HEИндивидуална стипендия2025–2027

POSSIS · Positive Solutions in the Sciences

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период: 2025-10-01 → 2027-09-30
Финансиране от ЕС: 202 125 €
Участници: 1
Схема: HORIZON-TMA-MSCA-PF-EF

Линиите свързват координатора с партньорите.

Накратко на български

Положителните решения на полиномни уравнения се анализират чрез реална алгебрична геометрия, като например при уравненията на Ландау в физиката на частиците. Това помага за разбирането на явления, които се наблюдават при експерименти по разсейване.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Positive Solutions in the Sciences

Polynomial equations are fundamental across various scientific disciplines, serving as powerful tools for modeling and solving real-world problems. Often, only the positive real solutions of these equations are of interest. These include applications like the Landau equations in particle physics, Nash equilibria in game theory, steady states of biochemical reaction networks, and statistical models in phylogenetics. While methods from applied algebraic geometry have already proven successful in studying complex solutions of these polynomial systems, investigating the positive solutions of these polynomials requires a paradigm shift toward real algebraic geometry. The primary objective of the project is to develop a method for computing the positive solutions of the Landau equations. These positive solutions are crucial because they lead to singularities in the physical region of Feynman integrals, which correspond to observable phenomena in scattering experiments. From a high-level perspective, the project aims to build bridges between real algebraic geometry and various scientific fields. While algorithms in Real Algebraic Geometry are often associated with poor worst-case complexity, many scientific problems do not fall into this category. In fact, these algorithms can often be optimized and applied efficiently by considering the specific characteristics of these problems. The goal of the project is to provide further evidence of this phenomenon and to extend the applicability of real algebraic geometry.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

Polynomial equations are fundamental across various scientific disciplines, serving as powerful tools for modeling and solving real-world problems. Often, only the positive real solutions of these equations are of interest. The goal of this project is to develop methods within the framework of real algebraic geometry, specifically aimed at solving problems related to the positive solutions of polynomials that arise in scientific applications.The main focus of this project is a classical problem that arises from the scattering of elementary particles in physics. The primary objective is to develop a method for computing the positive solutions of the Landau equations. These positive solutions are crucial because they lead to singularities in the physical region of Feynman integrals, which correspond to observable phenomena in scattering experiments.Beyond particle physics, this project aims to extend the applications of real algebraic geometry to the study of Nash equilibria in game theory, steady states of biochemical reaction networks, and statistical models in phylogenetics. In all these fields, the models are given by parametrized polynomial equation systems with parameters that share linear dependencies. While methods from applied algebraic geometry have already proven successful in studying complex solutions, investigating the positive solutions of these polynomials requires a paradigm shift toward real algebraic geometry.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITAET LEIPZIG · LeipzigКоординаторГермания