
Irina Holmes: Research

NSF Postdoctoral Fellow
Department of Mathematics
Michigan State University
holmesir@math.msu.edu


Overview
Postdoctoral Research:
My current research interests are in dyadic harmonic analysis, weighted inequalities,
Bellman functions, and multiparameter harmonic analysis. A lot of my postdoctoral work has been
in twoweight inequalities for commutators with CalderónZygmund operators.
For more details, see my
Research Statement.
Graduate Research:
My graduate research interests were infinitedimensional analysis, probability, functional
analysis and machine learning.
Together with my adviser, I worked on developing the Gaussian Radon
transform for Banach spaces, an infinitedimensional
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

Biparameter embedding and measures with restriction energy condition
 joint with Nicola Arcozzi, Pavel Mozolyako, and Alexander Volberg.

Obstacle problems generated by the estimates of square function
 joint with Alexander Volberg.

Bellman function sitting on a tree
 joint with Nicola Arcozzi, Pavel Mozolyako, and Alexander Volberg.

The Sharp Constant in the Weak (1,1) Inequality for the Square Function: A New Proof
 joint with Paata Ivanisvili and Alexander Volberg.

Two weight Commutators in the Dirichlet and Neumann Laplacian settings
 joint with Xuan Thinh Duong, Ji Li, Brett D. Wick, and Dongyong Yang (Submitted).

Weighted little bmo and twoweight 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 CalderónZygmund Operators
 joint with Brett D. Wick (Journal of Operator Theory 79, No. 1, 2018.).

Commutators in the TwoWeight Setting
 joint with Michael T. Lacey and Brett D. Wick (Mathematische Annalen
376, Issue 12, 2017).

Bloom's Inequality: Commutators in a TwoWeight 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)