Talks and Presentations
This page is a descendant of my preprints and publications page, specifically for notes from talks and other presentations. 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.
The Beamer presentations are mostly posted in "display" mode, in which overlays show up as separate pages. For a few recent ones I have added "handout" mode, in which overlays do not show up separately. (Think before you print!) For older ones, I will add handout versions by request.
Talks
Formats  Title and Venue 

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 SatoTate groups of abelian threefolds, Around Frobenius distributions and related topics, virtual conference, May 2020. 
pdf, handout  Effective methods for the multiplicative ManinMumford problem, UCSD RTG colloquium, May 2020. 
pdf, handout  The SatoTate 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 
SatoTate groups of abelian threefolds,
Arithmetic, Geometry, Cryptography and Coding Theory, CIRM, June 2019. A variant of these slides was used also at Mons. 
Companions in étale cohomology,
Colloquium, MIT,
February 2019. Variants of these slides were used also at Rutgers, Yale, CUNY, Penn, and Cornell. 

Computation of zeta and $L$functions: feasibility and applications, Simons Collaboration annual meeting, New York, January 2019.  
Hypergeometric Lfunctions via Frobenius structures, MIT, August 2018.  
Modp dihedral Galois representations of prime conductor, Algorithmic Number Theory Symposium (ANTSXIII), Madison, July 2018.  
Frobenius structures on hypergeometric equations, CIRM (Luminy), May 2018.  
Zeta functions of varieties: tools and applications, ICERM, May 2018.  
Tropical geometry of cluster varieties: a question from number theory, Institut MittagLeffler (Stockholm), April 2018.  
Jupyter  Frobenius structures on hypergeometric equations: computational methods, Hausdorff Center for Mathematics (Bonn), 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. 
Number theory in (and not (yet) in) Sage, IMA (Minneapolis), August 2017.  
Computing zeta functions of nondegenerate toric hypersurfaces, CIRM (Luminy), June 2017.  
Automata and (generalized) power series: beyond Christol, Bridges betweeen automatic sequences, algebra and number theory, CRM (Montréal), May 2017.  
Bhargava's work on padic analytic functions, Fields Medal Symposium, Toronto, November 2016.  
Mod 2 linear algebra and tabulation of rational eigenforms, Automorphic forms: theory and computation, London, September 2016.  
A census of zeta functions of quartic K3 surfaces over F_2, ANTSXII: Twelfth Algorithmic Number Theory Symposium, Kaiserslautern, August 2016.  
Auxiliary structures in number theory, Symposium for Undergraduates in the Mathematical Sciences, Brown, March 2016.  
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. 
SatoTate groups of higher weight motives, Explicit Methods for Modularity of K3 Surfaces and Other Higher Weight Motives, ICERM, Providence, October 2015.  
A brief (pre)history of perfectoid spaces, colloquium, Brown, October 2015.  
Recent progress in computing zeta functions of varieties, Number theory and physics, IMPA, Rio de Janeiro, June 2015.  
A survey of 15 years of padic pointcounting, padic methods in number theory (Coleman memorial conference), Berkeley, May 2015.  
A brief history of perfectoid spaces, AMS western sectional meeting, San Francisco, October 2014.  
SatoTate groups of genus 2 curves,
NATO Advanced Study Institute "Arithmetic of hyperelliptic curves",
Ohrid, Republic of Macedonia, AugustSeptember 2014.
See also my extended lecture notes. 

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.  
Almost purity and overconvergent Witt vectors, special session on Arithmetic and Differential Algebraic Geometry, AMS Western Sectional Meeting, Albuquerque, April 2014.  
SatoTate groups of abelian surfaces, Curves and Automorphic Forms, Arizona State, March 2014.  
Relative padic Hodge theory, Hot Topics: Perfectoid Spaces and their Applications, MSRI, February 2014.  
Computing zeta functions of nondegenerate toric hypersurfaces via controlled reduction, Sage Days: Computational Number Theory, Geometry, and Physics, Oxford, September 2013.  
SatoTate 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. 
SatoTate groups of motives, AMS special session on arithmetic statistics and big monodromy, Boulder, April 2013.  
Towards global (phi, Gamma)modules and comparison isomorphisms, AMS special session on Witt vectors, lifting, and descent, San Diego, January 2013.  
The Robbins phenomenon: cluster algebras and padic arithmetic, MSRI, Berkeley, November 2012.  
The Robbins phenomenon: padic stability of some nonlinear recurrences, Microsoft Research Summer Number Theory Day, Redmond, July 2012.  
SatoTate groups of abelian varieties, BarcelonaBostonTokyo number theory seminar, Barcelona, May 2012.  
Wittperfect rings and almost purity, Witt vectors in arithmetic, geometry, and topology, Albuquerque, May 2012.  
Convergence of solutions of padic differential equations, Hawaii conference in algebraic number theory, arithmetic geometry and modular forms, Honolulu, March 2012.  
On surjectivity of the Witt vector Frobenius, AMS western sectional meeting, Honolulu, March 2012.  
The SatoTate 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.)  
Controlled reduction in the padic cohomology of toric hypersurfaces, Number theory, algebraic geometry, and model theory, CIRM, Luminy, September 2011.  
Towards a precise SatoTate conjecture in genus 2, Explicit methods in number theory, Oberwolfach, July 2011.  
Toric coordinates in relative padic Hodge theory, Toric geometry and applications, Leuven, June 2011.  
Towards uniformity in p in padic Hodge theory, Théorie de Hodge padique, équations différentielles padiques et leurs applications, Lyon, June 2011.  
The padic arithmetic curve: algebraic and analytic aspects, Noncommutative geometry and arithmetic, Johns Hopkins, March 2011.  
Effective convergence bounds for Frobenius structures on connections, From padic differential equations to arithmetic algebraic geometry, Padova, February 2011.  
Absolute de Rham cohomology? A fantasy in the key of p, Witt vectors, foliations, and absolute de Rham cohomology, Nagoya, November 2010.  
Irregularity of flat meromorphic connections, Western Algebraic Geometry Symposium, Tucson, November 2010.  
Relative padic Hodge theory and RapoportZink period domains, International Congress of Mathematicians, Hyderabad, August 2010.  
Relative (phi, Gamma)modules, Galois representations in arithmetic and geometry (ICM 2010 satellite conference in number theory), International Centre, Goa, August 2010.  
Numerical padic integration and (potential) applications to rational points, Rational points: theory and experiment, ETH, Zürich, May 2010.  
Relative padic Hodge theory and RapoportZink period domains, Conférence JeanMarc Fontaine, Paris, March 2010.  
Getting precise about precision, Effective methods in padic cohomology, Oxford, March 2010.  
Slope filtrations and (phi, Gamma)modules in families, Galois Trimester, Paris, January 2010.  
Rigid cohomology and its coefficients, padic geometry and homotopy theory, Loen, August 2009.  
Semistable reduction for overconvergent Fisocrystals: 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. 

Computing Lseries of hyperelliptic curves and distributions of Frobenius eigenvalues, Park City Mathematics Institue, July 2009.  
Computing zeta functions of hyperelliptic curves, Leiden, April 2009.  
Semistable reduction for overconvergent Fisocrystals,
Recent progress in arithmetic Dmodules,
Strasbourg, October 2008.
I recommend looking at my Rennes notes instead; see above. 

Productfree 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. 

The differential Swan conductor, padic methods in arithmetic geometry and its applications, University of Tokyo, June 2007.  
A differential approach to computing zeta functions over finite fields, Joint AMSSMM Meeting, Zacatecas, May 2007.  
pdf, SAGE notebook 
Numerical computation of Coleman integrals,
padic Methods and Rational Points,
Rényi Institute, Budapest, May 2007.
The SAGE notebook was used as a demonstration during the talk. 
Recent progress on padic 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. 

Recent progress on padic computation of zeta functions, Number Theory and Cryptography: Open Problems, IPAM (UCLA), October 2006.  
Convergence of solutions of differential equations and higherdimensional ramification theory, Hodge Theory, Venice,
June 2006.
Some of the results promised in this talk will appear in "Semistable reduction IV"; see above. 

Computing zeta functions of surfaces using
padic cohomology, AMS Western Section
Meeting, San Francisco, CA, April 2006. For the paper corresponding to this talk, see "Bounding Picard numbers..." above. 

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. 

Primality testing made simple, notes for the MIT IAP 2006
Mathematics Lecture Series (27 Jan 2006). This is a presentation on the AgrawalKayalSaxena deterministic polynomial time primality test. 

Computing zeta functions on surfaces, AGCT10 (Arithmetic,
Geometry, and Coding Theory), CIRMLuminy, September 2005.
Caution: the code seems to have not been bugfree 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 padic cohomology" on my papers page. 

The Fourier transform on the affine line and the Weil Conjectures, AMS session on Dmodules, Atlanta, January 2005 (posted 9 Jan 2005).  
ppt  Problems talk, Math Circles and Olympiads workshop, MSRI, December 2004 (version of 18 Dec 2004). 
Solving padic differential equations on some twodimensional spaces, CNTA8, Toronto, June 2004 (version of 15 June 2004).  
Computing zeta functions using padic cohomology, ANTS VI, Vermont (Burlington), June 2004 (version of 16 Jun 2004).  
Relative Robba rings and pushforwards in rigid cohomology, Arithmetic Geometry, Tokyo, February 2004 (version of 17 Feb 2004).  
padic Lafforgue: a road map, Arithmetical Algebraic Geometry special session, AMSMAA Joint Meetings, Phoenix, January 2004 (version of 5 Jan 2004).  
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 1721, 2003 (version of 20 Aug 2003).  
Crystals, Crew's conjecture, and cohomology, notes from a series of three lectures at the University of Arizona given May 89, 2003 (version of 12 May 2003).  
padic 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.  
Interval arithmetic for function fields over finite fields, slides from a lecture at the Computational Algebraic and Analytic Geometry for Lowdimensional Varieties session, AMS meeting (Baltimore), January 2003 (version of 23 Dec 2002).  
tex, dvi, ps.gz  padic 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 MonskyWashnitzer cohomology, slides from a lecture at the Midwest Arithmetical Geometry in Cryptography conference, November 2001. 
Key to format types
 tex: TeX file (plain text)
 dvi: DVI file (view with xdvi)
 pdf: PDF file (view with Acrobat Reader, ggv, etc.)
 ps.gz: compressed Postscript file (uncompress with gunzip, then view with GhostScript; note that your browser may uncompress automatically)
 ppt: PowerPoint presentation (view with OpenOffice Impress)