325 Van Vleck Hall
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53706
I've been at Wisconsin since the fall of 2005. My field is arithmetic algebraic geometry: my specific interests include rational points on varieties, asymptotic enumeration of number fields and other arithmetic objects, incidence problems and algebraic methods in combinatorial geometry, Galois representations attached to varieties and their fundamental groups, representation stability and FI-modules, the geometry of large data sets, non-abelian Iwasawa theory, pro-p group theory, automorphic forms, stable cohomology of moduli spaces, the complex of curves, Hilbert-Blumenthal abelian varieties, Q-curves, Serre's conjecture, the ABC conjecture, and Diophantine problems related to all of the above. My research here is partially supported by an NSF grant, a Kellett Mid-Career Award, and the Office of the Vice Chancellor for Research and Graduate Education, with funding by the Wisconsin Alumni Research Foundation. I co-organize the Wisconsin number theory seminar. I am also a Discovery Fellow at the Wisconsin Institute for Discovery, where I am part of the Machine Learning group and the Institute for Foundations of Data Science. I am a member of the Science Board of IPAM.
I wrote a book called How Not To Be Wrong, published in 2014 by Penguin Press, and another called Shape that came out in 2021. See my author page for excerpts, reviews, event dates, and other author-related material.
In Fall 2022 I am teaching Math 521, the first semester of undergraduate real analysis.
NEW NEWS: I am an organizer of an upcoming IPAM workshop on machine-assisted proof in February 2023. We are hosting a workshop on Arithmetic and Topology over Global Fields in Madison on Oct 7-9 2022.
My students Soumya Sankar and Brandon Boggess organized a (virtual) conference on moduli spaces in Madison in Fall 2020.
Madison will host an AMS Sectional Meeting on September 14-15, 2019.
I am a co-organizer of Journees Arithmetiques, to be held in Istanbul in July 2019 (but unfortunately won't be able to be physically present there.)
Wilmar Bolaños, Ph.D. 2019 from Universidad de los Andes, is my first mathematical grandchild!
In April 2018 my student Wanlin Li organized a conference on the arithmetic of algebraic curves.
In October 12-15 2017 I organized a workshop on the geometry of redistricting, a satellite of the redistricting summer school at Tufts.
In May 2017 I organized a conference on Braids in Algebra, Geometry, and Topology at ICMS in Edinburgh (but unfortunately wasn't able to be present there.)
I appear for about ten seconds in the movie Gifted, released April 2017, playing "Professor." My Erdős-Bacon number is now 5.
In December 2016 I organized a very informal workshop on the polynomial method at Hebrew University.
I spoke at the first National Mathematics Festival in April 2015.
I gave an AMS-MAA Invited Address at the 2015 Joint Meetings in San Antonio about combinatorial designs and lottery schemes.
I was an organizer of the conference "Counting arithmetic objects," which will pay special attention to theorems and heuristics for ranks of elliptic curves, at CRM in Montreal, November 2014.
I was one of the speakers at the 2014 Arizona Winter School on arithmetic statistics in March 2014: the topic of my lectures was "Geometric Analytic Number Theory."
I was an organizer of the long program at IPAM on Algebraic Techniques for Combinatorial and Computational Geometry, in March-June 2014.
Alina Bucur, Chantal David and I organized a workshop at AIM on Arithmetic Statistics over Finite Fields and Function Fields in January 2014.
Nigel Boston and I organized a one-day miniconference here at UW-Madison: Group Theory, Number Theory, and Topology Day, on January 24, 2013. Nathan Dunfield, Alan Reid, and Tamar Ziegler spoke on topics at the interface of the three subjects.
Akshay Venkatesh and I organized a special session with the incredibly specific title of "Geometry and Number Theory" at the 2013 Joint Meetings in San Diego.
In February 2012, I was an organizer of an MSRI Hot Topics workshop on Thin Groups and Super-strong approximation. (Streaming video of talks available behind the link.)
On April 24-25, 2010, Jean-Luc Thiffeault and I organized a weekend workshop on pseudo-Anosovs with small dilatation, a subject that occupies a very interesting interface between topology, dynamics, and arithmetic.
I wrote a general-audience book about math, How Not To Be Wrong, which came out in the summer of 2014 from Penguin Press, and another one, Shape, in 2021. A long time ago I wrote a novel called The Grasshopper King, published by Coffee House Press in 2003. I also write the "Do The Math" column in Slate, and have written articles on mathematical topics for The New York Times, The Washington Post, The Wall Street Journal, The Boston Globe, Wired, and The Believer.
I used to live in Princeton, NJ; a popular feature of my old web page was How to Eat Dinner in Princeton. Warning: this page is accurate only up to August 2005.
My current graduate students, roughly in order of how soon you can hire them: Asvin G, Yu Fu, Di Chen, Sun Woo Park, Hyun Jong Kim, and Will Hardt, If you are considering joining this learned crew, you should read this page.
My former graduate students:
Teaching (thoughts from a long time ago)
Barry Mazur's Mathematical Genealogy (no longer updated in light of the Mathematics Genealogy Project)
Back to math department home page
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