Monday, 15 June 2026 @ 13:30–14:30 CET

On-site:

University of Vienna

Seminarraum 10

Kolingasse 14-16

1090 Vienna

Online:

Join Zoom Meeting https://univienna.zoom.us/j/65515534186?pwd=bKL9yevbJDe0lv3eaLQiVeQmvQuLaY.1

Meeting ID: 655 1553 4186

Passcode: 303100

From Continuous through Discrete to the Finite - Modeling to Computation

Abstract:

Mathematics underlying computation proceeds through an interplay of completion, representation, and truncation, with approximation governing errors throughout. Completion enriches structure, extending the rationals to the real numbers and finite-dimensional spaces to Hilbert spaces central to data analysis. Representation renders abstract objects concrete via coordinates, Fourier coefficients, or discrete samples, with discretization as a key instance. Truncation reduces these to finite vectors, matrices, and samples. Machine arithmetic itself is a truncated discretization of the reals. Across all stages, approximation replaces exact objects by tractable surrogates, enabling linearization, low-rank approximation, and low-dimensional representation. At its core lies a single demand: that mathematics remain faithful both to what it proves and to what it computes.