Jake's Homepage

I'm Jake Wellens, a third year graduate student in the MIT Math Department interested in the applications of Fourier analysis to things like computational complexity and additive combinatorics. I'm also heavy into Drake, Kazuo Ishiguro, Blue MachineĀ© and ducks, both wild and domestic, all in a very non-bandwagon way. In other words, I'm a bearded version of the other Jake, who was my roommate back at Caltech.

My advisor is Henry Cohn, who works on a bunch of cool things that I don't.

As of Fall 2017, I am a teaching assistant for 18.01, aka single variable calculus at MIT. You probably couldn't tell from my lectures, but I've always had a passion for teaching. In fact, it's kind of what got me into this mess. Other courses and educational activities I've been involved with include:

Papers

  1. On Graphs and the Gotsman-Linial Conjecture for d = 2 (w/ H. Kim and C. Maldonado, 2017) [shoutout to Jeremy Yodh for spotting the typo in the first word of the first paragraph]
  2. Subcritical behavior for quasi-periodic Schrodinger cocycles with trigonometric potentials (w/ C. Marx and L. Shou, 2015. to appear in the Journal of Spectral Theory)
  3. Continued Fraction Digit Averages and Maclaurin's Inequalities (w/ F. Cellarosi, D. Hensley, S. J. Miller, 2014. published in Experimental Mathematics)
  4. Sums and Differences of Correlated Random Sets (w/ T. Do, A. Kulkarni, S. J. Miller, D. Moon, 2014. published in the Journal of Number Theory)
  5. Sets Characterized by Missing Sums and Differences in Dilating Polytopes (w/ T. Do, A. Kulkarni, S. J. Miller, D. Moon, J. Wilcox, 2014. published in the Journal of Number Theory)

Other things

  1. A survey of the role of Fourier analysis in hardness of approximation I wrote for Dana Moshkovitz's advanced complexity class (18.405) in spring 2016
  2. Some notes from a talk I gave on (somewhat) recent progress towards the Log-Rank conjecture
  3. A bunch of exercise solutions and errata from chapters 7 and 8 of Ryan O'Donnell's book Analysis of Boolean Functions
  4. An unfinished and gentle introduction to group theory written with an inexplicably annoying tone
  5. The first little stab at math research I ever made (back in 2012 under the guidance of Michael Aschbacher)
Fig 1: Drake, drakes, and Jake, all attempting to do the same thing