Alexander Ortiz

Hi! I am a 5th year PhD student at MIT, advised by Larry Guth. Before that, I was an undergraduate at Northwestern University. I'm interested in the Fourier restriction phenomenon and connections with projection theory. I'm planning to graduate in May 2024.

Office: 2-333C

Email: aeortiz at mit dot edu

Papers

  1. A sharp Mizohata--Takeuchi type estimate for the cone in R^3 (2023). Submitted. [arXiv] [pdf]
  2. (with Heidi Morris) Description of the code ANVIL (ANisotropic Vhf Impulse Location) (2018). Published in Radio Science. [ieee]

Talks and travel

Upcoming travel:
  • JMM Special Session on Harmonic Analysis, Geometric Measure Theory, and Fractals on Jan. 3, 2024.
Past talks and presentations, including some links to slides.
  • [Slides] for my talk at IU Bloomington's analysis seminar on Sept. 20, 2023.
  • [Slides] for "A Study Guide for 'Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem,' by Orponen--Shmerkin--Wang" @UPenn Study Guide Writing Workshop 2023

Teaching

At MIT:
  • Fall 2023: TA for 18.100Q (Real Analysis, taught by Changkeun Oh)
  • Spring 2023: TA for 18.075 (Advanced Calculus for Engineers, taught by Hung Cheng)
  • Spring 2023: TA for 18.156 (Differential Analysis II, taught by David Jerison)
  • Fall 2022: recitation leader for 18.100Q (Real Analysis, taught by Dominique Maldague)
  • In Summer 2020, I was the instructor for the multivariable calculus course of MIT's Interphase EDGE program.
At Northwestern:
  • I was a teaching assistant for the single and multivariable calculus courses from 2016 until 2019.
  • I was both a participant, and later a teaching assistant in Northwestern's college Bridge program.

Service and outreach

  • (Summer 2021) I was a research mentor for two advanced high school students at RSI.
  • (2020--2021) Co-organizer of PuMaGraSS (pure math graduate student seminar), a weekly seminar for graduate students in the math department to give informal talks to their peers.

Undergraduate work

  • In 2018, I was a participant in the Santa Fe Institute's NSF REU. About seven riffle shuffles of a standard 52-card deck of playing cards is the gold standard for randomizing a deck of cards. I learned about Persi Diaconis' application of Fourier analysis to the study of this interesting probabilistic phenomenon.
  • At Los Alamos National Laboratory, I worked with Dr. Heidi Morris in the computational physics division on the problem of locating radio sources (such as a thunderstorm) based on time of arrival data from a configuration of satellites. We affectionately named the program I wrote "ANVIL" for ANisotropic Vhf Impulse Location after anvil clouds.
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