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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

UChicago Number Theory Seminar

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.

My student Spencer Dembner (a UChicago undergrad) has written some
notes
on the relationship between Galois groups and branched covers of Riemann surfaces.

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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.