I am Prof. Alan Chang. Actually, I'm not a professor yet, but hopefully I will be some day! Currently, I am a Ph.D. student and lecturer in the math department. My advisor is Marianna Csörnyei. I started at the University of Chicago in fall 2014. Before coming to Chicago, I was an undergraduate at Princeton.

On this page, you'll find some things that I've been working on. Alternatively, you can just ask my (former) roommate about me. I am not so good at making web pages look nice. But Umang is very skilled!

- Analytic capacity and projections

with Xavier Tolsa. - Small unions of affine subspaces and skeletons via Baire category. To appear in Advances in Mathematics.

with Marianna Csörnyei, Kornélia Héra, Tamás Keleti. - The Kakeya needle problem and the existence of Besicovitch and Nikodym sets for rectifiable sets

with Marianna Csörnyei. - The Whitney extension theorem in high dimensions. Rev. Mat. Iberoam. 33 (2017), no. 2, 623–632.

This is from my senior thesis, which was advised by Charles Fefferman. - Newman's conjecture in function fields. J. Number Theory 157 (2015), 154–169.

with David Mehrle, Steven J. Miller, Tomer Reiter, Joseph Stahl, Dylan Yott. - Newman's conjecture in various settings. J. Number Theory 144 (2014), 70–91

with Julio Andrade and Steven J. Miller.

This is from the 2013 SMALL REU. (I also took some photos of my time there.)

- Constructions of planar Besicovitch sets - My topic proposal, a requirement of the 2nd year students in the Ph.D. program.
- Aleksandrov's theorem: closed surfaces with constant mean curvature - My final project for Amie Wilkinson's spring 2015 course on Riemannian geometry. My advisor for this project was Luis Silvestre.
- On the Jones Polynomial and its Applications - My junior paper for the spring 2013 semester. My advisor was Zoltan Szabo. This paper was the basis for the PUMaC 2013 power round (see below).
- An Introduction to the Hamilton-Jacobi Equation - My junior paper for the fall 2012 semester. My advisor was Peter Constantin. This paper discusses Hamiltonian mechanics, symplectic geometry, first-order nonlinear PDE theory, optimal control theory, and viscosity solutions.

These are notes for lectures/talks that I have given. For some reason, when I write these kinds of notes for myself, I like to scribble. This are written for myself, so sorry if they're not readable!

Riemann mapping theorem - As a TA for Elias Stein's Complex Analysis class in Fall 2013, I gave a lecture on the Riemann mapping theorem.

Gauss circle problem: part 1, part 2, and outline - I have given several talks on the 2/3 bound on the Gauss circle problem: (1) In spring 2013, in Elias Stein's Topics in Harmonic Analysis junior seminar. (2) In April 2014, for the Princeton math department's graduate student seminar. (3) In January 2015, for the UChicago math department pizza seminar.

Combinatorial Game Theory - I was a counselor at PROMYS during the summer of 2011. These are notes written to accompany a one-hour talk I gave to high school students. Learn how to win any impartial combinatorial game! (Unfortunately, go is not impartial. Speaking of go, let's play! I have an account on KGS and IGS.)

Fall 2015, graduate analysis midterm - As Joey notes, "math can be really hard."

Book-stacking on PBS Infinite Series - Apparently I'm a winner for "who can build the coolest bridge"! Thanks to Nir for sending my picture in to PBS Infinite Series!

Manjul Bhargava: The Musical, Magical Number Theorist - In the spring of 2014, I agreed to be in a video, but I did not realize what it was for until I heard from two of my friends several months later.

- Ilkyoo Choi: "Guess who was in the introduction video of this year's Fields medalist, Professor Bhargava? You. A good 5 seconds. Twice."
- Bumsoo Kim: "Thought you might not know that the video was played on two really large screens and thousands of mathematicians were watching!"

Fall 2016, Studies in Mathematics - I taught an undergraduate number theory class for non-science majors.

2015-2016, Honors Analysis - I was the teaching assistant for the honors version of the year-long introductory analysis course. The Physical Sciences Division awarded me a teaching prize for my work as a TA. (Thanks to the students for nominating me!!)

(undergrad and earlier)

NLP reading group - Together with Christiane Fellbaum and Feng Zhu, I started a natural language processing reading group at Princeton in Spring 2014. Each week, Prof. Fellbaum and 5-8 undergraduates would meet for a few hours to discuss recent NLP and machine learning papers. One such paper examined the effectiveness of various ways of requesting pizza!

Princeton Math Club - I was the president of the math club in 2013. We have a lot of events to make sure that undergraduate math majors (and math enthusiasts) have a great time at Princeton: colloquia, social nights, meet-your-professor lunches, etc.

Mercer County Math Circle - I co-founded this math circle in fall 2013. The math circle meets biweekly at the Princeton Public Library, next to campus. It aims to bring the university and the community together through mathematics. We try to provide fun mathematical activities for students at various levels.

Princeton Cube Club - I was the president of the Princeton Rubik's Cube Club for two years. I organized the two cube competitions, Princeton Spring 2013 and Princeton Winter 2014. The club also organizes "Learn-to-cube nights," both on and off campus.

Princeton Splash - In 2012, I founded Princeton Splash, which runs a day-long event where high school students come onto campus to take a number of classes created and taught by Princeton students. Our goal is to support local high schools with non-traditional forms of education and foster a love of learning in the community. In our first Splash (2013), we attracted over 180 high school students and 80 student volunteers. The courses covered a wide array of interests including "Conceptual Quantum Mechanics," "Improv Comedy with Quipfire!", and "The Chemistry of Chocolate."

PUMaC - The Princeton University Math Competition is an annual high school math competition run by Princeton students. I was the head writer for the 2013 Power Round (problems and solutions) and the 2012 Team Round (problems and solutions). I also ran the Rubik's Cube mini-events in the afternoon.

NACLO - I participated in the North American Computational Linguistics Olympiad in 2010 (my senior year of high school). I received a bronze medal at the International Linguistics Olympiad in Sweden. Now, I submit problems for NACLO! One of my problems, "Warlpiri Kinship Groups," appeared in the second round of the 2013 NACLO.

Learn2cube.com - Learn how to solve the Rubik's cube with my website. I made it back in 7th grade (2004), and have been updating it since then.

Me playing piano! - Yikes, this is old! (But this is even older!)

Alan's Australian Adventure - I studied in Australia for a semester!

Send me an email! ac at math dot uchicago