I gave a talk on cosmological wavefunctions and the orthogonal Grassmannian in Pollica, Italy.
Amplitudes & positive geometry
Chia-Kai Kuo
Postdoctoral ResearcherMax Planck Institute for Physics · Garching, Germany
I study the geometric and analytic structures of quantum field theory, focusing on scattering amplitudes, correlation functions, and cosmological wavefunction coefficients. My aim is to understand how these observables can be constructed from geometry, symmetry, and their singularities.
I received my Ph.D. in theoretical physics from National Taiwan University in 2024 under the supervision of Song He and Yu-tin Huang.
What's new
Recent updates
The revised version of Beyond Discontinuities introduces an inversion formula and a complete four-point supersymmetric wavefunction coefficient.
Our paper Notes on off-shell conformal integrals and correlation functions at five points was published in Physical Review D 113, 105022.
01 Research
Research directions
Across these projects, I use geometry and singularities to find simpler representations of physical observables.
Quantum field theory describes particle interactions and quantum fluctuations in the early Universe. I study the mathematical structures behind its predictions: how geometry encodes them, how singularities constrain them, and how these structures lead to practical calculations.
Positive geometry
How does geometry encode scattering amplitudes?
In ABJM theory, a three-dimensional supersymmetric quantum field theory, I study positive geometries whose canonical forms encode loop integrands. With my collaborators, I develop chamber decompositions that organize physical cuts and yield explicit one- and two-loop results.
Loop amplitudes
What fixes the infrared structure of loop amplitudes?
Infrared singularities constrain how loop amplitudes behave when momenta become soft or collinear. I combine unitarity cuts with geometric triangulations to study these constraints. In ABJM theory, our scaffolding construction organizes the two-loop BDS integrand and its integrated result at arbitrary even multiplicity.
Correlation functions
How can geometry simplify correlation functions?
I study correlation functions, which describe relations between quantum fields at different points, in planar N=4 super Yang-Mills theory. Our chamber decomposition organizes four-point integrands through four loops. At five points, we construct pure two-loop integral bases and compute correlators at symbol level.
Cosmological wavefunctions
Can discontinuities determine cosmological wavefunctions?
Cosmological wavefunction coefficients encode interactions in an expanding universe. I study how their energy dependence can be reconstructed from discontinuities. Our recent work combines an inversion formula with supersymmetric Grassmannian representations, giving explicit tree-level three- and four-point coefficients and connecting them to scattering amplitudes in the flat-space limit.
02 Publications
Papers & preprints
Selected work
Cosmological wavefunctions
Beyond Discontinuities: Cosmological WFCs and the Supersymmetric Orthogonal Grassmannian
We combine an inversion formula with supersymmetric Grassmannian representations to reconstruct tree-level wavefunction coefficients from energy discontinuities. Explicit three- and four-point results connect the construction to scattering amplitudes in the flat-space limit.
Correlator geometry
Leading singularities and chambers of Correlahedron
We decompose the geometry of four-point correlators into chambers and relate their forms to local loop integrands. At four loops, this organization accommodates an elliptic contribution and guides the choice of pure integral bases.
Scattering from geometry
We construct a positive geometry for planar ABJM loop integrands and develop a chamber-based approach to its canonical forms. This yields explicit one-loop integrands through ten points and two-loop integrands through eight points.
All publications
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Beyond Discontinuities: Cosmological WFCs and the Supersymmetric Orthogonal Grassmannian
Y.-T. Huang, C.-K. Kuo, Y. Liu and J. Mei, preprint.
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2026
Notes on off-shell conformal integrals and correlation functions at five points
C.-K. Kuo and Q. Yang, Physical Review D 113, 105022.
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2026
Leading singularities and chambers of Correlahedron
S. He, Y.-T. Huang and C.-K. Kuo, JHEP 03, 071.
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2026
BDS ansatz in ABJM via scaffolding triangulations
Y.-T. Huang, C.-K. Kuo and C. Zhang, JHEP 02, 022.
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2024
All-loop geometry for four-point correlation functions
S. He, Y.-T. Huang and C.-K. Kuo, Physical Review D 110, L081701.
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2023
The ABJM Amplituhedron
S. He, Y.-T. Huang and C.-K. Kuo, JHEP 09, 165.
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2023
Emergent unitarity, all-loop cuts and integrations from the ABJM amplituhedron
S. He, C.-K. Kuo, Z. Li and Y.-Q. Zhang, JHEP 07, 212.
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2023
The two-loop eight-point amplitude in ABJM theory
S. He, Y.-T. Huang, C.-K. Kuo and Z. Li, JHEP 02, 065.
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2022
All-Loop Four-Point ABJM Amplitudes from Dimensional Reduction of the Amplituhedron
S. He, C.-K. Kuo, Z. Li and Y.-Q. Zhang, Physical Review Letters 129, 221604.
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2022
The momentum amplituhedron of SYM and ABJM from twistor-string maps
S. He, C.-K. Kuo and Y.-Q. Zhang, JHEP 02, 148.
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2018
Dualities for Ising networks
Y.-T. Huang, C.-K. Kuo and C. Wen, Physical Review Letters 121, 251604.
No publications found.
03 Talks
Talks & seminars
Selected seminars, workshop talks, and conference presentations.
Beyond Discontinuities: Cosmological wavefunctions and the orthogonal Grassmannian
Pollica, Italy.
Positive Geometry and Leading Singularities in Correlation Functions
New Ways to Higher Points, Humboldt University of Berlin, Germany.
BDS ansatz in ABJM via scaffolding triangulations
42nd International Conference on High Energy Physics, Prague, Czech Republic.
Geometry of the Four-Point Correlators
Kick-off Workshop on Positive Geometry in Particle Physics and Cosmology, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
The ABJM Amplituhedron
Amplitudes 2023, CERN, Switzerland.
All-Loop Four-Point ABJM Amplitudes from Dimensional Reduction of the Amplituhedron
2022 NTU-Kyoto High Energy Physics Workshop / Kawai Fest, National Taiwan University, Taiwan.
Academic experience
Teaching
At National Taiwan University, I was a teaching assistant for courses in Electricity and Magnetism, Quantum Mechanics, and Applied Mathematics I.
04 Curriculum vitae
Academic background
Before joining the Max Planck Institute for Physics in 2024, I completed my undergraduate and graduate studies at National Taiwan University.
Download CVUpdated
- Current position
- Postdoctoral Researcher, Max Planck Institute for Physics, Garching, Germany
- Ph.D.
- National Taiwan University, Theoretical Physics, 2024
- Thesis
- Loop Amplitudes of ABJM and Its Positive Geometry
- Awards
- NTU-CTP Best Student Paper Award; NCTS Student Outstanding Paper Award
05 Contact
Contact
For research discussions, seminar invitations, or potential collaborations, please get in touch by email.