Research

Research Interests

• Geometric Group Theory, Analysis on Metric Spaces

• Combinatorial and Algorithmic Methods to Solve Problems in Algebra

• Optimization Theory

Publications

 4.  Analytic and quasiregular distortion of Nagata dimension (with Jeremy T. Tyson), Arxiv preprint, 2026.

 3. On zero-divisors and units in group rings of torsion-free CAT(0) groups (with Igor Mineyev), Arxiv preprint 2025.

 2.  SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs (with T. Chang and K. Raghavan) In 2023 Winter Simulation Conference (WSC), pp. 3636-3646. IEEE, 2023. Arxiv link.

1.  Pseudo Orthogonal Latin Squares (with  S. Faruqi, S. A. Katre),  Discrete Mathematics and Applications, vol. 31, no. 1, 2021, pp. 5-17. 

 Invited Talks

1. Nagata dimension, mappings and boundaries of groups, Mary Winston Newson lecture, Kansas State University, April 2026

2.  Geodesic trees and the universal element, Analysis Seminar, Kansas State University, April 2026

3. Nagata dimension and mapping, Analysis Seminar, Ball State University, April 2026

4. Quasiregular and analytic distortion of Nagata dimension, Ohio River Analysis Meeting, March 2026

5. Geodesic trees and the universal element, Analysis Seminar, University of Tennessee, Knoxville, Feb 2026

6. Kaplansky’s conjectures and CAT(0) groups, Geometry Seminar, University of Tennessee, Knoxville, 2025

7. Units and zero-divisors in CAT(0) groups, Graduate Student Topology and Geometry Conference, Indiana University, Bloomington, 2024

8. Assouad-Nagata dimension and planar geometric maps, Differential geometry beyond Riemannian manifolds Conference, University of Bonn, Germany, 2025

9. Assouad-Nagata dimension and its distortion under geometric maps, Geometry and Topology Seminar, ETH, Zurich, 2025

10. Looking for units and zero-divisors in group rings, AMS Fall Western Sectional Meeting, 2024

11. Kaplansky’s Conjectures, National University of Singapore, 2024

12. Asymptotic Dimension and Nagata Dimension, Michigan State University, 2024

13. SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs at Winter Simulation Conference, 2023

14. Model Agnostic Data Sampling Techniques at Argonne National Lab, 2022

15. Model Agnostic Data Sampling Techniques at NSF MSGI Summer Research Symposium, 2022

16. On IC Coloring of graphs at ‘National Conference on Discrete Mathematics, Theoretical Computer Science, Computer Engineering and Applications’, TDPG College, Jaunpur, 2017

Published Mathematica Demonstrations*

1. Riemann's Almost Nowhere Differentiable Function

2. The Non-differentiable Functions of Weierstrass 

*All demonstrations were peer-reviewed before being published.