Slides
RG treatment of the 1D LR-Ising model with random fields
Monographs
Positive Mass Theorem: Undergraduate Friendly Monograph
2DXY RG Flows for the Intrepid Student
Undergrad Research
Energy Functional of Lipids: Worked under Prof. Ranjan Mukhopadhyay (Summer 2021- Spring 2022). Researched a differential-geometric calculus application on the surfaces generated by a cell membrane. In particular, I did theoretical research on the energy functional of almost-flat models of eukaryotic cell’s bilayers. Pattern Formation of Cellular Membrane’s Composition and Decomposition Curvature Coupling. Undergraduate Student Academic Spree Day and ClarkFest. (2022)
Machine Learning Models of Crumbled Paper Samples: Worked under Prof. Arshad Kurdolli; funded by the National Science Foundation (Summer 2020). With background in voronoi, delaunay, weight diagrams, as well as various complexes (e.g., alpha complexes, simplicial complexes), created and ran paper crumbling simulations using convolution neural networks. My responsibility was to make algorithms that could produce picture generative copies of what crumbling looks like on a graph. Produced thousands of pictures representing variations of three types of crumples. Picture recognition accuracy higher than 64%.
Proving A Graphical Case of The Horowitz-Myers Conjecture: Worked under Prof. Aghil Alaee (Winter 2021-2023). Researched a method to extend the positive mass theorem to an asymptotically hyperbolic Riemannian manifold with toroidal infinity. Positive Mass Theorem in All Dimensions. Undergraduate Student Academic Spree Day and Fall Fest. (2021)
Talks
“Low-energy excitation gap and phase transitions in one-dimensional long-range Ising model with random fields”; APS March Meeting 2025
”Energy Functional of Lipid Bilayers”, Harvard University; 89th New England Complex Fluids Meeting