Research

Research Interests

• Geometric Group Theory, Analysis on Metric Spaces

• Combinatorial and Algorithmic Methods to Solve Problems in Algebra

• Optimization Theory

Publications

 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. 

 Talks

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

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

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

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

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

6. Looking for units and zero-divisors in group rings, UIUC Groups, Geometry and Topology Seminar, 2024 

7. Kaplansky’s Conjectures, National University of Singapore, 2024*

8. Asymptotic Dimension and Nagata Dimension, Michigan State University, 2024*

9. Asymptotic Dimension, UIUC Graduate Geometry and Topology Seminar, 2024 

10. Nagata Dimension, UIUC Graduate Analysis Seminar, 2024

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

12. Model Agnostic Data Sampling Techniques at AWM Colloquium, 2022

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

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

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

*Invited talks

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.