Antonio Montalban: Measuring the Complexity of Countable Objects

Title: Measuring the Complexity of Countable Objects Speaker: Antonio Montalban (UC Berkeley) Abstract: Computability theory is the sub-area of mathematical logic that studies ways to measure the complexity of objects, constructions, theorems, and mathematical proofs related to countably infinite objects. On one hand, the natural objects seem to be linearly ordered from simpler to more complex, while, on the other hand the general objects are ordered in a chaotic way. This dichotomy between natural objects and objects in general is hard to study mathematically, as we don't have a formal definition of "natural object." The objective of this talk is to introduce Martin's conjecture (open for more than 40 years) and see how it explains this dichotomy. Note: Due to technical difficulties, the video for this talk cut off midway through the questions. Topos Institute Berkeley Seminar May 2, 2022