatoria aditiva: conjuntos suma, el fenómeno sumaproducto y el método polinomial'
8th  22nd August 2015, AGRA 2015: Summer school on arithmetic, groups and analysis, CIMPA, Cusco, Peru.
'Analytic techniques in additive combinatorics' (oneweek graduate course)
13th  16th October 2014, Additive Combinatorics Doctoral School, Freie Universität Berlin.
'Introduction to additive combinatorics'
23rd  25th January 2012, Premier Congrès FrancoChilien de Dynamique et Combinatoire, minicourse, SaintValérysurSomme, France.
'De la combinatoire additive à l'analyse harmonique d'ordre supérieur, et ses applications en théorie des nombres'
13th  16th June 2012, Colloque Jeunes Chercheurs en Théorie des Nombres, minicours, Ecole Normale Supérieure, Lyon.
'Introduction to Fourier analysis on finite Abelian groups with applications'
24th November and 1st December 2005, Universitat Politecnica de Catalunya, Barcelona, Spain.
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'The power of randomness'
30th April 2019, Oxford Mathematics Public Lecture, University of Oxford.
'Using randomness to find structure'
11th June 2018, British Mathematics Colloquium, public lecture, University of St Andrews.
'What's the(ir) difference? Primes, twin primes and other relatives.'
8th November 2017, Annual Coulter McDowell Lecture, Royal Holloway.
'One, two, red, blue'
21st September 2016, LMS Popular Lecture, Birmingham.
'One, two, red, blue'
29th June 2016, LMS Popular Lecture, London.
'How to make yourself heard at a rock concert'
13th October 2015, Public lectures in mathematics, University of Bristol.
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'In pursuit of structure: why a little randomness (almost) always helps'
3rd March 2023, Archimedeans, University of Cambridge.
'The power of randomness'
30th January 2023, Stokes Society, Pembroke College, Cambridge.
'Counting monochromatic structures in finite abelian groups'
5th March 2022, Tomorrow's Mathematicians Today, plenary talk, University of Greenwich.
'Addition, multiplication, and why they don't get along'
25th February 2019, Trinity Mathematical Society, University of Cambridge.
'Addition, multiplication, and why they don't get along'
17th August 2018, PROMYS guest lecture, University of Oxford.
'Combinatorics at Bristol and elsewhere'
18th December 2014, Prospects 2014, University of Oxford.
'One, two, ...  red, blue, ...'
19th November 2009, RUSMEO Lecture Series (formerly The Rutgers Pi Club), Piscataway, NJ.
'Calculus against the swine flu: modelling the spread of infectious disease'
5th November 2009, Mathematical Careers and Ideas Lecture Series, Rutgers University, Piscataway, NJ.
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