I am a PhD candidate at Caltech. My curiosities are spacetime, black holes, quantum particles/fields, and geometrical understandings of our universe. #General_Relativity #Scattering_Amplitudes #Twistor_Theory

My time in California marks a productive 5-year period with 16 papers and 5 invited talks (more to come). I investigated various topics in gravity, scattering theory, and differential geometry.

• Spinning Black Holes
• Classical Solutions: I discovered a new metric for a self-dual black hole by using classical double copy [5]. Using that as a crucial lemma, I finally figured what has been really going on beneath the mysterious “Newman-Janis trick” [8]. It turns out that the Kerr black hole was secretly a giant magnet made of two monopoles!
• Post-Minkowskian Gravity: Modern physicists approximate black holes as particles and describe their gravitaitonal-wave physics with Feynman diagrams. I derived all-orders exact worldline effective actions for spinning black holes while aiming for a reboot of the '70s “twistor particle program” [16,17], which also incorporated the updated physical understanding on the Newman-Janis trick. This enabled me to provide concrete predictions on the “Kerr Compton amplitudes” and uncover that the physical reason behind their spin exponentiation is a superintegrability of black hole dynamics in the self-dual sector [15].
• S-matrix in Massive Twistor Space: Ultimately, I believe this reboot of the twistor particle program should lead to a revival of the “twistor diagrams” story formerly established for massless amplitudes. Some attempts were given in [3], and more results are to come.

• Generalized Symmetries
• During an exciting collaboration, I discovered an exact one-form symmetry of dynamical gravity as an effective field theory [4]. This identifies a new symmetry in the standard model and sort-of explains why fermions have to exist in our universe. Moreover, it brought new perspectives on gravitational singularities or charges and suggested some curious parallels with lattice defects.

• Color-Kinematics Duality & Double Copy
• A conundrum in contemporary theoretical physics reads that perturbative quantum gravity is somehow isomorphic to Yang-Mills theory with some mystery Lie algebra. My advisor and I have explored various field-theoretic ideas to tackle this puzzle. I also developed some first-quantized (worldline) and ambitwistor-space ideas [11].

• Scattering Theory Foundations:
• Classical Eikonal (aka Magnusian): When working on the generalized symmetries project [4], I acquired something called the “Magnus expansion” while computing Wilson loops. At that moment, it was more of like an item gifted from an NPC in a game quest whose purpose appears mysterious. Amusingly, about one year later this item revealed its true purpose. I traveled to a conference in Korea, met people there, and suggested using Magnus expansion to compute the “log of the S-matrix.” Apparently, this has triggered a whole program in the community [7,12,14].
• S-symplectomorphism: In [14], I rigorously established that the classical counterpart of the S-matrix is the canonical transformation from the initial phase space to the final phase space (dubbed S-symplectomorphism), showed the converse statement that the S-matrix is the ħ-deformation of the S-symplectomorphism, and provided a systematic formulation and definition of the quantum Magnusian to all orders.
• I also implemented the worldline formalism in phase space [11], gathering the insights that I learned while practicing worldline formlism in massive twistor space (which is a Kähler manifold).

• Differential Geometry
• Riemannian: Geodesic devitaion to all orders from a new alternative to the Synge formalism [10]. This might seem like an overkill, but it is strictly necessary for grasping the all-orders-in-spin dynamics of spinning black holes [15,16,17]. It is also a versatile tool.
• Symplectic: I've been an perennial love with symplectic geometry. Some keywords are symplectic perturbation theory (abstraction of Souriau/Feynman method of minimal coupling), manifest gauge-covariance [11], constrained systems [1], etc.
• Spinspacetime: This is an interesting Poisson/symplectic geometry that reboots Newman's provisional ideas in the '70s and opens up a new chapter in relativity by providing many applications [3].