Talk
Introduction to Algebraic Analysis
Abstract
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04.11.2024, 13:30 (G3 10 (Lecture hall))
07.11.2024, 11:00 (E2 10 (Leon-Lichtenstein))
11.11.2024, 13:30 (G3 10 (Lecture hall))
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28.11.2024, 11:00 (G3 10 (Lecture hall))
02.12.2024, 13:30 (G3 10 (Lecture hall))
05.12.2024, 11:00 (G3 10 (Lecture hall))
09.12.2024, 13:30 (G3 10 (Lecture hall))
12.12.2024, 11:00 (G3 10 (Lecture hall))
16.12.2024, 13:30 (G3 10 (Lecture hall))
19.12.2024, 11:00 (G3 10 (Lecture hall))
Algebraic analysis investigates linear PDEs and their solution functions by algebraic methods. The main actor is the Weyl algebra, denoted D. It is a non-commutative ring that gathers linear differential operators with polynomial coefficients. The theory of D-modules provides deep classification results of linear PDEs, structural insights into problems in the sciences, as well as new computational tools. Functions that can be encoded by an annihilating D-ideal are called holonomic, and these are ubiquitous in the sciences.
The course is hands-on: the focus lies on the introduction of concepts from algebraic analysis and utilizing them for solving problems arising in applications, such as a systematic study of Feynman integrals from particle physics.