Research Interests

I am interested in Quantum Topology, Hyperbolic Geometry, Topological Quantum Field Theories, and Volume Conjecture. 

On the side, I am interested in some topics from mathematical physics, namely, topological phases of matter and topological quantum computing. 

Jun 2025 Topological phases of matter, Quantum Error Correction, and Topological twists, APL Quantum; 2 (3): 031501 

Feb, 2025 Adaptive Graph of Thoughts: Test-Time Adaptive Reasoning Unifying Chain, Tree, and Graph Structures, (Tushar et Al.),                                                                                 preprint: 2502.05078

July, 2024 Efficient variational quantum eigensolver methodologies on quantum processors, (Tushar et Al.), preprint: 2407.16107

June, 2024 Modeling Sea Level Rise Using Ensemble Techniques: Impacts on Coastal Adaptation, Freshwater Ecosystems, Agriculture and         Infrastructure, (Sambandh et. Al.), Analytics, 3(3):276-296

Feb, 2024 Generalized Bonahon-Wong-Yang volume conjecture of quantum invariants of surface diffeomorphisms I: the figure eight knot complement, (with Ka Ho Wong), preprint: 2402.04483 

Nov, 2023 The Bonahon-Wong-Yang volume conjecture for the four-puncture sphere, preprint: 2311.13151

Sep, 2023 Geometry of fundamental shadow link complements and applications to the 1-loop conjecture,  (with Ka Ho Wong), preprint:                                                                       2308.06643

Sep, 2022 Topological Characterization with a Twist, Condensation, and Reflection, (Joint with E. Dumitrescu), preprint: 2209.11126 

May 2021 On the asymptotic expansion for the relative Reshetikhin-Turaev invariants of fundamental shadow link pairs, (With Ka Ho                                                                       Wong), preprint 2105.08805

• BWY volume conjecture for incomplete structures,  Geometry/Topology seminar, Rutgers University

• Generalized BWY volume conjecture, Topology seminar, Michigan State University

• Quantum invariants for punctured sphere, Workshop in Geometric topology, Colorado college 

• ZX-live, Quantinuum hackathon, ICTP, Italy

• Quantum invariants for surface diffeomorphisms, AMS southeastern sectional meeting, Georgia institute of Technology

• Toric Code, Doubled Semion and Ising anyons, Quantum workshop, North Carolina State University

• From Jones Polynomial to Volume Conjecture, Low-Dimension Topology Seminar, Texas A&M University

• Category Theory and Topological phases of matter, Oak Ridge National Labs, Oak Ridge, TN

• Tetrahedral Decomposition, Graduate School on Geometric Group Theory and Low Dimension Topology, ICMAT, Madrid, Spain

• Brief History of Volume Conjecture, Braids in Low Dimension Topology, ICERM, Brown University, RI

• Topological data from the ground state Hamiltonian, (with Eugene Dumitrescu), NSF MSGI 2021 Summer Symposium, Oak Ridge National Labs, TN

• Art to Mathematics to Quantum, Gathering in Graduate Expository Mathematics, Texas A&M University, TX