In these proceedings, we discuss the recent approach of Ref. [1] for the construction of Ansätze for scattering amplitudes. The method builds powerful constraints on the analytic structure of the rational functions in amplitudes from numerical tests of their behavior close to singularity surfaces. We discuss how we systematically understand these surfaces and how the singular behavior of the rational function can be incorporated into an Ansatz using techniques from algebraic geometry. To perform the numerical sampling, we make use of $p$-adic numbers, a number-theoretical field that can be considered a cousin of finite fields. The $p$-adic numbers admit a non-trivial absolute value, as well as analytic functions such as the $p$-adic logarit...
We review techniques for more efficient computation of perturbative scattering amplitudes in gauge t...
Equations of hypertree divisors on the Grothendieck-Knudsen moduli space of stable rational curves, ...
The scattering equations, a system of algebraic equations connecting the space of kinematic invarian...
Rational coefficients of special functions in scattering amplitudes are known to simplify on singula...
Abstract Rational coefficients of special functions in scattering amplitudes are known to simplify o...
In this thesis we are investigating the mathematical dependence of scattering amplitudes on kinemati...
One of the main challenges in obtaining predictions for collider experiments from perturbative quant...
Several problems in computer algebra can be efficiently solved by reducing them to calculations over...
Several problems in computer algebra can be efficiently solved by reducing them to calculations over...
One of the main challenges in obtaining predictions for collider experiments from perturbative quant...
The scientific approach to understanding the laws of nature is based on the comparison between theor...
The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the ...
The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the ...
A central problem in quantum field theory is the computation of scattering amplitudes. However, trad...
A central problem in quantum field theory is the computation of scattering amplitudes. However, trad...
We review techniques for more efficient computation of perturbative scattering amplitudes in gauge t...
Equations of hypertree divisors on the Grothendieck-Knudsen moduli space of stable rational curves, ...
The scattering equations, a system of algebraic equations connecting the space of kinematic invarian...
Rational coefficients of special functions in scattering amplitudes are known to simplify on singula...
Abstract Rational coefficients of special functions in scattering amplitudes are known to simplify o...
In this thesis we are investigating the mathematical dependence of scattering amplitudes on kinemati...
One of the main challenges in obtaining predictions for collider experiments from perturbative quant...
Several problems in computer algebra can be efficiently solved by reducing them to calculations over...
Several problems in computer algebra can be efficiently solved by reducing them to calculations over...
One of the main challenges in obtaining predictions for collider experiments from perturbative quant...
The scientific approach to understanding the laws of nature is based on the comparison between theor...
The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the ...
The study of scattering amplitudes beyond one loop is necessary for precision phenomenology for the ...
A central problem in quantum field theory is the computation of scattering amplitudes. However, trad...
A central problem in quantum field theory is the computation of scattering amplitudes. However, trad...
We review techniques for more efficient computation of perturbative scattering amplitudes in gauge t...
Equations of hypertree divisors on the Grothendieck-Knudsen moduli space of stable rational curves, ...
The scattering equations, a system of algebraic equations connecting the space of kinematic invarian...