2026. 01. 19. 10:05 - 2026. 01. 19. 10:55
BME, Building H, Room 207 and Zoom
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Event type:
seminar
Organizer:
Institute
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BME Fractal Geometry Seminar
Description
Date: Monday, January 19, 2026
Time: 10:05-10:55 (CET)
Location: BME, Building H, Room 207 (new location!)
Zoom: https://us02web.zoom.us/j/84790223716?pwd=ipOteYh5W16eKGJ9pk3cmVDqfZ8GCw.1
Meeting ID: 847 9022 3716
Passcode: 777959
Time: 10:05-10:55 (CET)
Location: BME, Building H, Room 207 (new location!)
Zoom: https://us02web.zoom.us/j/84790223716?pwd=ipOteYh5W16eKGJ9pk3cmVDqfZ8GCw.1
Meeting ID: 847 9022 3716
Passcode: 777959
(new Zoom link!)
Speaker: Attila Gáspár (Eötvös Loránd University)
Title: Lipschitz surjections between self-similar sets
Abstract:
We consider the following problem: given two self-similar sets satisfying the SSC, does there exist a Lipschitz surjection between them? A positive answer was given by Balka and Keleti when the domain has strictly larger Hausdorff dimension than the codomain, however, the case of equal Hausdorff dimension is still open. We will restrict the problem to the case when one of the sets has logarithmically commensurable similarity ratios, that is, the ratios are integer powers of the same positive real number. Under this assumption, a complete characterization can be given for the existence of a Lipschitz surjection, generalizing previous results which assumed homogeneity. We will see how generalizing the problem to graph-directed fractals lets us to reduce the commensurable case to an essentially homogeneous case, allowing us to apply techniques from previous results of Xi and Xiong, and of Ruan and Xiao
Title: Lipschitz surjections between self-similar sets
Abstract:
We consider the following problem: given two self-similar sets satisfying the SSC, does there exist a Lipschitz surjection between them? A positive answer was given by Balka and Keleti when the domain has strictly larger Hausdorff dimension than the codomain, however, the case of equal Hausdorff dimension is still open. We will restrict the problem to the case when one of the sets has logarithmically commensurable similarity ratios, that is, the ratios are integer powers of the same positive real number. Under this assumption, a complete characterization can be given for the existence of a Lipschitz surjection, generalizing previous results which assumed homogeneity. We will see how generalizing the problem to graph-directed fractals lets us to reduce the commensurable case to an essentially homogeneous case, allowing us to apply techniques from previous results of Xi and Xiong, and of Ruan and Xiao