I am Prof. Alan Chang. Actually, I'm not a professor yet, but hopefully I will be some day! I'm just a graduate student for now; I started in fall 2014. My advisor is Prof. Marianna Csörnyei.
On this page, you'll find some things that I've been working on. Alternatively, you can just ask my (former) roommate about me.
Other than math, my interests include, mathematics education, computer science education, computer science, Rubik's cubes, fun math, taking pictures, linguistics, linguistics puzzles, learning languages. Oops, sorry, I got carried away!
I am not so good at making web pages look nice. But Umang is very skilled!
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 - For my senior thesis (advised by Prof. Charles Fefferman), I studied the construction of the extension operator in Whitney's theorem and study the growth of the operator norm as the number of dimensions increases. In this paper, I show that the growth can be reduced from exponential to polynomial using an averaging technique.
Newman's conjecture in various settings - At the 2013 SMALL REU, advised by Prof. Steven J. Miller and Julio Andrade, I looked at Newman's conjecture for the Riemann zeta function and formulated a generalization to function fields. (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 Prof. Amie Wilkinson's spring 2015 course on Riemannian geometry. My advisor for this project was Prof. Luis Silvestre.
An Introduction to the Hamilton-Jacobi Equation - on Hamiltonian mechanics, symplectic geometry, first-order nonlinear PDE theory, optimal control theory, and viscosity solutions. My junior paper for the fall 2012 semester. My adviser was Prof. Peter Constantin.
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 - I was a TA for Prof. Stein's Complex Analysis class in Fall 2013. I asked him to let me teach one class and he kindly gave me the opportunity! My lecture was on the Riemann Mapping Theorem.
Gauss Circle Problem, Part 1 - I participated in Prof. Stein's Topics in Harmonic Analysis junior seminar. In the seminar, I gave two 45 minute presentations, presenting the proof of the 2/3 bound on the Gauss Circle Problem. This is the first part.
Gauss Circle Problem, Part 2 - This is the second part.
Gauss Circle Problem, outline - I gave another talk on the Gauss Circle Problem at Princeton's graduate student seminar in April 2014. I used this outline to help organize and summarize the talk. Then I gave the talk again at UChicago's graduate student seminar in January 2015.
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.)
NLP reading group - Together with Prof. 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. 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-Prof. 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. In addition to running cubing competitions, the club also organizes "Learn-to-cube nights," both on and off campus.
Princeton Splash - I am the founder of 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 - I was the head writer for the 2013 Power Round and the 2012 Team Round for PUMaC (Princeton University Math Competition). The problems and solutions can be found on the PUMaC website. (Here are direct links to the 2013 power problems, 2013 power solutions, 2012 team problems, 2012 team 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.
Alan's Australian Adventure - I studied in Australia for a semester!
Send me an email! ac at math dot uchicago