Postdoctoral Researcher @ University of Wisconsin–Madison
I am a theoretical physicist studying high-energy physics, string theory, and cosmology. I also explore how machine learning and AI can help us tackle problems across physics, mathematics, and engineering.
I often think while walking, a habit I call Thinking While Walking. To me, my mind is my laboratory. Through thought alone, I can explore the vastness of the universe and delve into the microscopic quantum world. I believe this is the most romantic thing.
An all-loop construction expresses two-site cosmological wavefunction coefficients as sums of tree-level terms evaluated at shifted energies, including arbitrary tadpole contributions. The underlying geometry links Boolean lattices and permutohedra with finite differences, maximal chains, and graph tubings. These relations also apply to power-law FRW cosmologies before spatial loop-momentum integration.
Canonical differential equations for two-site one-loop bubble and tadpole diagrams extend kinematic flow to loop-level cosmological integrals in power-law FRW backgrounds. Twisted cohomology, integration-by-parts techniques, and marked tubing graphs reveal the distinct structures of these systems. The analysis also proposes an all-loop decomposition into shifted tree-level and bubble-like building blocks.
Gauge and gravitational equivalence theorems connect massive Kaluza-Klein scattering amplitudes to their Goldstone counterparts in compactified warped geometries. The relations hold for three- and four-point tree amplitudes and support a double-copy construction that is exact at three points and captures the leading high-energy behavior at four points.
At high energies, longitudinal Kaluza-Klein graviton amplitudes are related to their Goldstone counterparts by a gravitational equivalence theorem in compactified five-dimensional gravity. Together with a double-copy construction from gauge theory, this relation explains the cancellation of apparent E10 growth to E2 in four-graviton amplitudes and reveals further cancellations in the theorem's residual terms.
View on arXivA massive KLT-like relation connects closed-string amplitudes with Kaluza-Klein states to products of open-string amplitudes. Its field-theory limit gives a double-copy construction of massive graviton amplitudes from gauge-boson amplitudes. Exact four-point results agree with field-theory calculations, with the analysis also extending to five- and six-point scattering.
CosmoPINNs uses physics-informed neural networks to solve the differential systems governing cosmological integrals. It covers tree-level, one-loop, and two-loop examples in power-law FRW cosmologies, with transfer learning that reuses features learned from simpler graphs to train more complex systems.
View on GitHubLean projects for turning identities and theorems in theoretical physics into machine-checked proofs. Current topics include cosmological finite-difference identities and the Kaluza–Klein gravitational equivalence theorem. A local language model proposes proof steps, while Lean checks each candidate and returns feedback to guide further attempts.
View on GitHub