I usually prefer blackboard lectures, but every once in a while I have prepared slides (mostly for lectures in places where there was no blackboard, or when there wasn't enough time to do a good presentation on the board). I have collected the PDF files of these slides here, in reverse chronological order. Most are better watched in presentation mode.
In addition, I have started to add scans of my own notes for some blackboard lectures. These might be useful, although it should be kept in mind that the actual talk often diverged significantly from these notes. I have such scans for most (maybe all) talks from 2021 onwards, and I will add them in reverse chronological order.
When I have a (good) picture from the event on which occasion I gave the talk, I will also add some.

Spectral measures in tensor categories (blackboard)	These are the notes for my talk at the Erlangen Emmy Noether Seminar in June 2024; it concerns my ongoing work with A. Forey and J. Fresán concerning "spectral measures" for objects in tensor categories, and the application to limit theorems for fixed-point counts, in the setting of Knop's tensor envelopes.
Sieve in discrete groups (blackboard)	These are the notes for a talk at the conference "Computational aspects of thin groups" at IMS in Singapore, in June 2024. The lecture is a survey of sieve in discrete groups.
Toroidal averages (blackboard)	These are the notes for a talk in the introductory workshop of the Spring 2024 Analytic Number Theory Program at the Mittag Leffler Institute. The talk discussed various aspects of the "toroidal averages" for special values of Dirichlet L-functions that Fouvry, Michel and myself started exploring in 2023.
Convolution and equidistribution (blackboard)	These are the notes for my talk during the conference for Nick Katz's 80th birthday. It surveys my work with Forey and Fresán on the approach to equdistribution of exponential sums based on the tannakian formalism (generalizing the work of Katz for the multiplicative group).
Do pseudopolynomials dream of Galois groups? (blackboard)	These are the notes for a talk in the joint New York Number Theory Seminar in December 2023. This was a fairly speculative discussion of pseudopolynomials and the conjectures formulated by Forey, Fresán, myself and Soundararajan concerning the distribution of the number of their zeros, etc.
Dix ans après	These are the notes for a talk at the conference in honor of R. Heath-Brown's 70th birthday, held in Oxford in July 2023; it is a general history and survey of the work around trace functions, which started around 2011/2012 and was first presented in September 2012 in the conference for his 60th birthday. (There was a final part of the talk on the white boards, which is not represented in the slides.)
"Algebraic" ergodic averages (blackboard)	These are the notes for a talk at the University of Turku in June 2023. I discuss somewhat informally the problem of studying "ergodic" averages with trace functions.
Something old and something new (blackboard)	These are the notes for a talk in Bonn in April 2023. It concerns the use of tensor envelope categories to prove fixed-point theorems, along the lines of the "problème des rencontres".
Sidon sets in algebraic geometry (blackboard)	These are the notes for a talk at the Rényi Institute in February 2023, which was also dedicated to an explanation of the construction of Sidon sets using generalized jacobians, by Forey, Fresán and myself.
Sidon sets, generalized jacobians and monodromy (blackboard)	These are the notes for a talk at EPFL in January 2023, where I explained how Forey, Fresán and I used generalized jacobians to construct new examples of Sidon sets.
Equidistribution and L-functions (blackboard)	These are the notes for two talks in a conference in Korea in January 2023. The first talk is a general survey of the links between L-functions and equidistribution, whereas the second discusses the "Fourier" L-functions defined by Forey, Fresán and myself for the study of arithmetic Fourier transforms.
The problem of coincidences, revisited	These are the notes for a talk at the conference in honor of A. Granville's 60th birthday, held in Montréal in September 2022. Here is the French version.
Fourier analysis over commutative algebraic groups and Frobenius distribution	These are the notes for a talk at a conference on topics related to Frobenius distribution, organized by A.C. Cojocaru and F. Fité in June 2021. Like the previous one, the topic is related to my ongoing joint work with A. Forey and J. Fresán.
Exponential sums over finite fields	These are the notes for my invited lecture at the European Congress of Mathematics in June 2021. The topic is related to my ongoing joint work with A. Forey and J. Fresán concerning convolution and equidistribution over general commutative algebraic groups.
Remembrances of polynomials values: Fourier's way	These are the notes of a lecture in the Wisconsin Number Theory Seminar in March 2021, concerning ongoing joint work with K. Soundararajan (related, but different, from that in the January IST talk below).
Exponential sums, Sidon sets and tannakian categories	These are the notes of my lecture in the conference in honor of the 70th birthday of R. Balasubramanian ("Balu"). Like the FRG one, the topic is my ongoing joint work with A. Forey and J. Fresán on equidistribution for exponential sums parameterized by characters of a commutative algebraic group.
Twisted multiplicativity and exponential sums	These are the notes of a lecture at the IST Number Theory Seminar in January 2021, concerning ongoing joint work with K. Soundararajan; we expect to have a preprint available soon...
Equidistribution of L-functions modulo squarefree polynomials and applications	These are not really slides, but the notes (written on a tablet) of a talk in a Focus Research Group seminar at AIM on October 13, 2020; they present some of my ongoing joint work with A. Forey and J. Fresán (and also partly with W. Sawin) to generalize to arbitrary commutative group schemes the equidistribution theorem of Katz for the discrete Mellin transform on the multiplicative group. In fact, most of the talk concerns some of the applications, since these are the most relevant for the audience of the talk.
The work of R. P. Langlands	These are the slides for my talk presenting the work of Langlands during the SMG Abel Prize Day, on September 25, 2020.
Quantitative sheaf theory, d'après Sawin	These are the slides for a talk in the Oberwolfach conference "Automorphic forms and arithmetic", in September 2020.
Equidistribution from the Chinese Remainder Theorem	These are the slides for a talk in Zeev Rudnick's Zoom seminar, April 23, 2020.
Randonnée arithmétique	These are the slides for my talk at the Colloquium of the Institut Élie Cartan in Nancy, in January 2020.
Random / not Random	These are the slides for my talk at the 2019 Heilbronn annual conference.
Les graphes, un autre univers en expansion	Il s'agit de la présentation correspondant à mon exposé à la Bibliothèque Nationale de France le 20 Février 2019, dans le cadre du cycle «Un texte, un mathématicien» organisé par la BNF et la SMF, en partenariat avec Animath et la revue Tangente. L'exposé était consacré à Kolmogorov et à son article avec Barzdin où apparaissent les graphes expanseurs; la vidéo est disponible ici.
Some functional limit theorems in number theory	These are the slides for the fourth Strasbourg-Zürich analysis and probability meeting, November 3, 2016.
A geometric interpretation of additive problems for primes	These are the slides for the day of algebraic and arithmetic geometry, May 20, 2016, in Berlin.
The shape of exponential sums	These are slides for the conference in honor of N. Katz's 71st birthday that was held in Beijing in May 2015.
Graphes expanseurs	These are slides for the "Exposé Scientifique" I gave at the École Polytechnique on April 9, 2015. There is also an English version.
The geometry and probability of exponential sums	These are slides for Geneva Colloquium talk I gave on November 6, 2014.
A study in sums of products	These are slides for the Chicheley Hall Royal Society meeting on Function Fields and Number Fields, organized by J. Keating, Z. Rudnick and T. Wooley in May 2014.
Some local limit theorems in probability and number theory	These are the slides of a talk at the conference in honor of F. Delbaen's 60th birthday, held at ETH Zürich in September 2012.
Some recent applications of expanders in number theory	These slides were written for the special session on Expander Graphs, organized by A. Lubotzky and A. Salehi-Golsefidy at the Joint Mathematical Meeting in January 2011.
Families of L-functions and cusp forms	These rather informal slides accompanied my talk to the conference in honor of R. Bruggeman's 65th Birthday, in June 2009.
Some aspects and applications of the Riemann Hypothesis over finite fields	These are the slides of my talk for the Verbania Conference on the Riemann Hypothesis in April 2009.
Les nombres premiers	In March 2009, I gave a short lecture on prime numbers for the participants of the Swiss Mathematical Olympiad. The corresponding slides are in French.
An introduction to Magma	In October 2008, I gave a talk explaining some use of Magma so computer the equation of an integral polynomial with splitting field having Galois group isomorphic to the Weyl group of the exceptional group E8. The slides explain this as well as some basic Magma syntax and use.
The large sieve and L-functions over finite fields	These slides are rather older, dating to the time I was in Bordeaux, and correspond to a talk given at a special session of the joint meeting of the French and Italian mathematical societies in Torino in July 2006.