Ph.D., Brown University, 2016
M.S., Brown University, 2013
A.B., Mount Holyoke College, 2011
My research focuses on harmonic analysis, an area of mathematics that studies properties of functions (such as size, rate of increase, or behavior under certain transformations) by decomposing them into simpler, easier-to-understand components. In particular, I study weighted estimates, which are questions regarding the effect of transformations on the size of a function under different notions of “size”, and sparse domination principles, a novel and powerful technique for obtaining such weighted estimates. I am also interested in problems that lie at the intersection of harmonic analysis and analytic number theory, Fourier analysis, and problems regarding matrix measures.
I enjoy teaching courses of all levels in both pure and applied mathematics. Some of my favorite courses have been introductory calculus, linear algebra, and probability theory. In my classes, I encourage teamwork, communication, and building intuition first and foremost, often through independent projects or computer-assisted simulations. I strongly believe in learning with and from my students, especially those who doubt their mathematical abilities.
A. Culiuc, F. Di Plinio, and Y. Ou, Uniform sparse domination of singular integrals via dyadic shifts, Math. Res. Lett., Vol.25, no. 1, (2018), pp.21-42
J. Conde Alonso, A. Culiuc, F. Di Plinio, and Y. Ou, A sparse domination principle for rough singular integrals, Analysis & PDE , Vol. 10, no. 5 (2017), pp 1255-1284
A. Culiuc, F. Di Plinio, and Y. Ou, Domination of multilinear singular integrals by positive sparse forms, to appear in J. London Math. Soc. (2016)
K. Bickel, A. Culiuc, S. Treil, and B. Wick, Two weight estimates for well-localized operators with matrix weights, to appear in Trans. Amer. Math. (2016)
A. Culiuc and S. Treil, The Carleson Embedding Theorem with matrix weights, to appear in IMRN (2015)
Awards and Honors:
National Science Foundation Grant DMS-1800769 (2018–2021)
Class of 1940 Course Survey of Teaching Effectiveness Awards, Georgia Tech (2018)
Outstanding Teaching Award, Brown University (2016)