Seminar iz topologije

Vodji seminarja: Tina Sovič in Jernej Činč.
Predavanja potekajo ob petkih ob 13:00 v predavalnici 01/20.

Bodoča predavanja

Razpletne uganke: izvor, analiza in strategija reševanja

Predavatelj: Maj Turnšek

Povzetek: Razpletne uganke (ang. disentanglement puzzles) so vrsta mehanskih ugank, pri katerih je cilj s pomočjo topološkega razmisleka in prostorske predstave ločiti med seboj prepletene dele (npr. kovinske žice, obroče, vrvi, lesene objekte) brez uporabe sile ali rezanja. Na predavanju bodo obiskovancem na voljo štirje enostavni ter trije zahtevnejši primeri teh ugank, namenjeni interaktivni popestritvi.

Za začetek bomo predstavili eno najstarejših znanih tovrstnih ugank – kitajske obroče. S pomočjo binarnih števil bomo pokazali, kako poteka reševanje, ter opazovali zanimive vzorce v zaporedju korakov. Na tej osnovi bomo določili, koliko korakov je v splošnem potrebnih za rešitev uganke s poljubnim številom obročev.

Nato se bomo posvetili glavnemu delu – analizi ter strategiji reševanja ene od zahtevnejših ugank in skonstruirali t.i. “superalgoritem”, katerega lastnost ne bo rešila le uganke, ampak tudi osrednje vprašanje – ali ima lahko razpletna uganka več kot eno rešitev?

Predavanje bo 8. 5. 2026 ob 12:00 v predavalnici 01/20.

Minula predavanja

On pseudoarc and dynamics

Predavatelj: Piotr Oprocha (AGH University of Science and Technology, Krakow, Poland)

Abstract: The pseudoarc is an intriguing continuum that was discovered by Knaster 100 years ago. While its structure is very complicated, Bing proved that from topological perspective, pseudoarc is the typical continuum to encounter in the plane.
In this talk I will present selected results connecting pseudoarc as topological object with selected properties of dynamical systems.

Dynamics and complicated continua

Predavatelj: Udayan B. Darji (University of Louisville)

Abstract: Suppose we have a continuum X and f a continuous surjection of X. In this talk we will discuss some results in which dynamics of f imply complicated structure of X as well as the inverse limit determined by (X,f). All notions will be defined. The talk will be accessible to graduate students and nonspecialists.

A classification of strange attractors: the inverse limit approach

Predavatelj: Jan Boroński (AGH University of Science and Technology)

I will present my joint work with Sonja Štimac on classification of strange attractors. Among the many results, our work relies on the notion of mild dissipation [CP], which allows for an inverse limit description, in terms of densely branching trees [BS].

For a large family of attractors, that include those of Lozi and Henon, two strange attractors are equivalent if and only if their kneading sequences coincide, if and only if their folding patterns agree.

References:
[BC] M. Benedicks, L.A.E. Carleson, The dynamics of the Henon map, Annals of Mathematics 133 (1991), 73–169.
[BS] J. Boroński, S. Štimac, Densely branching trees as models for Henon-like and Lozi-like attractors, preprint 2021, arXiv:2104.14780
[CP] S. Crovisier, E. Pujals, Strongly dissipative surface diffeomorphisms, Commentarii Mathematici Helvetici 93 (2018), 377–400.
[MS] M. Misiurewicz, S. Štimac, Symbolic dynamics for Lozi maps, Nonlinearity 29 (2016), 3031–3046.
[WY] Wang, Q.; Young, L.-S. Strange attractors with one direction of instability. Comm. Math. Phys. 218 (2001), 1–97.

Arcs, circles and inverse limits

Predavateljica: Sina Greenwood (Univerza v Aucklandu, Auckland, Nova Zelandija)

Povzetek: In this talk I will give a characterisation of inverse limits of continuous functions on intervals that are arcs. In addition, I will discuss inverse limits of set-valuad functions that are graphs, and in particular, arcs or circles.

Predavanje bo v prostoru 0/103 na Koroški cesti 160.

Štiri črte

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Dve črti

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Entropija (3. del)

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Entropija (2. del)

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS teams – za vstop v predavalnico uporabite kodo w20dsjj

Entropija (1. del)

Predavatelj: Iztok Banič
Predavanje bo na daljavo v MS Teams – za vstop v predavalnico uporabite kodo w20dsjj

 

Trees and inverse limits of set-valued functions on intervals

Predavateljica: Sina Greenwood (Univerza v Aucklandu, Nova Zelandija)

Povzetek: I will consider inverse limits of sequences of upper semicontinuous set-valued functions on intervals for which the graph of each bonding function is an arc. I will show how to construct any finite tree as such an inverse limit, and one for which each bonding function is one of two specified functions. I will also touch on infinite trees.

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