Overview
My current research interests are in dyadic harmonic analysis, weighted inequalities,
Bellman functions, and multiparameter harmonic analysis.
Graduate Research:
My graduate research interests were infinite-dimensional analysis, probability, functional
analysis and machine learning.
Together with my adviser, I worked on developing the Gaussian Radon
transform for Banach spaces, an infinite-dimensional
generalization of the classical Radon transform,
and applications of this transform to machine learning.
For more details,
see my
Graduate Research Statement,
or my thesis.
Undergraduate Research:
As an undergraduate at LSU, I worked as a research student at
CCT.
In particular, I worked with Horst Beyer on the Kerr metric of rotating black holes.
Publications
-
Sharp restricted weak-type estimates for sparse operators
- joint with Guillermo Rey and Kristina Ana Skreb (2024) - Submitted.
-
Paraproducts, Bloom BMO and Sparse BMO Functions
- joint with Valentia Fragkiadaki,
(Rev. Mat. Iberoam., 39 (2023), no. 6).
-
Borderline estimates for weighted singular operators and concavity
- joint with Alexander Volberg,
(Harmonic Analysis and Convexity, Berlin, Boston: De Gruyter, 2023).
-
Bi-parameter embedding and measures with restriction energy condition
- joint with Nicola Arcozzi, Pavel Mozolyako, and Alexander Volberg,
(Mathematische Annalen, 377, 2020)
-
The Sharp Constant in the Weak (1,1) Inequality for the Square Function: A New Proof
- joint with Paata Ivanisvili and Alexander Volberg.
(Revista Matematica Iberoamericana, Vol 36, Issue 3, 2020).
-
Bellman function sitting on a tree
- joint with Nicola Arcozzi, Pavel Mozolyako, and Alexander Volberg
(International Mathematics Research Notices, rnz224, 2019).
-
Two weight Commutators in the Dirichlet and Neumann Laplacian settings
- joint with Xuan Thinh Duong, Ji Li, Brett D. Wick, and Dongyong Yang
(Journal of Functional Analysis, Volume 276, Issue 4, 2019).
-
Weighted little bmo and two-weight inequalities for Journé commutators
- joint with Stefanie Petermichl and Brett D. Wick (Analysis & PDE
11, No 7, 2018).
-
Commutators with Fractional Integral Operators
- joint with Robert Rahm and Scott Spencer (Studia Mathematica
233, no. 3, 2016).
-
Two Weight Inequalities for Iterated Commutators with Calderón-Zygmund Operators
- joint with Brett D. Wick (Journal of Operator Theory 79, No. 1, 2018.).
-
Commutators in the Two-Weight Setting
- joint with Michael T. Lacey and Brett D. Wick (Mathematische Annalen
376, Issue 1-2, 2017).
-
Bloom's Inequality: Commutators in a Two-Weight Setting
- joint with Michael T. Lacey and Brett D. Wick (Archiv der Mathematik 106, no. 1, 2016).
-
The Gaussian Radon Transform in Classical Wiener Space
- joint with Ambar Sengupta
(Communications on Stochastic Analysis 8, no. 2, 2014).
-
The Gaussian Radon Transform and Machine Learning
- joint with Ambar Sengupta
(Infinite Dimensional Analysis, Quantum Probability and Related Topics, 18, no. 3, 2015).
-
An Inversion Formula for the Gaussian Radon Transform for Banach Spaces
(Infinite Dimensional Analysis, Quantum Probability and Related Topics, 16, no. 4, 2013).
-
A Gaussian Radon Transform for Banach Spaces
- joint with Ambar Sengupta
(Journal of Functional Analysis 263, no. 11, 2012).
-
On a new symmetry of the solutions of the wave equation in the background of a Kerr black hole
- joint with Horst R. Beyer
(Classical and Quantum Gravity, 25, no. 13, 2008)
-
On a Problem in the Stability Discussion of Rotating Black Holes
(Proceedings of The National Conference On Undergraduate Research (NCUR) 2006)
-
A comparison of box and Carleson conditions on bi-trees
- joint with Georgios Psaromiligkos and Alexander Volberg. (Preprint)
-
Obstacle problems generated by the estimates of square function
- joint with Alexander Volberg. (Submitted)
-
Dyadic bi-parameter repeated commutator and dyadic product BMO
- joint with Sergei Treil and Alexander Volberg. (Preprint)
-
Dyadic bi-parameter simple commutator and dyadic little BMO
- joint with Sergei Treil and Alexander Volberg. (Preprint)
