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University of Hamburg

The goal of this conference is to present a panorama of research directions in mathematics and mathematical physics related to the scientific program of our CRC 1624 „Higher structures, moduli spaces and integrability". The CRC 1624 has started in the spring of 2024. It aims to stimulate interactions between highly active topics in mathematics such as higher structures and their applications in TQFT and CFT, the geometry of moduli spaces with their applications in SUSY QFT and string theory like the swampland program, and integrability with its multitude of applications in quantum field theory and string theory. As most of the early career researchers participating in the CRC have arrived by now, we regard the first anniversary of the start of the CRC as a good time for having an opening conference. With this conference we aim to stimulate new interactions between mathematics and theoretical physics by bringing together leading representatives of these research directions.

Connecting algebra and geometry to quantum field theory and string theory

Mathematical Physics,    Astronomy, Astrophysics and Cosmology

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Simons Laufer Mathematical Sciences Institute (SLMath)

This summer school will offer a hands-on introduction to discriminants, with a view towards modern applications. Starting from the basics of computational algebraic geometry and toric geometry, the school will gently introduce participants to the foundations of discriminants. A particular emphasis will be put on computing discriminants of polynomial systems using computer algebra software. Then, we will dive into three applications of discriminants: algebraic statistics, geometric modeling, and particle physics. Here, discriminants contribute to the study of maximum likelihood estimation, to finding practical parametrizations of geometric objects, and to computations of scattering amplitudes. We will explain recently discovered unexpected connections between these three applications. In addition to lectures, the summer school will have daily collaborative exercise sessions which will be guided by the teaching assistants and will include software demonstrations.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)