A physical law must possess mathematical beauty.
Research domains
Mathematical physics
Multiple Mellin-Barnes integrals, GKZ hypergeometric systems and multivariate hypergeometric functions, with series representations from conic hulls and triangulations, analytic continuation, high-precision evaluation and the method of brackets.
Feynman integrals
Analytic and numerical evaluation of multi-loop, multi-scale Feynman integrals, such as conformal hexagon, double box and one-loop n-point integrals, sunset integrals in chiral perturbation theory, and their ε-expansion in dimensional regularization.
Multi-Higgs physics
Extended scalar sectors such as the 2HDM, the N2HDM and Higgs triplets, confronted with the di-photon excesses near 95 and 152 GeV at the LHC, differential top-quark distributions, the W mass and electric dipole moments.
Computational tools
Open-source Mathematica packages: MBConicHulls for multiple Mellin-Barnes integrals, FeynGKZ for Feynman integrals via GKZ systems, and HyperPrecision for multivariate hypergeometric functions.
Effective field theory
The Standard Model effective field theory and the renormalization group: two-loop anomalous dimensions of baryon-number-violating operators for proton decay, two-loop running with scalar leptoquarks, and the summation of large logarithms.
Exotic particles
Scalar leptoquarks beyond the Standard Model: two-loop renormalization group evolution, the unification of gauge and Yukawa couplings, and one-loop matching onto the SMEFT.
Selected work
A map of the papers
Each dot is one of the 30 papers, placed by the words its title and abstract share with the others, so that papers on the same subject sit close together. A line joins each paper to the three closest to it.
One integral, two series
Closing the contour of a Mellin-Barnes integral to the right or to the left picks up different poles, and gives a different series for the same function. Each series converges in a region of its own, and each is the analytic continuation of the other. Here is the integral of the slide What is a Mellin-Barnes integral? in the tour above, with the number of terms on a slider.
I(x) = ∫ dz/2πi (−x)z Γ(−z) Γ(−½ + z) = −2√π (1 − x)½
- Closing to the right, on the poles of Γ(−z): Σn Γ(n − ½) xn/n!, which converges for |x| ≤ 1
- Closing to the left, on the poles of Γ(−½ + z): (−x)½ Σn Γ(n − ½) x−n/n!, which converges for |x| ≥ 1
- The function itself, −2√π (1 − x)½
Software
The open-source Mathematica packages and the library that came out of this research, developed with my collaborators. Each one opens on the Software page, with its versions, requirements and installation.
Contact
Feel free to get in touch. I am always happy to hear from you.
Send an email or find me on INSPIRE, GitHub and LinkedIn.