H2020Индивидуална стипендия2021–2022

ModSingLDT · Moduli Spaces associated with Singularities

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2021-01-01 → 2022-12-31
Финансиране от ЕС: 151 851 €
Участници: 1
Схема: MSCA-IF

Линиите свързват координатора с партньорите.

Накратко на български

Модулните пространства, свързани със сингулярности (точки с необичайно поведение), се анализират чрез търсене на числени характеристики, като например при схемите на Хилберт. Тези резултати от чистата математика помагат за развитието на теоретичната физика и алгебрата.

Този кратък обзор е генериран от изкуствен интелект

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

Резултати накратко

Moduli Spaces associated with Singularities

Moduli spaces are central objects of modern algebraic geometry. They have a strong relationship to natural enumerative questions. In many cases they are associated to a base variety and they contain a large amount of information about the geometry and topology of this base. In this project we investigated moduli spaces that were associated with singular spaces. These spaces have special points, or 'singularities', where the behavour of the space is different from what is expected. As our problems were in pure mathematics, our work is in general important for the wider scientific community including researchers in other areas such as theoretical physics or pure algebra. The main aim of the project was to find enumerative invariants of certain moduli spaces, for example Hilbert schemes and to obtain mathematical results on them.

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

Цел на проекта

The aim of this project is to investigate enumerative invariants of the Hilbert schemes parametrizing zero-dimensional subschemes of some basic classes of surface singularities as well as of its higher rank analogues, and find connections between these enumerative invariants and the Chern-Simons theories on the links of the singularities. This question will open brand new relations between algebraic and topological invariants of these singularities. The main tool to approach the problem will be to develop representations of vertex algebras on the cohomologies or derived categories of these moduli spaces conjecturally giving rise to analogues of the Nekrasov parition function on the singularities. Then we will use recent new developements about a specific motivic measure with values in the Grothendieck ring of geometric dg categories to prove some simplification of the aimed correspondence. In the end we will raise these simplified results to the general level.This project will allow the researcher to broaden his area of expertise as well as to develop new directions in his research lines. He will complement his knowledge in low-dimensional topology at one of the most prestigious research institutes and under the guidance of one of the worldwide leaders in this field.

Оригинален текст от CORDIS (на английски).

Участници

HUN-REN RENYI ALFRED MATEMATIKAI KUTATOINTEZET · BudapestКоординаторУнгария