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.

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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.

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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.

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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.

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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.

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Date/Time : 19 Aug 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Clement Yung, University of Toronto

In the past century, the insight behind the original Ramsey’s theorem proved to be applicable to a wide range of mathematics, such as number theory, functional analysis and topology. This spurred two particular directions of Ramsey theory: The first one is known as topological Ramsey theory, a general procedure developed by Carlson and Simpson to prove many seemingly unrelated Ramsey’s theorem-like results. The second one is the Ramsey theory of Banach spaces, kickstarted by Gowers’ unexpected application of Ramsey theory to resolve a long-standing open problem in Banach space theory. In this talk, I introduce the theory of weak A2 spaces, which serves as a possible intersection between these two Ramsey theories and discuss how several infinite games that appeared in these Ramsey theories (the Kastanas game, the Gowers game and the asymptotic game) are closely related.

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Date/Time : 12 Aug 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Wang Wei, Sun Yat-Sen University

A (binary) tree is positive iff its infinite paths form a set with positive Lebesgue measure. It is a well-known phenomenon in algorithmic randomness that positive trees contain infinite paths with weak computational power. By Cantor, positive trees always have perfect subtrees and even positive perfect subtrees. Chong et al. [1] studied computational power of perfect subtrees of positive trees, and to some extend showed that positive trees also contain perfect subtrees of weak computational power. This work was followed up by Barmpalias and Wang [2], by Barmpalias and Zhang [3], and also by Greenberg, J. Miller and Nies [4]. This talk will survey the main results in the above works, and also sketch a recent result that every ∆n positive tree contains a lown perfect subtree.

[1] Chong, Chitat and Li, Wei and Wang, Wei and Yang, Yue, On the com-putability of perfect subsets of sets with positive measure, Proceedings of the Amer-ican Mathematical Society, vol. 147 (2019), no. 9, pp. 4021–4028.
[2] Barmpalias, George and Wang, Wei, Pathwise-randomness and models of second-order arithmetic, Information and Computation, vol. 299 (2024), 105181.
[3] Barmpalias, George and Zhang, Xiaoyan, Growth and irreducibility in path-incompressible trees, Information and Computation, vol. 297 (2024), 105136.
[4] Greenberg, Noam and Miller, Joseph S. and Nies, André, Highness prop-erties close to PA completeness, Israel Journal of Mathematics, vol. 244 (2021), pp. 419–465.

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Date/Time : 08 Apr 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Frank Stephan, National University of Singapore

Many-one degrees and one-one degrees are basic degree structures in recursion theory and since Young’s result 1966, that every nonrecursive many-one degree either coincides with a one-one degree or embeds every possible countable linear order inside the structure of its one-one degrees, the question whether this is also true for partial orders received attention. Dëgtev showed in 1976 that this is true for all nonrecursive and recursively enumerable many-one degrees. Odifreddi in 1981 made the special case whether every nonrecursive many-one degree either contains an antichain of one-one degrees or coincides with a single one-one degree formally an open question. Since then for long time no progress was made until Batyrshin confirmed this for all limit-recursive many-one degrees. The present work shows this then also for all many-one degrees except for the greatest recursive many-one degree which is a special case by having a two-element antichain but not a longer one in its one-one degrees. Furthermore, the talk will also look at degree structures between one-one and many-one, namely the finite-one and bounded finite-one degrees. Finite-one degrees were introduced by Maslova 1979, but up to now did not find the attention they deserved.

This is joint work of Linus Richter, Frank Stephan and Xiaoyan Zhang.

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Date/Time : 25 Mar 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Josiah Jacobsen-Grocott, Nanyang Technological University

Hyperenumeration reducibility was first introduced by Sanchis. A set $A$ is hyperenumeration reducible to $B$, $A\le_{he} B$, if there is a c.e.\ set $W$ such that
$x\in A \iff \forall f\in \omega^{\omega}\exists v,n \in \omega [\langle f{\restriction} n,x,v\rangle\in W \land D_v\subseteq B]$. The relationship between hyperenumeration and hyperarithmetic reducibility shares many parallels with the relationship between enumeration and Turing reducibility, like the fact that the hyperarithmetic degrees properly embed into the hyperenumeration degrees. However, not all properties transfer from the enumeration degrees; for instance, Selman’s Theorem is known to be false in the hyperenumeration degrees.

In this talk we look the downwards density property of the enumeration degrees, and show that it does transfer to the hyperenumeration degrees. This involves transferring injury arguments from a finite context into constructions in $L_{\omega_1^{CK}}$, and finding tools to overcome some of the limitations of hyperenumeration operators.

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