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Talks and Presentations

This page is a descendant of my preprints and publications page, specifically for notes from talks and other presentations (and video links when available). Many of these were produced using Beamer; some of the older ones were produced using Prosper. For more on formats, see the key to format types. In most cases, I have corrected typos that I found during the presentation (but there may be more lurking).

Talks are in one list, sorted in reverse chronological order.

I also keep a list of talks I have given, with or without notes.

Older Beamer presentations are posted in "display" mode, in which overlays show up as separate pages. Newer ones are also posted in "handout" mode, in which overlays do not show up separately. (Think before you print!) I am happy to generate handout versions of older presentations upon request.

Talks

Formats Title and Venue
pdf, handout Problemas de números de clase relativos para cuerpos de funciones (Relative class number problems for function fields), Number Theory in the Americas 2, BIRS-CMO, Oaxaca, September 2024.
pdf, handout Zeta functions of algebraic varieties over finite fields, Quantum computer science seminar, Google, virtual, August 2024.
pdf, handout Computing hypergeometric L-functions in average polynomial time, Number theory and physics, ICTP, Trieste, June 2024.
pdf, handout Census-taking for curves over finite fields, CAVARET (Curves, Abelian VArieties, and RElated Topics), Barcelona, June 2024.
pdf, handout Roots of unity in geometry (and elsewhere), Math Olympiad Program, Carnegie Mellon, June 2024.
pdf, handout Tetrahedra with rational dihedral angles, Number Theory and Combinatorics in Duluth: A conference to honor Joe Gallian and 45 years of the Duluth REU, Duluth, July-August 2023.
pdf, handout The relative class number one problem for function fields, III, LMFDB, Computation, and Number Theory (LuCaNT), ICERM, Providence, July 2023.
pdf, handout The relative class number one problem for function fields, II, Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, Luminy, June 2023.
pdf, handout Frobenius structures on hypergeometric equations, An Expedition into Arithmetic Geometry, Lorentz Center, Leiden, May 2023.
pdf, handout, annotated Uniformities for F-isocrystals on curves, Dwork seminar (online), April 2023.
pdf, handout Zeta functions of algebraic varieties: theory and algorithms, Number theory meeting on Ramanujan's 135th birth year, IIT Kanpur, February-March 2023.
pdf, handout The relative class number one problem for function fields, Number theory seminar, MIT, September 2022.
I gave a similar seminar in Barcelona also.
pdf, handout, video The relative class number one problem for function fields, I, Algorithmic Number Theory Symposium (ANTS-XV), Bristol, August 2022.
pdf, handout Weil polynomials for fun and profit, Park City Mathematics Institute, Park City, July 2022.
pdf, handout Quantum complexity and L-functions, Quantum Algorithms in Number Theory, Fields Institute (virtual), April 2022.
pdf Angle ranks of abelian varieties, Stanford algebraic geometry seminar, April 2022.
pdf, handout Orders of abelian varieties over F_2, Number Theory Web Seminar, December 2021.
A previous version of these slides was presented in the UC San Diego number theory seminar. This version has a running joke in the slide titles.
pdf, handout The tame Belyi theorem in positive characteristic, Stockholm algebra/geometry seminar (virtual), September 2021.
pdf, handout Abelian varieties over F_2 of prescribed order, Explicit Methods in Number Theory (hybrid), Oberwolfach, July 2021.
pdf, handout Drinfeld's lemma for F-isocrystals, Mathematical Congress of the Americas (virtual), special session on Galois representations and automorphic forms, July 2021.
pdf, handout Sato-Tate groups of abelian threefolds: adventures in SU(3), Poznań-Szczecin arithmetic geometry seminar (virtual), July 2021.
pdf, handout, video Banach bundles, Columbia-CUNY-NYU number theory seminar (virtual), April 2021.
These are an updated version of my slides from Berkeley a few days earlier.
pdf, handout, video Ángulos racionales entre vectores en el espacio, Seminario Latinoamericano de Teoría de Números (virtual), March 2021.
These slides are a direct Spanish translation of my Claremont slides from September 2020 (see below).
pdf, handout Drinfeld's lemma for F-isocrystals, Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems, Imperial College, London (virtual conference), December 2020.
pdf, annotated, video Several forms of Drinfeld's lemma, RAMpAGe virtual seminar, November 2020.
pdf, handout Étale and crystalline companions, Algebraic and arithmetic geometry seminar (virtual), Pisa, September 2020.
pdf, handout Space vectors forming rational angles, Claremont colloquium (virtual), September 2020.
pdf, handout Beyond Pick's theorem: Ehrhart polynomials and mixed volumes, PROMYS (virtual), July 2020.
pdf, handout
live: pdf, handout 		Hypergeometric L-functions in average polynomial time, Algorithmic Number Theory Symposium (virtual), July 2020.
pdf, handout An overview of the p-adic local Langlands correspondence, Online Conference in Automorphic Forms, June 2020.
pdf, handout Torsion closures of ideals, Global Virtual Sage Days 109, May 2020.
pdf, handout Towards explicit realizations of the Sato-Tate groups of abelian threefolds, Around Frobenius distributions and related topics (virtual), May 2020.
pdf, handout Effective methods for the multiplicative Manin-Mumford problem, UCSD RTG colloquium (virtual), May 2020.
pdf, handout The Sato-Tate conjecture and its generalizations, VaNTAGe virtual seminar, March 2020.
pdf, handout Computing Coleman integrals on modular curves, AMS Special Session on Rational Points on Algebraic Varieties: Theory and Computation, Joint Mathematics Meetings, Denver, January 2020.
pdf, handout Sato-Tate groups of abelian threefolds, Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, June 2019.
A variant of these slides was used also at Mons.
pdf Companions in étale cohomology, Colloquium, MIT, February 2019.
Variants of these slides were used also at Rutgers, Yale, CUNY, Penn, and Cornell.
pdf Computation of zeta and $L$-functions: feasibility and applications, Simons Collaboration annual meeting, New York, January 2019.
pdf Hypergeometric L-functions via Frobenius structures, MIT, August 2018.
pdf Mod-p dihedral Galois representations of prime conductor, Algorithmic Number Theory Symposium (ANTS-XIII), Madison, July 2018.
pdf Frobenius structures on hypergeometric equations, CIRM (Luminy), May 2018.
pdf Zeta functions of varieties: tools and applications, ICERM, May 2018.
pdf Tropical geometry of cluster varieties: a question from number theory, Institut Mittag-Leffler (Stockholm), April 2018.
Jupyter Frobenius structures on hypergeometric equations: computational methods, Hausdorff Center for Mathematics (Bonn), March 2018.
video The Riemann extension theorem, Hot Topics: The homological conjectures, MSRI, March 2018.
pdf, Jupyter $L$-functions and deformations: from hyperelliptic curves to hypergeometric motives, ICTP (Trieste), September 2017.
The Jupyter notebook was run as a demonstration during the lecture, using a customized version of Sage.
pdf Number theory in (or not (yet) in) Sage, IMA (Minneapolis), August 2017.
pdf Computing zeta functions of nondegenerate toric hypersurfaces, CIRM (Luminy), June 2017.
pdf Automata and (generalized) power series: beyond Christol, Bridges betweeen automatic sequences, algebra and number theory, CRM (Montréal), May 2017.
video p-adic periods via perfectoid spaces, Hot Topics: Galois theory of periods and applications, MSRI, March 2017.
pdf Bhargava's work on p-adic analytic functions, Fields Medal Symposium, Toronto, November 2016.
pdf Mod 2 linear algebra and tabulation of rational eigenforms, Automorphic forms: theory and computation, London, September 2016.
pdf A census of zeta functions of quartic K3 surfaces over F_2, ANTS-XII: Twelfth Algorithmic Number Theory Symposium, Kaiserslautern, August 2016.
pdf Auxiliary structures in number theory, Symposium for Undergraduates in the Mathematical Sciences, Brown, March 2016.
pdf Equidistribution of Frobenius eigenvalues, colloquium, University of Maryland, February 2016.
I used similar slides for talks at Michigan, Connecticut, Purdue, and Rice.
pdf, jpg The étale theta function of S. Mochizuki, The IUT theory of Shinichi Mochizuki, Clay Math Institute, Oxford, December 2015.
The JPG file is a photo (taken by me) of a diagram (drawn by Ivan Fesenko) of the tower of covers used in the talk.
pdf Sato-Tate groups of higher weight motives, Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives, ICERM, Providence, October 2015.
pdf A brief (pre)history of perfectoid spaces, colloquium, Brown, October 2015.
pdf Recent progress in computing zeta functions of varieties, Number theory and physics, IMPA, Rio de Janeiro, June 2015.
pdf A survey of 15 years of p-adic point-counting, p-adic methods in number theory (Coleman memorial conference), Berkeley, May 2015.
pdf A brief history of perfectoid spaces, AMS western sectional meeting, San Francisco, October 2014.
pdf Sato-Tate groups of genus 2 curves, NATO Advanced Study Institute "Arithmetic of hyperelliptic curves", Ohrid, Republic of Macedonia, August-September 2014.
See also my extended lecture notes.
pdf How many points on a random curve over a finite field?, Number fields and function fields: coalescences, contrasts and emerging applications, The Royal Society at Chicheley Hall, May 2014.
pdf Almost purity and overconvergent Witt vectors, special session on Arithmetic and Differential Algebraic Geometry, AMS Western Sectional Meeting, Albuquerque, April 2014.
pdf Sato-Tate groups of abelian surfaces, Curves and Automorphic Forms, Arizona State, March 2014.
pdf, video Relative p-adic Hodge theory, Hot Topics: Perfectoid Spaces and their Applications, MSRI, February 2014.
pdf Computing zeta functions of nondegenerate toric hypersurfaces via controlled reduction, Sage Days: Computational Number Theory, Geometry, and Physics, Oxford, September 2013.
pdf Sato-Tate groups of abelian surfaces and threefolds, SIAM meeting on applied algebraic geometry, session on arithmetic geometry, Fort Collins, August 2013.
pdf (part 1), pdf (part 2) Christol's theorem and its analogue for generalized power series (two lectures), Challenges in Combinatorics on Words, Fields Institute, Toronto, April 2013.
pdf Sato-Tate groups of motives, AMS special session on arithmetic statistics and big monodromy, Boulder, April 2013.
pdf Towards global (phi, Gamma)-modules and comparison isomorphisms, AMS special session on Witt vectors, lifting, and descent, San Diego, January 2013.
pdf The Robbins phenomenon: cluster algebras and p-adic arithmetic, MSRI, Berkeley, November 2012.
pdf The Robbins phenomenon: p-adic stability of some nonlinear recurrences, Microsoft Research Summer Number Theory Day, Redmond, July 2012.
pdf Sato-Tate groups of abelian varieties, Barcelona-Boston-Tokyo number theory seminar, Barcelona, May 2012.
pdf Witt-perfect rings and almost purity, Witt vectors in arithmetic, geometry, and topology, Albuquerque, May 2012.
pdf Convergence of solutions of p-adic differential equations, Hawaii conference in algebraic number theory, arithmetic geometry and modular forms, Honolulu, March 2012.
pdf On surjectivity of the Witt vector Frobenius, AMS western sectional meeting, Honolulu, March 2012.
pdf The Sato-Tate conjecture for elliptic and hyperelliptic curves, New Zealand Mathematical Society colloquium, December 2011. (I used similar slides for talks at CSU Dominguez Hills, UCLA, and National University of Singapore.)
pdf Controlled reduction in the p-adic cohomology of toric hypersurfaces, Number theory, algebraic geometry, and model theory, CIRM, Luminy, September 2011.
pdf Towards a precise Sato-Tate conjecture in genus 2, Explicit methods in number theory, Oberwolfach, July 2011.
pdf Toric coordinates in relative p-adic Hodge theory, Toric geometry and applications, Leuven, June 2011.
pdf Towards uniformity in p in p-adic Hodge theory, Théorie de Hodge p-adique, équations différentielles p-adiques et leurs applications, Lyon, June 2011.
video Computing zeta functions of curves with automorphisms, MSRI, April 2011.
pdf The p-adic arithmetic curve: algebraic and analytic aspects, Noncommutative geometry and arithmetic, Johns Hopkins, March 2011.
pdf Effective convergence bounds for Frobenius structures on connections, From p-adic differential equations to arithmetic algebraic geometry, Padova, February 2011.
pdf Absolute de Rham cohomology? A fantasy in the key of p, Witt vectors, foliations, and absolute de Rham cohomology, Nagoya, November 2010.
pdf Irregularity of flat meromorphic connections, Western Algebraic Geometry Symposium, Tucson, November 2010.
pdf Relative p-adic Hodge theory and Rapoport-Zink period domains, International Congress of Mathematicians, Hyderabad, August 2010.
pdf Relative (phi, Gamma)-modules, Galois representations in arithmetic and geometry (ICM 2010 satellite conference in number theory), International Centre, Goa, August 2010.
pdf Numerical p-adic integration and (potential) applications to rational points, Rational points: theory and experiment, ETH, Zürich, May 2010.
pdf Relative p-adic Hodge theory and Rapoport-Zink period domains, Conférence Jean-Marc Fontaine, Paris, March 2010.
pdf Getting precise about precision, Effective methods in p-adic cohomology, Oxford, March 2010.
pdf Slope filtrations and (phi, Gamma)-modules in families, Galois Trimester, Paris, January 2010.
pdf Rigid cohomology and its coefficients, p-adic geometry and homotopy theory, Loen, August 2009.
pdf Semistable reduction for overconvergent F-isocrystals: geometric aspects of the proof, Journées de Géométrie Arithmétique de Rennes, July 2009.
These slides can be used as a summary of my four papers on this topic; they are a modified version of my Strasbourg slides. For more information, see my project page.
pdf Computing L-series of hyperelliptic curves and distributions of Frobenius eigenvalues, Park City Mathematics Institue, July 2009.
pdf Computing zeta functions of hyperelliptic curves, Leiden, April 2009.
pdf Semistable reduction for overconvergent F-isocrystals, Recent progress in arithmetic D-modules, Strasbourg, October 2008.
I recommend looking at my Rennes notes instead; see above.
pdf Product-free subsets of groups, then and now, Communicating mathematics, University of Minnesota, Duluth, July 2007.
This presentation was made in honor of Joe Gallian's 65th birthday, and the 30th anniversary of the REU (Research Experience for Undergraduates) program he runs every summer. Joe has a famous predilection for all things Beatles; the slide titles are a running joke based on this.
pdf The differential Swan conductor, p-adic methods in arithmetic geometry and its applications, University of Tokyo, June 2007.
pdf A differential approach to computing zeta functions over finite fields, Joint AMS-SMM Meeting, Zacatecas, May 2007.
pdf, SAGE notebook Numerical computation of Coleman integrals, p-adic Methods and Rational Points, Rényi Institute, Budapest, May 2007.
The SAGE notebook was used as a demonstration during the talk.
pdf Recent progress on p-adic computation of zeta functions, Computational Challenges Arising in Algorithmic Number Theory and Cryptography, Fields Institute (Toronto), October 2006.
This is similar but not identical to the following talk.
pdf Recent progress on p-adic computation of zeta functions, Number Theory and Cryptography: Open Problems, IPAM (UCLA), October 2006.
pdf Convergence of solutions of differential equations and higher-dimensional ramification theory, Hodge Theory, Venice, June 2006.
Some of the results promised in this talk will appear in "Semistable reduction IV"; see above.
pdf Computing zeta functions of surfaces using p-adic cohomology, AMS Western Section Meeting, San Francisco, CA, April 2006.
For the paper corresponding to this talk, see "Bounding Picard numbers..." above.
pdf Slope filtrations for relative Frobenius, AMS Eastern Section Meeting, Durham, NH, April 2006.
For the paper corresponding to this talk, see "Slope filtrations for relative Frobenius" or "Notes on slope filtrations" above.
pdf Primality testing made simple, notes for the MIT IAP 2006 Mathematics Lecture Series (27 Jan 2006).
This is a presentation on the Agrawal-Kayal-Saxena deterministic polynomial time primality test.
pdf Computing zeta functions on surfaces, AGCT-10 (Arithmetic, Geometry, and Coding Theory), CIRM-Luminy, September 2005.
Caution: the code seems to have not been bug-free when I prepared the examples in the talk, so the accuracy (especially of the timings) of those examples is dubious. For corrected examples and the Magma code, see the paper "Bounding Picard numbers of surfaces using p-adic cohomology" on my papers page.
pdf The Fourier transform on the affine line and the Weil Conjectures, AMS session on D-modules, Atlanta, January 2005 (posted 9 Jan 2005).
ppt Problems talk, Math Circles and Olympiads workshop, MSRI, December 2004 (version of 18 Dec 2004).
pdf Solving p-adic differential equations on some two-dimensional spaces, CNTA8, Toronto, June 2004 (version of 15 June 2004).
pdf Computing zeta functions using p-adic cohomology, ANTS VI, Vermont (Burlington), June 2004 (version of 16 Jun 2004).
pdf Relative Robba rings and pushforwards in rigid cohomology, Arithmetic Geometry, Tokyo, February 2004 (version of 17 Feb 2004).
pdf p-adic Lafforgue: a road map, Arithmetical Algebraic Geometry special session, AMS-MAA Joint Meetings, Phoenix, January 2004 (version of 5 Jan 2004).
pdf Frobenius slope filtrations and Crew's conjecture, notes from the workshop "Current trends in arithmetic geometry and number theory" at the Banff International Research Station, August 17-21, 2003 (version of 20 Aug 2003).
pdf Crystals, Crew's conjecture, and cohomology, notes from a series of three lectures at the University of Arizona given May 8-9, 2003 (version of 12 May 2003).
pdf p-adic cohomology and zeta functions: the case of hyperelliptic curves, slides from a lecture at the conference "Computational Aspects of Algebraic Curves, and Cryptography" (Florida), March 2003.
pdf Interval arithmetic for function fields over finite fields, slides from a lecture at the Computational Algebraic and Analytic Geometry for Low-dimensional Varieties session, AMS meeting (Baltimore), January 2003 (version of 23 Dec 2002).
tex, dvi, ps.gz p-adic cohomology and the computation of zeta functions, slides from a lecture at the Elliptic Curve Cryptography conference (Essen), September 2002 (version of 12 Sep 2002).
tex, dvi, ps.gz Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, slides from a lecture at the Midwest Arithmetical Geometry in Cryptography conference, November 2001.

Key to format types