Schedule and abstracts

DATES

Arrival: 07/07/2024
(Welcome Drink and Registration)
Talks: 08/07 - 12/07

Excursion: 10/07
Conference Dinner: 11/07
Departure: 13/07

SCIENTIFIC PROGRAMME

The scientific programme consists of invited plenary talks, invited semi-plenary talks and contributed talks.
Contributed talks will be 30mins long (including 5mins for discussion), semi-plenary ones 45mins (including 5mins for discussion), and plenary ones 60mins (including 10mins for discussion).

The schedule is provisional and subject to changes.

FULL SCHEDULE

invited plenary talks invited semi-plenary talks contributed talks

	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday
08:45-09:00		Opening
09:00-10:00		Tholen	Soukup	Kwietniak	Bonet	Walters-Wayland
10:00-10:30		Coffee Break
10:30-11:30		Parallel Sessions	Parallel Sessions	Parallel Sessions	Parallel Sessions	Parallel Sessions
11:30-12:30		Verberne
12:30-14:15		Lunch
14:15-15:00		Dahmen \| Reggio	Carvalho \| Zhang	Excursion	Guzman \| Arrieta	Parallel Sessions
15:00		Parallel Sessions	Parallel Sessions		Parallel Sessions	Parallel Sessions
15:15-16:15						Pinsker
16:15						Closing
16:30-17:00		Coffee Break			Coffee Break
17:00-18:00		Parallel Sessions	Parallel Sessions		Parallel Sessions
18:00-19.30	Welcome Reception
19:30-20:30	Welcome Reception				Conference Dinner
					Conference Dinner

DAILY SCHEDULE

Monday, July 08, 2024

	Plenary Talk Room Pedro Nunes (ground floor)
09:00 - 10:00	From distances and operator norms to normed categories Walter Tholen (York University, Toronto, Canada) Abstract For the study of normed vector spaces or of similar structures one may not like to be confined from the outset to the consideration of morphisms that respect the algebraic and metric structure of the objects of interest as smoothly as the 1-Lipschitz linear operators do. At least initially it may be preferable to work in a categorical environment with less perfectly behaved morphisms, but that instead comes with an operator norm which, amongst all linear maps, will then help to pinpoint classes of topologically or metrically interesting morphisms, such as the bounded or the 1-Lipschitz operators. Having such general categorical environment, the first questions we may want to ask are: What does Cauchy convergence mean? What is completeness with respect to such a notion of convergence, and do completions exist? Is there a “mother category” which, in normed category theory, may play the role that Set plays in ordinary category theory? Are there protagonist normed categories, and is the category of normed vector spaces and linear operators amongst them? Are there unexpected examples, and how do the notions designed for large categories fare when applied to an individual space considered as a small normed category, like a metric space? In this talk we will try to address all of these questions. While we base our approach on the notion of normed category as suggested by Lawvere [1], unlike several later articles on the subject we do not amend his axioms but follow rather strictly the original design of the normed structure as an enrichment. Indeed, the guidance of enriched category theory has helped us finding answers to some of the questions posed. Although we allow norms to be quantale-valued, rather than just real-valued, and thereby substantially increase the range of potential applications, the talk should remain understandable for an audience with basic knowledge of category theory, including that of adjunctions. This presentation was preceded by the talks [3, 4]. Other than to the original work [1], we also refer to the article [2] which has influenced our choice of examples. For further literature and all mathematical details not covered in the talk, we refer to the paper [5]. References: [1] F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rend. Sem. Mat. Fis. Milano 43, 135–166, 1973. Republished in: Reprints in Theory Appl. Categories 1, 2002. [2] W. Kubis, Categories with norms, 2017. https://arxiv.org/pdf/1705.10189 . [3] W. Tholen, Quantale-weighted Categories, Talk given at: 106th Peripatetic Seminar on Sheaves and Logic, Brno, May 2022. http://www.math.muni.cz/ bourkej/PSSL106.html . [4] D. Hofmann, Cauchy completeness for normed categories, Talk given at: Coimbra Category Seminar, October 2023. https://www.mat.uc.pt/ categ/pcs14/slides/Hofmann.pdf . [5] M.M. Clementino, D. Hofmann and W. Tholen, Cauchy convergence in V-normed categories, 2024. https://arxiv.org/abs/2404.09032 .
10:00 - 10:30	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
10:30 - 11:00	An invitation to cellular-Lindelöf spaces Santi Spadaro Abstract
11:00 - 11:30	Products of uniform realcompactifications Ana S. Meroño Abstract
11:30 - 12:00	On ω-Corson and NY compact spaces Mikolaj Krupski Abstract
12:00 - 12:30	Embeddings of mappings via products and universal mappings Athanasios C. Megaritis Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
10:30 - 11:00	Local mean dimension theory for sofic group actions Yonatan Gutman Abstract
11:00 - 11:30	Lelek fan as an inverse limit of Cantor fans with a single bonding function Iztok Banic Abstract
11:30 - 12:00	Strong Mazurkiewicz manifolds Vladimir Todorov Abstract
12:00 - 12:30	Weak containment for topological actions Riley Thornton Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
10:30 - 11:00	Embedding the free topological group F(Xⁿ) into F(X) Arkady Leiderman Abstract
11:00 - 11:30	Adherence determined convergences Szymon Dolecki Abstract
11:30 - 12:00	The Baire property and precompact duality Isabel Sepúlveda Alvarado Abstract
12:00 - 12:30	Equivariant means and ℤ₂-ARs Ananda López Poo Cabrera Abstract
	Session: Topology and Categories Room 2.5 (2nd floor)
10:30 - 11:00	Enriched Hausdorff and Vietoris functors Dirk Hofmann Abstract
11:00 - 11:30	A pair of monads Ando Razafindrakoto Abstract
11:30 - 12:00	Monoidal closedness of complete residuated lattice-valued generalized convergence groups T.M.G. Ahsanullah Abstract
12:00 - 12:30	Free distributive and extensive categorical structures Fernando Lucatelli Nunes Abstract
12:30 - 14:15	Lunch
	Semi-plenary Talk Room Pedro Nunes (ground floor)
14:15 - 15:00	Isometry groups as topological groups Rafael Dahmen (Karlsruhe Inst. Technology, Germany) Abstract Metric geometry is an active field of mathematical research with numerous impressive results and tons of open questions. This fascinating area of mathematics is connected to the world of topological algebra via the isometry group: Given a metric space (X, d), the group of isometric bijections Iso(X, d) can be endowed with a natural topology, turning it into a topological group. It can be shown that every complete topological group can be realized as the isometry group of a suitable metric space, so the isometry group Iso(X, d) of a general metric space (X, d) can be very complicated in general. Therefore, it is a natural question under which additional assumptions on the space (X, d) we obtain more well-behaved topological groups as Iso(X, d). There are many results in that direction, for example Iso(X, d) is a Lie group if (X, d) is a Riemannian manifold, endowed with its standard distance function. In this talk, I will give a survey about isometry groups and how geometric properties of the space correspond to topological and algebraic properties of the group. I will also address an interesting open question about certain infinite-dimensional metric spaces and pro-Lie groups (in the sense of Hofmann/Morris).
	Semi-plenary Talk Room 17 de Abril (ground floor)
14:15 - 15:00	Game comonads: logical and homotopical aspects Luca Reggio (Univ. College London, UK) Abstract Game comonads were introduced in [1, 5] to provide a categorical approach to finite model theory and descriptive complexity, which typically focus on logic fragments with a finite amount of logical resources, such as finite-variable logics or logics with bounded quantifier rank, and the corresponding combinatorial parameters of (relational) structures. In many cases, equivalence in these logic fragments can be captured in a syntax-free way by means of model-comparison games, such as Ehrenfeucht–Fraïssé and pebble games. The key insight underlying game comonads is that collections of plays in these games can be naturally organised into endofunctors on categories of relational structures that carry the structure of comonads, and their coalgebras encode both the corresponding logic fragments and the combinatorial parameters. This idea has proved to be very robust and the whole pattern, covering a range of resource-bounded logics, has been axiomatised at a general categorical level in [2, 3]. These results have led to new connections between two areas within logic in computer science that have largely been disjoint: finite model theory and descriptive complexity, and semantics and categorical structures of computation. In this talk, I will give an overview of the main ideas underpinning game comonads, with an emphasis on their: (i) Logical aspects, including a categorical view on homomorphism counting results [6, 7] and equi-resource homomorphism preservation theorems [4]; (ii) Homotopical aspects, including the use of upgrading arguments in preservation theorems, akin to small object arguments in abstract homotopy, and a homotopical view of modal logic and the Łoś-Tarski preservation theorem [8]. References: [1] Abramsky, S.; Dawar, A.; Wang, P. The pebbling comonad in finite model theory. 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LiCS), 2017, 1–12. [2] Abramsky, S.; Reggio, L. Arboreal categories and resources. 48th International Colloquium on Automata, Languages, and Programming (ICALP), 2021, 115:1–115:20. [3] Abramsky, S.; Reggio, L. Arboreal categories: An axiomatic theory of resources. Logical Methods in Computer Science, 2023, 14:1–14:36. [4] Abramsky, S.; Reggio, L. Arboreal categories and equi-resource homomorphism preservation theorems. Annals of Pure and Applied Logic, 2024, 103423. [5] Abramsky, S.; Shah, N. Relating structure and power: Comonadic semantics for computational resources. 27th EACSL Annual Conference on Computer Science Logic (CSL), 2018, 2:1–2:17. [6] Dawar A.; Jakl, T; Reggio, L. Lovász-type theorems and game comonads. 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LiCS), 2021. [7] Reggio, L. Polyadic sets and homomorphism counting. Advances in Mathematics, 2022, 108712. [8] Reggio, L. A model category for modal logic. https://arxiv.org/abs/2310.12068.
	Session: Set-theoretic Topology Room Pedro Nunes (ground floor)
15:00 - 15:30	Betweenness and equidistance in metric spaces Aisling McCluskey Abstract
15:30 - 16:00	The shape of compact covers Paul Gartside Abstract
16:00 - 16:30	Topological remarks on end and edge-end spaces Leandro Aurichi Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
15:00 - 15:30	Persistent properties from Gromov-Hausdorff viewpoint Abdul Gaffar Khan Abstract
15:30 - 16:00	Graphs with tranches Michał Kowalewski Abstract
16:00 - 16:30	Alpha limit sets Veronika Rýžová Abstract
	Session: Topological Dynamics and Continuum Theory Room 2.4 (2nd floor)
15:00 - 15:30	Fans of Cook continua Teja Kac Abstract
15:30 - 16:00	Specification properties in CR-dynamical systems Ivan Jelić Abstract
	Session: Set-Theoretic Topology Room 2.4 (2nd floor)
16:00 - 16:30	Every finite-dimensional analytic space is σ-homogeneous Andrea Medini Abstract
	Session: Topology in Logic and Computer Science Room 2.5 (2nd floor)
15:00 - 15:30	Semi-topological properties of the K-topological version of the Jordan curve theorem and its applications Sang-Eon Han Abstract
15:30 - 16:00	A topological bottleneck in Quantum Information Stuart Wayland Abstract
16:00 - 16:30	Divergence measures over the set of persistence diagrams Martín Mijangos Abstract
16:30 - 17:00	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
17:00 - 17:30	Remotely sequential spaces Michael Hrusak Abstract
17:30 - 18:00	Function spaces of Corson-like compacta Krzysztof Zakrzewski Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
17:00 - 17:30	Tameness and amorphic complexity of constant length substitution systems Elżbieta Krawczyk Abstract
17:30 - 18:00	Hyperspace shadowing Udayan Darji Abstract

Tuesday, July 09, 2024

	Plenary Talk Room Pedro Nunes (ground floor)
09:00 - 10:00	Resolvable and irresolvable spaces Lajos Soukup (Alfréd Rényi Inst. Mathematics, Budapest, Hungary) Abstract A topological space is resolvable if it can be partitioned into two dense subsets. Otherwise, it is termed irresolvable. A topological space X is considered maximally resolvable if it is ∆(X)-resolvable, where ∆(X) is the minimum cardinality of a non-empty open subset. Examples of maximally resolvable spaces include metric, ordered, compact, or pseudo-radial spaces. However, there exist countable, dense-in-itself, irresolvable spaces. In this presentation we investigate the resolvability of different classes of topological spaces, such as Lindelöf, pseudocompact, countably compact, and monotone normal spaces. We investigate what can we say on the resolvability of product of spaces. Although the problems seems to be purely topological, we will encounter many statements that are independent of ZFC, and we can not avoid mentioning large cardinals as well. References: [1] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. On resolvability of products. Fund. Math. 260 (2023), no. 3, 281–295. [2] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. On the resolvability of Lindelöf-generated and (countable extent)-generated spaces. Topology Appl. 259 (2019), 267–274. [3] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. Coloring Cantor sets and resolvability of pseudocompact spaces. Comment. Math. Univ. Carolin. 59 (2018), no. 4, 523–529. [4] Soukup, Lajos ; Stanley, Adrienne. Resolvability in c.c.c. generic extensions. Comment. Math. Univ. Carolin. 58 (2017), no. 4, 519–529. [5] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. Regular spaces of small extent are -resolvable. Fund. Math. 228 (2015), no. 1, 27–46. [6] Soukup, Dániel T. ; Soukup, Lajos. Partitioning bases of topological spaces. Comment. Math. Univ. Carolin. 55 (2014), no. 4, 537–566. [7] Juhász, István ; Shelah, Saharon ; Soukup, Lajos. Resolvability vs. almost resolvability. Topology Appl. 156 (2009), no. 11, 1966–1969. [8] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. Resolvability and monotone normality. Israel J. Math. 166 (2008), 1–16. [9] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. Resolvability of spaces having small spread or extent. Topology Appl. 154 (2007), no. 1, 144–154. [10] Juhász, István ; Soukup, Lajos ; Szentmiklóssy, Zoltán. D-forced spaces: a new approach to resolvability. Topology Appl. 153 (2006), no. 11, 1800–1824.
10:00 - 10:30	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
10:30 - 11:00	Permutation models arising from topological spaces Justin Young Abstract
11:00 - 11:30	Does ω* know its right hand from its left? Will Brian Abstract
11:30 - 12:00	Menger and Consonant spaces in the Sacks model Valentin Haberl Abstract
12:00 - 12:30	Scales and combinatorial covering properties Michał Pawlikowski Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
10:30 - 11:00	More on hyperspaces of knots Paweł Krupski Abstract
11:00 - 11:30	Characterizing inverse sequences for which their inverse limits are homeomorphic Matevž Črepnjak Abstract
11:30 - 12:00	On w-unicoherence, top-irreducibility and n-cells at the top Hugo Villanueva Abstract
12:00 - 12:30	Generically hereditarily equivalent Peano continua Bryant Rosado Silva Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
10:30 - 11:00	Bohr compactification of discrete groups and Schur ultrafilters Serhii Bardyla Abstract
11:00 - 11:30	Automatic continuity and the Effros property Andrea Medini Abstract
11:30 - 12:00	On certain cardinality observations of characterized subgroups and its variants Pratulananda Das Abstract
12:00 - 12:30	Construction of Hartman-Mycielski and separation axioms on semitopological groups Marcela López Gaytán Abstract
	Sessions: Topology and Order - Topology in Logic and Computer Science Room 2.5 (2nd floor)
10:30 - 11:00	Canonical extensions of frames via fitted sublocales and strongly exact filters Tomas Jakl Abstract
11:00 - 11:30	Raney extensions of frames as frame versions of canonical extensions Anna Laura Suarez Abstract
11:30 - 12:00	Vietoris endofunctor for closed relations Marco Abbadini Abstract
12:00 - 12:30	Applications of dimension theory to embeddability problems in topological data analysis: the case study of the Gromov-Hausdorff distance Nicolò Zava Abstract
12:30 - 14:15	Lunch
	Semi-plenary Talk Room Pedro Nunes (ground floor)
14:15 - 15:00	Shift operators on Banach spaces Maria Pires de Carvalho (University of Porto, Portugal) Abstract This talk is about linear dynamics in infinite dimensional Banach spaces. Suppose one takes a sequence of bidimensional matrices and, at each vector in ℓ_p(ℝ²), applies the matrices coordinatewise and then shifts the resulting sequence. What is the expected dynamics of such a linear operator in ℓ_p(ℝ²)? Is it hyperbolic? Has it non-trivial recurrence? Does it satisfy the shadowing property? I will present a recent joint work with Udayan Darji and Paulo Varandas where we address these and analogous questions for a new family of linear bounded invertible maps, which we call shift operators. This family comprises weighted backward shifts and (up to linear conjugation) finite products of weighted shifts and dissipative composition operators. I will illustrate the variety of dynamical properties this family exibits, explain how we classify a large class of these shift operators and prove that, for them, generalized hyperbolicity is equivalent to shadowing.
	Semi-plenary Talk Room 17 de Abril (ground floor)
14:15 - 15:00	Topological structures on real-enriched categories Dexue Zhang (Sichuan University, China) Abstract This talk concerns extensions of Scott topology to real-enriched categories. A real- enriched category is a category with real numbers as enrichment. The definition is as follows. For each continuous t-norm & on the unit interval [0, 1], V = ([0, 1], &, 1) is a complete and symmetric monoidal closed category. A V-category is then a pair (X, α), where X is a set and α : X × X → [0, 1] is a function such that (i) α(x, x) = 1 for all x ∈ X; and (ii) α(y, z) & α(x, y) ≤ α(x, z) for all x, y, z ∈ X. Such V-categories are called real-enriched categories. If we interpret the value α(x, y) as the truth degree that x precedes y, then (i) is reflexivity and (ii) is transitivity. So, real-enriched categories may be viewed as many-valued ordered sets. Since the quantale ([0, ∞]op, +, 0) is isomorphic to ([0, 1], ·, 1), quasi-metric spaces are natural examples of real-enriched categories. We focus on topological structures of real-enriched categories, including classical topo- logical structures and V-approach structures. A V-approach structure on a set is a map δ : X × 2^X → [0, 1] such that for all x ∈ X and all A, B ∈ 2^X, (A1) δ(x, {x}) = 1; (A2) δ(x, ∅) = 0; (A3) δ(x, A ∪ B) = δ(x, A) ∨ δ(x, B); (A4) δ(x, A) ≥ (inf_b∈B δ(b, A))& δ(x, B). The value δ(x, A) is interpreted as the truth degree that x is close to A. So, a V-approach structure is a many-valued topology, a V-valued topology to be precise. Scott topology is an important topology on partially ordered sets, it makes every directed subset converge to its supremum. In this talk we discuss extensions of Scott topology to the realm of real-enriched categories. References: [1] M.M. Bonsangue, F. van Breugel, J.J.M.M. Rutten, Generalized metric space: completion, topology, and powerdomains via the Yoneda embedding, Theoretical Computer Science 193 (1998) 1-51. [2] R.C. Flagg, R. Kopperman, Continuity spaces: Reconciling domains and metric spaces, Theoretical Computer Science 177 (1997) 111-138. [3] R.C. Flagg, P. Sünderhauf, The essence of ideal completion in quantitative form, Theoretical Computer Science 278 (2002) 141-158. [4] R.C. Flagg, P. Sünderhauf, K.R. Wagner, A logical approach to quantitative domain theory, Topology Atlas Preprint No. 23, 1996. http://at.yorku.ca/e/a/p/p/23.htm [5] P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker Inc., New York and Basel, 1982. [6] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, D.S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003. [7] J. Goubault-Larrecq, Non-Hausdorff Topology and Domain Theory, Cambridge University Press, Cambridge, 2013. [8] J. Goubault-Larrecq, K.M. Ng, A few notes on formal balls, Logical Methods in Computer Science 13(4:18) (2017) 1-34. [9] G. Gutierres, D. Hofmann, Approaching metric domains, Applied Categorical Structures 21 (2013) 617-650. [10] P. Hájek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. [11] D. Hofmann, G.J. Seal, W. Tholen (eds.), Monoidal Topology: A Categorical Approach to Order, Metric, and Topology, Cambridge University Press, Cambridge, 2014. [12] E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000. [13] H. Lai, W. Tholen, Quantale-valued approach spaces via closure and convergence, Topology and its Applications 230 (2017) 599-620. [14] H. Lai, D. Zhang, G. Zhang, The saturated prefilter monad, Topology and its Applications 301 (2021) 107525. [15] F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matématico e Fisico di Milano 43 (1973) 135-166. [16] W. Li, D. Zhang, Scott approach distance on metric spaces, Applied Categorical Structures 26 (2018) 1067-1093. [17] R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, 1997. [18] R. Lowen, Index Analysis, Approach Theory at Work, Springer, 2015. [19] M. B. Smyth, Quasi-uniformities: Reconciling domains with metric spaces, in: Mathematical Foundations of Programming Language Semantics, Lecture Notes in Computer Science, vol 298, pp. 236-253, Springer, Berlin, 1988. [20] M. B. Smyth, Completeness of quasi-uniform and syntopological spaces, Journal of London Mathematical Society 49 (1994) 385-400. [21] K.R. Wagner, Liminf convergence in Ω-categories, Theoretical Computer Science 184 (1997) 61-104. [22] B. Windels, The Scott approach structure: an extension of the Scott topology for quantitative domain theory, Acta Mathematica Hungarica 88 (2000) 35-44. [23] J. Yu, D. Zhang, Continuous [0, 1]-lattices and injective [0, 1]-approach spaces, Fuzzy Sets and Systems 444 (2022) 49-78.
	Session: Set-theoretic Topology Room Pedro Nunes (ground floor)
15:00 - 15:30	On the localization of antisymmetric T₀-quasi-metric spaces Filiz Yildiz Abstract
15:30 - 16:00	Spaces with an M-diagonal David Guerrero Sánchez Abstract
16:00 - 16:30	Functionally countability vs exponential separability Rodrigo Hernández-Gutiérrez Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
15:00 - 15:30	Pseudo-orbits in linear dynamics Alfred Peris Abstract
15:30 - 16:00	Fractal dimension and common hypercyclicity Quentin Menet Abstract
16:00 - 16:30	Chain recurrence is not hereditary in Linear Dynamics Antoni López-Martínez Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
15:00 - 15:30	Hypercyclic and mixing composition operators on O_M(ℝ) Adam Przestacki Abstract
15:30 - 16:00	Equivariant extension operators Ricardo Ramírez Luna Abstract
	Session: Set-theoretic Topology Room 2.4 (2nd floor)
16:00 - 16:30	External q-hyperconvexity in T₀-quasi-metric spaces Collins Amburo Agyingi Abstract
	Session: Topology and Categories Room 2.5 (2nd floor)
15:00 - 15:30	Quantale-valued maps and partial maps Lili Shen Abstract
15:30 - 16:00	Cartesian closed and stable subconstructs of [0,1]-Cat Hongliang Lai Abstract
16:00 - 16:30	Kuratowski convergence in approach spaces Meryem Ateş Abstract
16:30 - 17:00	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
17:00 - 17:30	Pseudocompact MAD families under weaker assumptions Vinicius Rodrigues Abstract
17:30 - 18:00	Relations between symmetric density and local symmetric connectedness Nezakat Javanshir Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
17:00 - 17:30	Dynamics of weighted composition operators Jaun Pablo Bès Abstract
17:30 - 18:00	Mixing composition operators and Kitai's criterion Karl Grosse-Erdmann Abstract

Wednesday, July 10, 2024

	Plenary Talk Room Pedro Nunes (ground floor)
09:00 - 10:00	An anti-classification theorem for the topological conjugacy problem for Cantor minimal systems Dominik Kwietniak (Jagiellonian University, Krakow, Poland) Abstract The isomorphism problem in dynamics dates back to a question of von Neumann from 1932: Is it possible to classify the ergodic measure-preserving diffeomorphisms of a compact manifold up to isomorphism? Foreman, Rudolph and Weiss proved an anti-classification theorem that rigorously explains why, in a certain sense, such a classification is impossible [1]. We study a topological analogue of von Neumann's problem. Let Min(C) stand for the Polish space of all minimal homeomorphisms of the Cantor set C. Recall that a homeomorphism T : C → C is minimal if every orbit of T is dense in C. We say that S and T in Min(C) are topologically conjugate if there is a homeomorphism h: C → C such that S ◦ h = h ◦ T . We will discuss an anti-classification result, saying that it is impossible to tell if two minimal Cantor set homeomorphisms are topologically conjugate using only a countable amount of information and computation. We will explain, how to understand such an anti-classification result and why it suffices to show that the topological conjugacy relation of Cantor minimal systems treated as a subset of Min(C) × Min(C) is complete analytic, so a non-Borel subset of Min(C) × Min(C). References: [1] Matthew Foreman, Daniel J. Rudolph, Benjamin Weiss, The conjugacy problem in ergodic theory. Ann. of Math. (2) 173 (2011), no. 3, 1529-1586.
10:00 - 10:30	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
10:30 - 11:00	A small Boolean algebra that is Grothendieck but not Nikodym Damian Głodkowski Abstract
11:00 - 11:30	Persistent properties in uniform box products Jocelyn Bell Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
10:30 - 11:00	An uncountable family of smooth fans that admit transitive homeomorphisms Goran Erceg Abstract
11:00 - 11:30	On the entropy paradox on tame graphs Jakub Tomaszewski Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
10:30 - 11:00	On topological properties connected with some nonlinear operators in spaces of almost periodic functions Dariusz Bugajewski Abstract
11:00 - 11:30	On uniformly continuous surjections between function spaces Vesko Valov Abstract
	Session: Topology and Order Room 2.5 (2nd floor)
10:30 - 11:00	Point-free Hausdorff axioms, and why the plural Aleš Pultr Abstract
11:00 - 11:30	The T_D axiom in a pointfree setting Anneliese Schauerte Abstract
	Plenary Talk Room Pedro Nunes (ground floor)
11:30 - 12:30	Pseudo-Anosov homeomorphisms Yvon Verberne (University Western Ontario, London, Canada) Abstract The mapping class group is the group of orientation preserving homeomorphisms of a surface up to isotopy. In particular, the mapping class group encodes information about the symmetries of a surface. The Nielsen-Thurston classification states that elements of the mapping class group are of one of three types: periodic, reducible, and pseudo-Anosov. In this talk, we will focus our attention on the pseudo-Anosov elements, which are the elements of the mapping class group which mix the underlying surface in a complicated way. In this talk, we will discuss both classical and new results related to pseudo-Anosov mapping classes, as well as the connections to other areas of mathematics. References: [1] A. Bar-Natan and Y. Verberne. The grand arc graph. Mathematische Zeitschrift 305:2 (2024). [2] Y. Verberne. A contruction of pseudo-Anosov homeomorphisms using positive twists. Algebraic & Geometric Topology 23:4 (2023) 1601–1639.
12:30 - 14:15	Lunch
14:15 - 20:00	Excursion

Thursday, July 11, 2024

	Plenary Talk Room Pedro Nunes
09:00 - 10:00	Ergodic theory for operators and applications to generalized Cesàro operators José Bonet (Polytechnical University Valencia, Spain) Abstract In the first part of this lecture we will review classical results about power bounded and mean ergodic operators acting on Banach and more general spaces. Theorems by Eberlein, Yosida and Lin will be stated. Compactness plays an important role in these results. Some new abstract results will be presented. They will be utilized to investigated the behaviour of generalized Cesàro operators when acting on sequence spaces and spaces of analytic functions on the disc of the complex plane. The generalized Cesàro operators C_t, for t ∈ [0, 1], acts from ℂ^ℕ₀ into itself (with ℕ₀ := 0, 1, 2, ...) is given by C_tx := ( tⁿx₀ + tⁿ⁻¹x₁ + ... + x_n n + 1 ) _n∈ℕ₀, x = (x_n)_n∈ℕ₀ ∈ ℂ^ℕ₀. (1) For t = 0 note that C₀ is a diagonal operator and for t = 1 that C₁ is the classical Cesàro averaging operator. These operators act continuously in many classical Banach sequence spaces such as ℓ^p, c₀, c. In the setting of analytic functions C_t has the integral representation C_tf(0) := f(0) and C_tf (z) := 1 z ∫ f(ζ) 1-tζ dζ, z ∈ 𝔻 \ {0}, (2) for every f ∈ H(𝔻 ). References: [1] A. A. Albanese, J. Bonet, W. J. Ricker, Spectral properties of generalized Cesàro operators in sequence spaces. RACSAM 117 (2023), Article number 140. [2] A. A. Albanese, J. Bonet, W. J. Ricker, Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms. Collectanea Math. (to appear).
10:00 - 10:30	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
10:30 - 11:00	On quasi b-metric spaces, quasi metrizability and bicompletions Seithuti Moshokoa Abstract
11:00 - 11:30	The modular metric topology Olivier Olela-Otafudu Abstract
11:30 - 12:00	On completeness-type properties of hyperspace topologies László Zsilinszky Abstract
12:00 - 12:30	On disjoint π-bases Hector Barriga-Acosta Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
10:30 - 11:00	Return time sets and product recurrence Jian Li Abstract
11:00 - 11:30	A homological bound on entropy in arbitrary compact spaces Luis Hernández-Corbato Abstract
11:30 - 12:00	On limit sets and equicontinuity in the hyperspace of continua in dimension one Domagoj Jelić Abstract
12:00 - 12:30	Chaos on Peano continua Klára Karasová Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
10:30 - 11:00	On spaces ℓ_∞ and c₀ with the pointwise topology embedded into spaces C_p(X) Jerzy Kąkol Abstract
11:00 - 11:30	On Cauty’s example of a metric linear space without the extension property Tadeusz Dobrowolski Abstract
11:30 - 12:00	Compactness and averaging operators on function spaces Katsuhisa Koshino Abstract
12:00 - 12:30	Renorming Problem for non-archimedean normed spaces Albert Kubzdela Abstract
	Sessions: Topology and Order - Topology in Logic and Computer Science Room 2.5 (2nd floor)
10:30 - 11:00	Localic uniform completions via Cauchy sequences Graham Manuell Abstract
11:00 - 11:30	On the torsion ideal of a homomorphism Oghenetega Ighedo Abstract
11:30 - 12:00	A study of a new dimension for finite lattices Dimitris Georgiou Abstract
12:00 - 12:30	Homomorphic reverse diferentiation for partial features Fernando Lucatelli Nunes Abstract
12:30 - 14:15	Lunch
	Semi-plenary Talk Room Pedro Nunes (ground floor)
14:15 - 15:00	What are construction schemes? Osvaldo Guzman (UNAM, Morelia, Mexico) Abstract The method of construction/capturing schemes was introduced by Todorčević. This technique is a powerful tool that allows us to build uncountable structures with finite approximations. We will review this method and some applications. This talk will be an introduction and no previous knowledge of the topic is assumed.
	Semi-plenary Talk Room 17 de Abril (ground floor)
14:15 - 15:00	Quantale-enriched lower separation axioms and the principle of enriched continuous extension Igor Arrieta (University of Birmingham, UK) Abstract Quantale-enriched topological spaces provide a convenient framework to unify constructions from different areas of mathematics such as closed left ideal lattices of non-commutative C^∗-algebras, approach spaces, or quantale-valued topological spaces (see [2]). In this talk, we present a quantale-enriched version of the lower separation axioms, with the goal of proving the principle of enriched continuous extension for quantale-enriched topological spaces. This includes a version of the regularity axiom based on the cocompleteness of 𝔔-enriched topologies viewed as 𝔔^t-enriched categories and requires the concept of closed 𝔔-enriched presheaves. Moreover, forced by the non-idempotency of the quantale multiplication we also present a completely new and weaker form of regularity, under which the Kolmogoroff, Fréchet and Hausdorff separation axioms are all equivalent. Further, and more importantly, weak regularity is sufficient for the formulation of the principle of continuous extension. As a remarkable result, among other things, we point out that in the case of a commutative Girard quantale 𝔔, every projective 𝔔-module in Sup provided with the interval 𝔔-topology is a Hausdorff and weakly regular 𝔔-enriched topological space. This talk is based on [1] and is joint work with Javier Gutiérrez García (University of the Basque Country UPV/EHU) and Ulrich Höhle (Bergische Universität). References: [1] I. Arrieta, J. Gutiérrez García, and U. Höhle, Enriched lower separation axioms and the principle of enriched continuous extension, Fuzzy Sets and Systems 468, art. no. 108633, 2023. [2] J. Gutiérrez García, U. Höhle, and T. Kubiak, Basic concepts of quantale-enriched topologies, Applied Categorical Structures 29, 983-1003, 2021.
	Session: Set-theoretic Topology Room Pedro Nunes (ground floor)
15:00 - 15:30	Cardinal inequalities for Urysohn spaces involving variations of the almost Lindelöf degree Ivan S. Gotchev Abstract
15:30 - 16:00	Hurewicz sets and products in the Laver model Piotr Szewczak Abstract
16:00 - 16:30	More about non-trivial autohomeomorphisms Alan Dow Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
15:00 - 15:30	On ω_{𝒩_T}-limit sets of discrete dynamical systems Michaela Záškolná Abstract
15:30 - 16:00	Renormalization in Lorenz maps – Completely invariant sets and periodic orbits Łukasz Cholewa Abstract
16:00 - 16:30	Choquet simplex of invariant measures for minimal homeomorphisms on manifolds Sejal Babel Abstract
	Session: Topological Dynamics and Continuum Theory Room 2.4 (2nd floor)
15:00 - 15:30	Classification of trees that inscribe hyperbolic ε-rectangles Ulises Morales-Fuentes Abstract
15:30 - 16:00	Endpoint-homogeneous smooth fans Rene Gril Rogina Abstract
16:00 - 16:30	On the dynamics of triangular map and its non-autonomous components Deepanshu Dhawan Abstract
	Session: Topology and Categories - Topology and Order Room 2.5 (2nd floor)
15:00 - 15:30	Complete congruences of completely distributive lattices Luigi Santocanale Abstract
15:30 - 16:00	Closure operators for semitopogenous spaces Tom Richmond Abstract
16:00 - 16:30	An algorithm to detect non-order-preserving braids Nancy Scherich Abstract
16:30 - 17:00	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
17:00 - 17:30	Higher dimensional compactness properties Paul Szeptycki Abstract
17:30 - 18:00	ℕ-compactness and ℕ-compact extensions in the absence of the Axiom of Choice Eliza Wajch Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
17:00 - 17:30	Continuum-wise hyperbolicity Bernardo Carvalho Abstract
17:30 - 18:00	Interval maps with dense periodicity Piotr Oprocha Abstract
19:30	Conference Dinner

Friday, July 12, 2024

	Plenary Talk Room Pedro Nunes (ground floor)
09:00 - 10:00	The appeal of Pointfree Topology (to classical topologists): These are a few of my favorite things Joanne Walters-Wayland (Chapman University, Orange, USA) Abstract It is over half a century since John Isbell's seminal paper “Atomless Parts of Spaces” appeared in Mathematica Scandinavica. The last five decades have witnessed a wonderful expansion and understanding of his vision, much of it led by Bernhard Banaschewski. I will attempt to convince the audience that some of my favourite constructions/ideas in frame/locale theory may be of use to classical topologists. In particular, I will consider Isbell's density theorem, the Lindelöf (co)reflection (and κ generalizations), the “cozero” scaffolding and hollowness, and the paracompact (co)reflection of completely regular frames. If time permits, I will also mention the Bruns-Lakser completion (of a meet-semilattice).
10:00 - 10:30	Coffee Break
	Session: Set-Theoretical Topology Room Pedro Nunes (ground floor)
10:30 - 11:00	Fixed points results in M-metric space with applications to LCR circuits Barakah Almarri Abstract
11:00 - 11:30	Filters on ω and convergence of measures on Boolean algebras Tomasz Żuchowski Abstract
11:30 - 12:00	Game-theoretic results in regards to cardinal functions Lucas Chiozini de Souza Abstract
12:00 - 12:30	r-skeletons and ω-monotone functions Cenobio Yescas-Aparicio Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
10:30 - 11:00	Dynamics of induced mappings on symmetric products Verónica Martínez De la Vega Abstract
11:00 - 11:30	(Strong) sensitive dependence on initial conditions of Mahavier dynamical systems Tina Sovič Abstract
11:30 - 12:00	On equivalence of asymptotic average shadowing and vague specification properties for topological dynamical systems Melih Emin Can Abstract
12:00 - 12:30	Orbit structure in CR-dynamical systems Andrew Wood Abstract
	Session: Topological Methods in Algebra and Analysis Room 2.4 (2nd floor)
10:30 - 11:00	A topological insight into the polar involution of convex sets Natalia Jonard-Pérez Abstract
11:00 - 11:30	Normed and Banach groups Saak Gabriyelyan Abstract
11:30 - 12:00	On commutators acting on some Fréchet spaces over non-Archimedean fields Agnieszka Ziemkowska-Siwek Abstract
12:00 - 12:30	Dynamics of primitive elements under group actions Pratyush Mishra Abstract
	Session: Topology and Order Room 2.5 (2nd floor)
10:30 - 11:00	An introduction to Lebesgue integration in σ-frames Raquel Bernardes Abstract
11:00 - 11:30	Localic properties at infinity Simo S. Mthethwa Abstract
11:30 - 12:00	On some ideals of ℛL Mack Matlabyana Abstract
12:00 - 12:30	Upper powerdomains of quasicontinuous dcpos Zhenchao Lyu Abstract
12:30 - 14:15	Lunch
	Session: Set-theoretic Topology Room Pedro Nunes (ground floor)
14:15 - 14:45	On some applications of the Steinhaus chessboard theorem Michał Dybowski Abstract
14:45 - 15:15	On property (B) in function spaces Kacper Kucharski Abstract
	Session: Topological Dynamics and Continuum Theory Room 17 de Abril (ground floor)
14:15 - 14:45	The specification property of homeomorphisms on tree-like continua Christopher Mouron Abstract
14:45 - 15:15	Dynamics admitted by the Lelek fan Judy Kennedy Abstract
	Session: Topology and Categories Room 2.5 (2nd floor)
14:15 - 14:45	On effective descent morphisms of lax comma categories of ordered sets Maria Manuel Clementino Abstract
14:45 - 15:15	Effective descent morphisms: reflection and preservation Rui Prezado Abstract
	Plenary talk Room Pedro Nunes (ground floor)
15:15 - 16:15	Reconstructing the topology of algebraic structures: how and why Michael Pinsker (Technische Universität Wien, Austria) Abstract Many mathematical objects are naturally equipped with both an algebraic and a topological structure. For example, the automorphism group of any first-order structure is, of course, a group, and in fact a topological group when equipped with the topology of pointwise convergence. While in some cases, e.g. the additive group of the reals, the algebraic structure of the object alone carries strictly less information than together with the topological structure, in other cases its algebraic structure is so rich that it actually determines the topology (under some requirements on the topology): by a result of Kechris and Solecki, the pointwise convergence topology is the only compatible separable topology on the full symmetric group on a countable set. Which topologies are compatible with a given algebraic object has intrigued mathematicians for decades: for example, Ulam asked whether there exists a compatible locally compact Polish topology on the full symmetric group on a countable set (by the above, the answer is negative). The reconstruction of the topologies of automorphism groups, endomorphism monoids, and polymorphism clones of first-order structures is primarily motivated by model-theoretic questions, but also has applications in theoretical computer science. In the case of automorphism groups, the question of the relationship between the algebraic and the topological structure has been pursued actively over the past 40 years. It turns out that many of the most popular automorphism groups, including that of the order of the rationals and of the random graph, have unique Polish topologies. Endomorphism monoids are algebraically not as rich, and often allow many different compatible topologies. We show, however, that there is a unique compatible Polish topology on the endomorphism monoids of the random graph, the weak linear order of the rational numbers, the random poset, and many more.
16:15 - 16:30	Closing
16:30 - 17:00	Coffee Break