PhD Candidate · Mathematics · UConn

Yukta Lodha

Research in functional inequalities, partial differential equations, and harmonic analysis, with emphasis on sharp constants, extremizers, stability, and domains with boundary.

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yukta.lodha@uconn.edu
MONT 213, University of Connecticut
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About

Hello!

Portrait of Yukta Lodha

I am a Ph.D. candidate in the Department of Mathematics at the University of Connecticut, working under the supervision of Professor Guozhen Lu and co-advised by Prof. Ambar N. Sengupta and Prof. Nguyen Lam.

My research lies in functional inequalities, partial differential equations, and harmonic analysis. I am particularly interested in sharp constants, extremizers, stability, and spectral methods, with current work involving the Heisenberg uncertainty principle, Caffarelli–Kohn–Nirenberg inequalities, weighted Poincaré inequalities, and related problems on domains with boundary.

Before beginning my current research in analysis, I worked on problems in graph theory and combinatorics, including the study of isomorphism classes of alternating sign matrices. Alongside research, I enjoy teaching undergraduate mathematics and mentoring students through guided mathematical reading.

Quick Info

Institution
Department of Mathematics
University of Connecticut, Storrs CT
Advisor
Prof. Guozhen Lu
Co-advisor
Prof. Ambar N. Sengupta
External advisor
Prof. Nguyen Lam
Office
MONT 213
Office Hours
By appointment
Email
yukta.lodha@uconn.edu
Research

Research Interests

Sharp Functional Inequalities

Best constants, extremizers, and equality cases for Heisenberg, Hardy, Caffarelli–Kohn–Nirenberg, and weighted Poincaré inequalities.

Stability and Spectral Methods

Quantitative stability estimates, spectral gaps, spherical harmonics, and related methods for measuring distance from extremizers.

Domains with Boundary

The effect of geometric constraints and boundary structure on sharp inequalities, including problems on half-spaces, orthants, and broader classes of domains.

Earlier Work in Combinatorics

Structural and classification questions for alternating sign matrices, with connections to graph-theoretic ideas.

Current and Future Research Directions

Sharp Functional Inequalities Beyond First-Order Settings

My current research investigates sharp constants, extremizers, and stability for first-order functional inequalities on domains with boundary, using spectral methods and related analytic techniques. Future directions include L^p extensions, higher-order inequalities involving second-order derivatives, inequalities on manifolds, and problems on more general classes of domains with boundary.

Publications

Papers

  1. Heisenberg Uncertainty Principle on Half Spaces and Orthants: Best Constants, Optimizers and Stability
    Nguyen Lam, Yukta Lodha, Guozhen Lu, Ambar N. Sengupta
    Advanced Nonlinear Studies, 2026
    Published arXiv:2602.18810
Other Works
  1. Isomorphic Classes of Alternating Sign Matrices
    Yukta Lodha · Advisor: Dr. Biswajit Deb
    M.S. Thesis, Sikkim Manipal Institute of Technology (2022)
    View Thesis
Presentations

Talks & Conferences

Teaching

Teaching

Current & Recent

  • Spring 2025 Business Calculus Instructor
  • 2024–2026 Multivariable Calculus Teaching Assistant

Previous Courses

  • 2023–2024 Calculus I & Calculus II Teaching Assistant

Directed Reading Program

  • Mentor · Guided an undergraduate student through an independent mathematical reading course at the University of Connecticut.
Curriculum Vitae

Education & Experience

Education

2023 — Present
Ph.D. in Mathematics
University of Connecticut, Storrs CT
Advisors: Guozhen Lu, Ambar N. Sengupta · External: Nguyen Lam
2025
M.S. in Mathematics
University of Connecticut, Storrs CT
2020 — 2022
M.S. in Mathematics
Sikkim Manipal Institute of Technology, India
Ranked #1 in programme · Advisor: Dr. Biswajit Deb

Service & Activities

2026
Mathematics Continued Conference
Participant & Presenter
2023 — Present
Directed Reading Program Mentor
University of Connecticut
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Contact

Get in Touch

I welcome correspondence about functional inequalities, PDEs, harmonic analysis, stability questions, research seminars, and possible collaborations. Feel free to reach out by email.

For prospective students interested in analysis or PDEs at UConn, I am happy to share information about the programme and my experience.

Contact Details

Email
yukta.lodha@uconn.edu
Office
MONT 213
University of Connecticut
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Google Scholar
Department
UConn Mathematics Profile