Wenshin Lee (University of Stirling) Title: From computer algebra to signal processing Abstract: In 1795, the French mathematician de Prony published a method to fit a realvalued exponential model to some uniformly collected samples. This classical method in approximation theory is based on a linear recurrence relation among the data. After two centuries, in the field of computer algebra, Ben-Or and Tiwari presented an algorithm for interpolating sparse multivariate polynomials. Interestingly, these two methods are closely related. The cross-fertilization between these two has led to a series of exciting developments in exponential analysis and its applications in signal processing, including a multivariate exponential analysis method that does not suffer from the well-known curse of dimensionality, a validated exponential analysis approach based on subsampling, and the breaking of the Nyquist constraint that has underpinned almost all digital signal applications so far.
Stephen Wolfram (Wolfram Research) Title: Relating Symbolic Computation to the Foundations of Science Abstract: It started with a breakthrough in fundamental physics in 2020. And now it’s becoming clear that the foundations of science are deeply connected to ideas in symbolic computation. The result is emerging unification that relates term rewriting to black holes, metamathematical space to SETI, biological evolution undecidability, and much more. This talk will discuss both new theoretical perspectives and results, and some of their practical implications, notably in emerging features of the Wolfram Language.
Kazuhiro Yokoyama (Rikkyo University) Title: Operations on Parametric Ideals Abstract: We deal with ideals generated by polynomials with parametric coefficients, and introduce the notion of stabilities on ideal structures based on stability of forms of Gröbner bases. For these computations, we can apply comprehensive Gröbner systems effectively. Then, we consider stabilities on basic operations on ideals, such as intersection, quotient, saturation, and radical, and show that those are computable with help of comprehensive Gröbner systems. Moreover, as an advanced operation, we consider primary decomposition and discuss its computational tractability.
Masahiko Sato (Kyoto University) Title: Proof Assistants and Foundations of Mathematics Abstract: Reflecting on the history of the developments of mathematics and proof assistants, I will propose a design principle of a new proof assistant which provides an environment where mathematcics and metamathematics can be developed simultaneously in a seemless manner.
