Date/Time : 28 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ye Jinhe, University of Hong Kong

The classical inverse Galois problem asks whether every finite group occurs as a Galois group over ℚ. A geometric generalization is the regular inverse Galois problem over a field K, which asks for regular realizations over K(t). For K = ℚ, such realizations yield solutions to the classical problem by Hilbert irreducibility. While the regular inverse Galois problem remains open over ℚ, it is known to have a positive solution over large fields. In this talk, I will discuss a positive solution over curve-excluding fields, which are existentially closed among fields avoiding a fixed curve and provide a class of non-large fields over which the problem can be solved.

Add to calendar :

Date/Time : 21 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nurlan Markhabatov, Eurasian National University (Astana, Kazakhstan)

This talk investigates model-theoretic properties of pseudofinite unars (where a unar is an algebra with a single unary operation). A criterion for the uncountable categoricity of pseudofinite unar theories is obtained. Examples of pseudofinite unar theories are constructed that are superstable but not ω-stable, ω-stable but not strongly minimal, and ω-stable but not uncountably categorical. It is also shown that the theory of every bounded unar is pseudofinite and ω-stable. During the talk, we will also attempt to formulate a general criterion for the pseudofiniteness of unars.

Add to calendar :

Date/Time : 14 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Jia Zekun, National University of Singapore

Post’s program asks for a structural thinness property of the complement of an r.e. set that forces Turing incompleteness. The program seemed to collapse when Yates built a complete maximal set. In the 1970s Degtev and Marchenkov revived it by relativizing Post’s notions to an r.e. equivalence relation η: nonrecursive r.e. semirecursive η-maximal sets exist, and every such set is Turing incomplete. The existence of maximal sets is strong. It is equivalent to IΣ₂ over PA⁻ + BΣ₂ (Chong–Yang), and for admissible α it holds exactly when the S₃-projectum of α is ω (Lerman). Downey conjectured that η-maximal sets are easier to obtain. In my previous talk, I showed that PA⁻ + IΣ₁ proves they exist. This talk extends that result in two directions. In each, η-maximal sets turn out to be no harder to build than Friedberg–Muchnik pairs, up to the best current results.

In reverse recursion theory, PA⁻ + IΣ₀ + BΣ₁ + EXP, the theory in which Chong and Mourad proved the Friedberg–Muchnik theorem, proves the existence of a nonrecursive r.e. semirecursive η-maximal set. Moreover, we will outline how a Post-style solution to Post’s problem can be carried out in this theory by bypassing the classical detour through η-hyperhypersimplicity.

In ordinal recursion theory, we show that every limit ordinal β admits a β-r.e. equivalence relation η and a non-β-recursive β-r.e. η-maximal set A. When the Σ₁-cofinality of β is at least its Σ₁-projectum (in particular, when β is admissible), both A and the graph of η can be made regular, tame and strongly β-r.e. This is the same hypothesis under which Friedman obtained regular, strongly β-r.e. Friedberg–Muchnik pairs under <wβ. (When the Σ₁-cofinality of β is less than its Σ₁-projectum, the Friedberg–Muchnik theorem with respect to ≤wβ is generally false and the same theorem with respect to ≤β remains open.

Add to calendar :

Date/Time : 07 Oct 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Neil Barton and Zachary Goodsell, National University of Singapore

In light of the development of forcing, philosophers and mathematicians have wondered whether the truths of mathematics might be contingent. This talk investigates that idea in the framework of higher-order logic. Our main result is that forcing-related contingency (e.g., contingency of the continuum hypothesis) is consistent in the higher-order logic Bacon and Dorr call Classicism + Rigid Comprehension, which permits quantification over both properties and modally rigid classes.

Add to calendar :

Date/Time : 23 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Péter Komjáth, Eötvös Loránd University

To be announced.

Add to calendar :

Date/Time : 16 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nikolay Bazhenov, Nanyang Technological University

In recent years, there has been renewed interest in the algorithmic aspects of various Stone-type dualities. For instance, Harrison-Trainor, Melnikov, and Ng (2020) proved that a Boolean algebra B has a computable isomorphic copy if and only if its dual Stone space St(B) is homeomorphic to a computable Polish space. In this talk, following the approach of Ershov and Schwidefsky, we work with effective presentations of topological T_0-spaces with base. We establish a computable version of a Stone-type duality due to Schwidefsky (2023), and we discuss its applications in computable topology.

This is joint work with Iskander Kalimullin and Marina Schwidefsky.

Add to calendar :

Date/Time : 02 Sep 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Erik Walsberg, University of Vienna

I will introduce trace definability between first order structures/theories and explain how it can be used to give dichotomies between linearity and field structure in certain settings.

Add to calendar :

Date/Time : 02 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Roy Shalev, University of Toronto

It is well-known that the product of two normal topological spaces need not be normal, but what about the normality of the product of a normal space X with the unit interval [0, 1]? A counterexample space X is called a “Dowker space”. In 1971, Rudin proved that such a space exists, but it remains open whether there must exist a Dowker space of size ℵ1. In this talk, I shall report on a joint work with Rinot and Todorčević in which we present a weak sufficient condition for the existence of a small Dowker space.

Add to calendar :

Date/Time : 26 Aug 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Rod Downey, Victoria University of Wellington

A computable Banach space X = (X, || · ||, +, ·) is a Banach space with a computable dense sequence of points which makes X a computable metric space using the norm, for which the operations are computable functions.  Most, but not all, familiar spaces of analysis and physics commonly met are such spaces. In the same way as classical vector space theory revolves around (Hamel) bases, Banach spaces are best understood using what is called a Schauder basis. There are many, many questions around this concept, both classically and in the effective content.

In this talk I will overview many of the questions and results we have so far, and particularly report on some recent work seeking to understand the effective content of Kadets’ Theorem, which states (more or less) that all infinite dimensional Banach spaces look the same if we forget the norm: any two infinite-dimensional, separable Banach spaces are homeomorphic as topological spaces. Surprisingly, this result can be proven for computable Banach spaces using only the halting problem, which seems rare in effective topology.

Add to calendar :