Seminar series
Date
Fri, 26 Jan 2024
16:00
16:00
Location
L1
Speaker
Dr Cedric Pilatte (North Wing) and Dr Boris Shustin (South Wing)
Speaker: Cedric Pilatte
Title: Convolution of integer sets: a galaxy of (mostly) open problems
Abstract: Let S be a set of integers. Define f_k(n) to be the number of representations of n as the sum of k elements from S. Behind this simple definition lie fascinating conjectures that are very easy to state but seem unattackable. For example, a famous conjecture of Erdős and Turán predicts that if f_2 is bounded then it has infinitely many zeroes. This talk is designed as an accessible overview of these questions.
Speaker: Boris Shustin
Title: Manifold-Free Riemannian Optimization
Abstract: Optimization problems constrained to a smooth manifold can be solved via the framework of Riemannian optimization. To that end, a geometrical description of the constraining manifold, e.g., tangent spaces, retractions, and cost function gradients, is required. In this talk, we present a novel approach that allows performing approximate Riemannian optimization based on a manifold learning technique, in cases where only a noiseless sample set of the cost function and the manifold’s intrinsic dimension are available.