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Brian Lawrence

Department of Mathematics

University of Chicago

I am currently an NSF postdoc at the University of Chicago. Previously I was at Columbia, and before that I was a graduate student at Stanford. My advisor was Akshay Venkatesh (now here).

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Seminars, Past and Present

Crystalline Cohomology (organized with Shizhang Li)

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Papers

A density result for real hyperelliptic curves (appeared in Comptes rendus). I have recently learned that Andrey Bogatyrev proved this result some years ago. See Theorem 5 and Lemma 1 of this paper (Effective computation of Chebyshev polynomials for several intervals, 1999, Sbornik: Mathematics, vol. 190, no. 11).

Diophantine problems and the p-adic Torelli map (draft, with Akshay Venkatesh)

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Teaching

Analysis in R^n, regular track: an introduction to metric spaces.
Handouts, quizzes, and exams from Winter 2019.

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Lecture Notes, etc.

Various expository notes I wrote during my time at Stanford.

Here are some notes from an introductory talk on schemes.

Here are some notes on polynomials on lattices.

Fibonacci Numbers mod p (Stanford SUMO talk, Apr. 10, 2014)

Introduction to Heights (Arithmetic Dynamics talk, Apr. 29, 2014)

In 2013-2014 I ran Stanford's Student Algebraic Geometry Seminar.