Ryan E. G. Bushling

Teaching

Office

Padelford C-8E

Winter 2024 Office Hours

Thursdays 10:00 am - 12:00 pm, PDL C-8 Wing

Courses

Winter 2024: MATH 525 - Real Analysis II
Fall 2023: MATH 524 - Real Analysis I, MATH 399 B - Undergraduate Research
Spring 2023: MATH 428 - Complex Analysis, MATH 398 B - Special Topics
Winter 2023: MATH 525 - Real Analysis II, MATH 398 B - Special Topics
Fall 2022: MATH 207 DA/DB/DC - Differential Equations
Summer 2022: MATH 207 B - Differential Equations*, MATH 530 - Seminar in Analysis*
Winter 2022: MATH 525 - Real Analysis II
Fall 2021: MATH 125 DD - Calculus with Analytic Geometry II
Summer 2021: MATH 126 D - Calculus with Analytic Geometry III*
Spring 2021: MATH 424 A/B - Fundamental Concepts of Analysis I
Winter 2021: MATH 327 A / 574 A - Introductory Real Analysis I
Fall 2020: MATH 125 FA - Calculus with Analytic Geometry II
Summer 2020: MATH 126 B/E - Calculus with Analytic Geometry III
Spring 2020: MATH 126 DC/DD - Calculus with Analytic Geometry III
Winter 2020: MATH 125 AC/AD - Calculus with Analytic Geometry II
Fall 2019: MATH 124 DA/DB - Calculus with Analytic Geometry I

* Primary instructor

Qualifications

Walter J. Michaelis Graduate Fellow (Fall 2023)
WXML Graduate Mentor (Fall 2023)
MATH 597 B - Seminar on Teaching Math (Summer 2022)
MS Mathematics, University of Washington (Spring 2022)
TA Mentor (Fall 2021)
MATH 597 A - Seminar on Teaching Math (Summer 2021)
GRDSCH 501 - TA Training (Fall 2019)
BS Mathematics, University of Washington (Spring 2019)

GSAS

In spring 2022, I established the UW Math Department's Graduate Student Analysis Seminar (GSAS), generously funded by Prof. Bobby Wilson's Rainwater Faculty Fellowship.

GSAS provides graduate students interested in mathematical analysis the opportunity to grow as mathematicians by engaging new material in diverse subfields. A founding tenet of the organization is that it should afford its members resources to explore and experiment, to find their identities as professional mathematicians in a low stakes, minimal pressure environment. Please contact me to request additional information or to subscribe to our mailing list.

Contact

Research

As an undergraduate, I analyzed the stability of the focusing mKdV and Benjamin-Ono equations, a project that yielded Python software and numerical data. Later, I studied the symmetries of PDE with Ravi Shankar, with emphasis on the Monge-Ampère equation.

I also worked with a small team of applied mathematicians at ChefSteps, Inc. on problems pertaining to heat flow. One of our many projects involved optimizing the parameters of a modified heat equation under nonlinear constraints using our own experimental data, a task that entailed cleaning large amounts of data and fine-tuning a compass search algorithm to identify critical points in a four-dimensional parameter space.

I currently study geometric measure theory and harmonic analysis under my PhD adviser, Prof. Bobby Wilson. Early in my studies, I proved several Hausdorff density theorems in Banach spaces, and more recently I generalized a result of Orponen concerning exceptional sets of orthogonal projections in Rⁿ. Presently, I am collaborating with Iqra Altaf of the University of Chicago on problems in classical fractal geometry; with Max Goering of the University of Jyväskylä on sets of finite perimeter; and with Jake Fiedler of the University of Wisconsin on effective methods in geometric measure theory.

Publications

(February 2024) A study guide to "Kaufman and Falconer estimates for radial projections", joint work with Paige Bright, Caleb Marshall, and Alex Ortiz
(December 2023) A decomposition theorem for balanced measures, joint work with Gregory Baimetov, Ansel Goh, Raymond Guo, Owen Jacobs, and Sean Lee
(May 2023) Distance sets bounds for polyhedral norms via effective dimension, joint work with Iqra Altaf and Bobby Wilson
(April 2023) A singular integral identity for surface measure, Journal of Geometric Analysis
(November 2022) Exceptional projections of sets exhibiting almost dimension conservation, Annales Fennici Mathematici
(October 2022) Exceptional sets of orthogonal projections: From classical results to current research

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';