Weighted inequalities and singular integrals
My research is in real-variable harmonic analysis, at the intersection of Calderón–Zygmund theory and weighted norm inequalities. I study singular integral operators, maximal operators, and the Bergman projection in both the scalar and matrix weighted settings, using dyadic and Bellman function techniques.
Multiplier weak-type inequalities
Weak-type estimates in which the weight acts as a multiplier on the operator rather than as a measure, introduced by Muckenhoupt and Wheeden. Recent work characterizes the weights for the maximal operator when p > 1; ongoing work with D. Cruz-Uribe and K. Moen treats two weights.
Multilinear operators
Sharp weighted weak-type bounds for multilinear singular integrals, valid for any multilinear operator with a sparse form domination, in both the change of measure and multiplier settings.
The Bergman projection
Weak-type estimates for the Bergman projection on planar domains, and harmonic analysis techniques for operators in several complex variables.
T(b) theorems
T(b) theorems for singular integral operators on spaces of homogeneous type and in the Dunkl setting.
Bellman functions
Sharp dyadic estimates for A2 weights via non-infinitesimal Bellman majorants, where the extremal functions do not arise from a PDE.
Wavelets and signals
A longer-term interest in wavelet analysis and its applications to signal processing and the biomedical sciences.
Funding
National Science Foundation, MPS-Ascend Postdoctoral Research Fellowship, DMS-2402316 (2024–2027)
Harmonic Analysis Techniques in the Study of Operators in Several Complex Variables
Conference talks
- AMS Spring Southeastern Sectional MeetingInvitedUpcomingSpecial Session on Recent Developments in Harmonic Analysis and PDE, University of Alabama at Birmingham
- AMS Fall Central Sectional MeetingInvitedSpecial Session on Harmonic Analysis and Intersections Therewithin, University of Minnesota Duluth
- AMS Fall Southeastern Sectional MeetingInvitedThree talks, in the Special Sessions on New Developments in PDEs, Harmonic Analysis, and Fractal Geometry; New Developments in Discrete Harmonic Analysis and Applications; and Advances in Harmonic Analysis, Kennesaw State University
- AMS Fall Eastern Sectional MeetingInvitedSpecial Session on Harmonic Analysis and PDEs, George Washington University
- 21st Prairie Analysis SeminarKansas State University
- AMS Fall Central Sectional MeetingInvitedSpecial Session on Real and Complex Function Theory, Saint Louis University
- 14th Ohio River Analysis MeetingUniversity of Cincinnati
- Joint Mathematics MeetingsInvitedAMS Special Session on New Faces in Operator Theory, Seattle, WA
- Operators on Analytic Function SpacesCIRM, Marseille
- Virginia Operator Theory and Complex Analysis MeetingInvitedUniversity of Richmond, 50-minute talk
- AMS Fall Eastern Sectional MeetingInvitedSpecial Session on Recent Advances in Harmonic Analysis, University at Albany
- AMS Spring Central Sectional MeetingInvitedSpecial Session on Recent Developments in Harmonic Analysis, University of Wisconsin–Milwaukee
- AMS Spring Southeastern Sectional MeetingInvitedSpecial Session on Geometric Measure Theory and Partial Differential Equations, Florida State University
- 13th Ohio River Analysis MeetingUniversity of Kentucky
- Joint Mathematics MeetingsInvitedAMS Special Session on New Faces in Operator Theory and Function Theory, San Francisco, CA
- Workshop in AnalysisInvitedGeorgia Institute of Technology
- 19th Prairie Analysis SeminarKansas State University
- AMS Spring Central Sectional MeetingInvitedSpecial Session on Inequalities in Harmonic Analysis, University of Cincinnati
- 12th Ohio River Analysis MeetingUniversity of Cincinnati
- 39th Southeastern Analysis MeetingClemson University
- AMS Fall Southeastern Sectional MeetingInvitedSpecial Session on Harmonic Analysis and Spectral Theory, University of South Alabama (virtual)
- 17th Prairie Analysis SeminarKansas State University (virtual)
- AMS Spring Central Sectional MeetingInvitedSpecial Session on Sharp Estimates in Harmonic Analysis, University of Cincinnati (virtual)
- 10th Ohio River Analysis MeetingUniversity of Kentucky (virtual)
- 37th Southeastern Analysis MeetingUniversity of Florida (virtual)
Seminar and colloquium talks
- Analysis Seminars at Clemson University (Oct), Washington University in St. Louis (Aug), and the University of Pittsburgh (Apr)
- Analysis Seminars at Auburn University (Dec), Brown University (Apr), and the University of Calgary (Apr)
- Analysis Seminars at Vanderbilt University (Nov), the University of Missouri (Nov), and Temple University (Feb); Colloquium, Saint Louis University (Sep)
- Analysis Seminars at the University of Alabama (Oct) and Washington University in St. Louis (Sep)
- Analysis Seminars at the University of Alabama (Sep) and Clemson University (Sep)
- Analysis Seminar, University of Alabama (Jan)
Conference and session organization
- Expanding Pathways in Harmonic Analysis 2027With A. Chang, B. Foster, H. Martikainen, C. Pereyra, E. Pozzi, and B. D. Wick
- 48th Summer Symposium in Real AnalysisWith A. Chang, P. Humke, C.-H. Pan, K. Taylor, B. D. Wick, and S. Zimmerman
- AMS Fall Eastern Sectional MeetingSpecial Session on Current Developments in Harmonic Analysis, with A. W. Green, C. B. Stockdale, and N. A. Wagner
- AMS Fall Central Sectional MeetingSpecial Session on Harmonic Analysis and Partial Differential Equations, with A. W. Green, H. Martikainen, and B. D. Wick
- Expanding Pathways in Harmonic Analysis 2025With E. Pozzi and B. D. Wick
- Joint Mathematics MeetingsSpecial Session on New Directions in Harmonic Analysis, with A. W. Green, C. B. Stockdale, and N. A. Wagner