Leon Pernak (Université de la Sarre)
Quadratic equations in wreath products of abelian groups abstract
Abstract:
One of the strongest results that one can hope for when studying decidability questions in groups is the decidability of equations - is there an algorithm that, if we feed it a group equation, tells us if the equation has or does not have a solution in a given group? I will discuss this problem in the setting of wreath products of abelian groups. In particular, I will explain how to prove that the problem is decidable for quadratic equations, using techniques and intuitions inspired by commutative algebra. This is joint work with Ruiwen Dong and Jan-Philipp Wächter.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Lukas Vandeputte (Université de Louvain)
Conjugacy separability and the Conjugacy problem abstract
Abstract:
One of the classical motivations for conjugacy separability, is that conjugacy separable groups which are finitely presented have solvable conjugacy problem. In this talk we study the interplay between these concepts in more detail.
11:20 • Université de Genève, Conseil Général 7-9, Room 1-05
Hao Chen (University of California, Davis, USA)
Change-point detection for modern complex data abstract
Abstract:
Change-point analysis is thriving in this big data era, addressing problems that arise across many fields where massive data sequences are collected to study complex phenomena over time. It plays a crucial role in processing these data by segmenting long sequences into homogeneous parts for subsequent studies. Observations could be high-dimensional or not lie in the Euclidean space, such as network data, which are challenging to characterize using parametric models. We utilize the inter-point information of the observations and propose a series of nonparametric methods to address the issue. In particular, we take into account a pattern caused by the curse of dimensionality so that the proposed methods can accommodate a broad range of alternatives. Additionally, we work out ways to analytically approximate the p-values of the test statistics, enabling rapid type I error control. The methods are applied to Neuropixels data in the analysis of thousands of neurons’ activities.
15:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1