Upcoming Events

Logic Colloquium

April 04, 2025, 4:10 PM

60 Evans Hall

Ronnie Chen
University of Michigan

An introduction to (regular) countably copresented space

Polish spaces, i.e., separable completely metrizable spaces, form the standard topological context for classical descriptive set theory. Over the past 10-15 years, it has become known that Polish spaces may be usefully regarded as “dual” algebraic structures; namely, their topologies may be presented by countably many generators and relations (and obey the T₃ separation axiom). Many fundamental concepts and results in classical descriptive set theory have simple explanations from this point of view, such as the hyperspace of closed sets and Sierpinski’s theorem that continuous open topological quotients are well-behaved. This talk will give an overview of the algebraic view of Polish spaces and its applications, including a recent (2023) new proof of the Becker–Kechris topological realization theorem for Polish group actions and several generalizations thereof.

Logic Colloquium

April 11, 2025, 4:10 PM

60 Evans Hall

Francesca Zaffora Blando
CMU

Algorithmic randomness and the weak merging of computable probability measures

I will present a general framework for studying “merging randomness”: namely, notions of algorithmic randomness defined via suitably effectivized notions of merging of opinions. The most well-known merging-of-opinions theorem is the Blackwell-Dubins Theorem (Blackwell and Dubins, 1962), which is concerned with predictions about infinite-horizon events, and where the distance between probabilistic forecasts is given in terms of the total variation distance. In this talk, I will instead focus on a weaker notion of merging between probability measures, first studied by Kalai and Lehrer (1994), which is concerned with one-step-ahead predictions. However, rather than merely focusing on the total variation distance, I will also consider notions of merging randomness defined in terms of the Hellinger distance and the Kullback-Leibler divergence. The main results I will present are novel characterizations of Martin-Löf randomness and Schnorr randomness—two canonical algorithmic randomness notions—in terms of weak merging of opinions and the Kullback-Leibler divergence. These results are joint work with Simon Huttegger (UC Irvine) and Sean Walsh (UCLA).

Logic Colloquium

May 02, 2025, 4:10 PM

60 Evans Hall

Omer Ben-Neria
UCLA

Logic Colloquium

May 09, 2025, 4:10 PM

60 Evans Hall

Johan van Benthem
Stanford University, University of Amsterdam and Tinsghua University