Interactions between fractal geometry, harmonic analysis, and dynamical systems
September 2 - December 11, 2026
The purpose of the semester is to unite experts working at the interfaces between fractal geometry, harmonic analysis, and dynamical systems. These areas have become increasingly intertwined in the 2000s. Some of the most striking recent progress in each of fields has resulted from surprising input from the two others. The three main aims of the semester are to discover further connections between the fields, to facilitate experts in one field to rapidly gain a deeper understanding of the other two, and to provide junior mathematicians a unique opportunity gain experience in all three areas, early-on in their careers.
Examples of specific topics covered by the semester include (i) problems in continuum incidence geometry related to Kakeya sets, distance sets, and projections, sum-product theory, and finding patterns in fractal sets, (ii) connections between these problems with Fourier restriction and decoupling theory, fractal uncertainty principles in quantum chaos, and Fourier decay problems for dynamically defined fractal measures, (iii) the theory of effective equidistribution of random walks on groups.
The scientific programme of the semester will contain two week-long workshops, and several weekly seminars.
Workshop 1: September 21 — September 25
Workshop 2: November 16 — November 20
Seminars Scroll to the next upcoming seminar
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Manfred Einsiedler: Measure rigidity for diagonalisable flows (generic rank two tori in split groups) September 03 11:00 - 12:00 -
Alexia Yavicoli: On the Erdős Similarity Conjecture September 08 11:00 - 12:00 Alexia Yavicoli: On the Erdős Similarity Conjecture
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Iqra Altaf: Decoupling on the fractal sets of the Parabola September 08 14:00 - 15:00 Iqra Altaf: Decoupling on the fractal sets of the Parabola
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Timothée Bénard: Bounded harmonic functions on Lie groups September 10 11:00 - 12:00 Timothée Bénard: Bounded harmonic functions on Lie groups
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Hrit Roy: Nikodym maximal function with restricted directions September 15 11:00 - 12:00 Hrit Roy: Nikodym maximal function with restricted directions
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Ville Suomala: Sharp asymptotic Favard length for random Cantor sets September 15 14:00 - 15:00 Ville Suomala: Sharp asymptotic Favard length for random Cantor sets
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Paige Bright: TBA September 17 11:00 - 12:00 Paige Bright: TBA
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Joshua Zahl [WS1]: On the existence of Nikodym-type sets September 21 09:30 - 10:30 Joshua Zahl [WS1]: On the existence of Nikodym-type sets
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Amlan Banaji [WS1]: TBA September 21 11:15 - 12:15 Amlan Banaji [WS1]: TBA
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Ana de Orellana [WS1]: TBA September 21 14:00 - 15:00 Ana de Orellana [WS1]: TBA
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Jonathan Fraser [WS1]: TBA September 21 15:45 - 16:45 Jonathan Fraser [WS1]: TBA
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Semyon Dyatlov [WS1]: Fractal uncertainty principle and projection theory September 22 09:30 - 10:30 Semyon Dyatlov [WS1]: Fractal uncertainty principle and projection theory
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Weikun He [WS1]: TBA September 22 11:15 - 12:15 Weikun He [WS1]: TBA
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Mike Hochman [WS1]: TBA September 22 14:00 - 15:00 Mike Hochman [WS1]: TBA
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Joel Moreira [WS1]: TBA September 23 09:30 - 10:30 Joel Moreira [WS1]: TBA
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Ariel Rapaport [WS1]: Dimension of self-conformal measures associated to exponentially separated analytic IFSs September 23 11:15 - 12:15 Ariel Rapaport [WS1]: Dimension of self-conformal measures associated to exponentially separated analytic IFSs
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Jialun Li [WS1]: TBA September 23 14:00 - 15:00 Jialun Li [WS1]: TBA
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Rajula Srivastava [WS1]: Counting Rational Points Near Space Curves September 23 15:45 - 16:45 Rajula Srivastava [WS1]: Counting Rational Points Near Space Curves
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Ruixiang Zhang [WS1]: TBA September 24 09:30 - 10:30 Ruixiang Zhang [WS1]: TBA
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Meng Wu [WS1]: TBA September 24 11:15 - 12:15 Meng Wu [WS1]: TBA
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Florian Richter [WS1]: TBA September 24 14:00 - 15:00 Florian Richter [WS1]: TBA
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Zhongkai Tao [WS1]: Escape of mass for finite-area hyperbolic surfaces September 24 15:45 - 16:45 Zhongkai Tao [WS1]: Escape of mass for finite-area hyperbolic surfaces
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Alex Iosevich [WS1]: Spectral synthesis, geometry, and complexity September 25 09:30 - 10:30 Alex Iosevich [WS1]: Spectral synthesis, geometry, and complexity
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Nicolas de Saxcé [WS1]: TBA September 25 11:15 - 12:15 Nicolas de Saxcé [WS1]: TBA
Recordings
Participants
| Name | University | Country | Arrival and Departure |
|---|---|---|---|
| Giovanni Alberti | University: University of Pisa | Country: Italy | Arrival and Departure: Dec 1 - Dec 11 |
| Amir Algom | University: University of Haifa–Oranim | Country: Israel | Arrival and Departure: Oct 4 - Oct 9 (1st visit) |
| Amir Algom | University: University of Haifa–Oranim | Country: Israel | Arrival and Departure: Nov 15 - Nov 20 (2nd visit) |
| Iqra Altaf | University: University of California | Country: United States | Arrival and Departure: Sep 6 - Sep 28 |
| Roope Anttila | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Nov 27 - Dec 11 |
| Simon Baker | University: Loughborough University | Country: United Kingdom | Arrival and Departure: Oct 11 - Oct 23 |
| Amlan Banaji | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 20 - Oct 1 (1st visit) |
| Amlan Banaji | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Nov 15 - Nov 21 (2nd visit) |
| Timothée Bénard | University: CNRS - Université Sorbonne Paris-Nord | Country: France | Arrival and Departure: Sep 7 - Sep 14 |
| Michael Bersudsky | University: Max Planck Institute for Mathematics in the Sciences | Country: Germany | Arrival and Departure: Nov 22 - Dec 5 |
| Kristian Bjerklöv | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Michael Björklund | University: Chalmers University of Technology | Country: Sweden | Arrival and Departure: Sep 1 - Dec 11 |
| Tainara Borges | University: University of Pennsylvania | Country: United States | Arrival and Departure: Oct 30 - Nov 15 |
| Emmanuel Breuillard | University: University of Oxford | Country: United Kingdom | Arrival and Departure: Sep 28 - Dec 11 |
| Paige Bright | University: Massachusetts Institute of Technology | Country: United States | Arrival and Departure: Sep 2 - Oct 31 (1st visit) |
| Paige Bright | University: Massachusetts Institute of Technology | Country: United States | Arrival and Departure: Nov 11 - Dec 11 (2nd visit) |
| Alex Cohen | University: New York University | Country: United States | Arrival and Departure: Nov 11 - Nov 23 |
| Emilio Corso | University: Pennsylvania University | Country: United States | Arrival and Departure: Sep 27 - Oct 18 |
| Marianna Csörnyei | University: University of Chicago | Country: United States | Arrival and Departure: Nov 13 - Dec 11 |
| Damian Dabrowski | University: Institute of Mathematics of the Polish Academy of Sciences | Country: Poland | Arrival and Departure: Sep 20 - Oct 2 |
| Ana de Orellana | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 19 - Nov 21 |
| Nicolas de Saxcé | University: Centre National de la Recherche Scientifique – Université Sorbonne Paris Nord | Country: France | Arrival and Departure: Sep 7 - Dec 11 |
| Yiheng Dong | University: Stony Brook University, Institute of Mathematics of the Polish Academy of Sciences | Country: Poland | Arrival and Departure: Sep 9 - Sep 28 |
| Semyon Dyatlov | University: Massachusetts Institute of Technology | Country: United States | Arrival and Departure: Sep 20 - Sep 26 |
| Samuel Edwards | University: Uppsala University | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Manfred Einsiedler | University: ETH Zürich | Country: Switzerland | Arrival and Departure: Sep 1 - Sep 12 |
| Kenneth Falconer | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Oct 10 - Oct 30 |
| De-Jun Feng | University: The Chinese University of Hong Kong | Country: Hong Kong, China | Arrival and Departure: Nov 28 - Dec 11 |
| Zhou Feng | University: Technion – Israel Institute of Technology | Country: Israel | Arrival and Departure: Nov 20 - Dec 6 |
| Vincent Ferrari-Dominguez | University: IRMA | Country: France | Arrival and Departure: Oct 17 - Oct 31 |
| Jonathan Fraser | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Sep 20 - Sep 26 (1st visit) |
| Jonathan Fraser | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Nov 15 - Nov 21 (2nd visit) |
| Katrin Fässler | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 1 - Sep 15 |
| Shengwen Gan | University: University of Wisconsin-Madison | Country: United States | Arrival and Departure: Sep 2 - Sep 27 |
| Alexander Gorodnik | University: University of Zurich | Country: Switzerland | Arrival and Departure: Nov 22 - Nov 28 |
| Shaoming Guo | University: Chern Institute, Nankai University | Country: China | Arrival and Departure: Sep 1 - Dec 12 |
| Weikun He | University: Academy of Mathematics and System Science, Chinese Academy of Sciences | Country: China | Arrival and Departure: Sep 2 - Oct 7 |
| Jonathan Hickman | University: University of Edinburgh | Country: United Kingdom | Arrival and Departure: Nov 24 - Dec 11 |
| Michael Hochman | University: The Hebrew University of Jerusalem | Country: Israel | Arrival and Departure: Sep 13 - Sep 27 |
| Alex Iosevich | University: University of Rochester | Country: United States | Arrival and Departure: Sep 1 - Sep 13 (1st visit) |
| Alex Iosevich | University: University of Rochester | Country: United States | Arrival and Departure: Sep 20 - Oct 1 (2nd visit) |
| Natalia Jurga | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Sep 2 - Sep 16 |
| Tamás Keleti | University: Eötvös Loránd University | Country: Hungary | Arrival and Departure: Nov 1 - Nov 14 (1st visit) |
| Tamás Keleti | University: Eötvös Loránd University | Country: Hungary | Arrival and Departure: Nov 28 - Dec 11 (2nd visit) |
| Osama Khalil | University: University of Illinois Chicago | Country: United States | Arrival and Departure: Nov 15 - Nov 28 |
| Elena Kim | University: Harvard University | Country: United States | Arrival and Departure: Oct 25 - Oct 31 |
| Henna Koivusalo | University: University of Bristol | Country: United Kingdom | Arrival and Departure: Oct 25 - Dec 12 |
| Istvan Kolossvary | University: Alfréd Rényi Institute of Mathem | Country: Hungary | Arrival and Departure: Oct 25 - Nov 15 |
| Vjekoslav Kovac | University: University of Zagreb | Country: Croatia | Arrival and Departure: Nov 15 - Nov 21 |
| Pär Kurlberg | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Antti Käenmäki | University: University of Eastern Finland | Country: Finland | Arrival and Departure: Sep 1 - Sep 9 (1st visit) |
| Antti Käenmäki | University: University of Eastern Finland | Country: Finland | Arrival and Departure: Oct 18 - Oct 25 (2nd visit) |
| Gaétan Leclerc | University: University of Helsinki | Country: France | Arrival and Departure: Sep 2 - Dec 11 |
| Felix Lequen | University: Université Sorbonne Paris Nord | Country: France | Arrival and Departure: Sep 7 - Oct 10 |
| Jialun Li | University: Fudan University | Country: China | Arrival and Departure: Sep 19 - Nov 7 |
| Jianhui Li | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Nov 20 - Dec 4 |
| Zuo Lin | University: University of California, Berkeley | Country: China | Arrival and Departure: Sep 2 - Nov 30 |
| Elon Lindenstrauss | University: Institute for Advanced Study and The Hebrew University of Jerusalem | Country: United States | Arrival and Departure: Nov 15 - Nov 28 |
| Dominique Maldague | University: University of Cambridge & University of California, Los Angeles | Country: United States | Arrival and Departure: Oct 25 - Nov 24 |
| Alexandre Minetto | University: University of Helsinki | Country: Finland | Arrival and Departure: Sep 6 - Sep 9 |
| Joel Moreira | University: University of Warwick | Country: United Kingdom | Arrival and Departure: Sep 14 - Sep 25 |
| Arian Nadijmzadah | University: University of California, Los Angeles | Country: United States | Arrival and Departure: Sep 1 - Dec 12 |
| Will O'Regan | University: University of British Columbia | Country: Canada | Arrival and Departure: Sep 7 - Dec 11 |
| Tuomas Orponen | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 1 - Oct 17 (1st visit) |
| Tuomas Orponen | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Nov 15 - Nov 20 (2nd visit) |
| Wenyu Pan | University: University of Toronto | Country: Canada | Arrival and Departure: Nov 15 - Dec 11 |
| Sampo Paukkonen | University: University of Helsinki | Country: Finland | Arrival and Departure: Sep 2 - Sep 8 |
| Mark Pollicott | University: University of Warwick | Country: United Kingdom | Arrival and Departure: Sep 19 - Sep 26 |
| Aleksi Pyörälä | University: University of Oulu | Country: Finland | Arrival and Departure: Nov 29 - Dec 5 |
| Ariel Rapaport | University: Technion – Israel Institute of Technology | Country: Israel | Arrival and Departure: Sep 15 - Sep 30 |
| Haojie Ren | University: Technion – Israel Institute of Technology | Country: Israel | Arrival and Departure: Oct 1 - Oct 8 |
| Florian Richter | University: École polytechnique fédérale de Lausanne (EPFL) | Country: Switzerland | Arrival and Departure: Sep 11 - Sep 30 |
| Hrit Roy | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 11 - Sep 18 |
| Alex Rutar | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Sep 1 - Dec 12 |
| Tuomas Sahlsten | University: University of Helsinki | Country: Finland | Arrival and Departure: Sep 2 - Dec 12 |
| Pablo Shmerkin | University: University of British Columbia | Country: Canada | Arrival and Departure: Sep 1 - Sep 19 (1st visit) |
| Pablo Shmerkin | University: University of British Columbia | Country: Canada | Arrival and Departure: Sep 27 - Oct 17 (2nd visit) |
| Pablo Shmerkin | University: University of British Columbia | Country: Canada | Arrival and Departure: Oct 31 - Nov 20 (3rd visit) |
| Olof Sisask | University: Stockholm University | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Yotam Smilansky | University: University of Manchester | Country: United Kingdom | Arrival and Departure: Oct 10 - Oct 18 |
| Boris Solomyak | University: Bar Ilan University | Country: Israel | Arrival and Departure: Nov 8 - Nov 12 |
| Rajula Srivastava | University: University of Wisconsin-Madison | Country: United States | Arrival and Departure: Sep 9 - Nov 8 |
| Lauritz Streck | University: University of Edinburgh | Country: United Kingdom | Arrival and Departure: Sep 2 - Sep 12 (1st visit) |
| Lauritz Streck | University: University of Edinburgh | Country: United Kingdom | Arrival and Departure: Oct 24 - Nov 29 (2nd visit) |
| Andreas Strömbergsson | University: Uppsala University | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Donald Stull | University: University of Chicago | Country: United States | Arrival and Departure: Oct 1 - Oct 15 |
| Ville Suomala | University: University of Oulu | Country: Finland | Arrival and Departure: Sep 6 - Sep 20 (1st visit) |
| Ville Suomala | University: University of Oulu | Country: Finland | Arrival and Departure: Oct 4 - Oct 18 (2nd visit) |
| Nattalie Tamam | University: Imperial College London | Country: | Arrival and Departure: Oct 12 - Oct 25 |
| Zhongkai Tao | University: Institut des hautes études scientifiques | Country: France | Arrival and Departure: Sep 2 - Oct 30 |
| Sascha Troscheit | University: Uppsala University | Country: Sweden | Arrival and Departure: Sep 2 - Dec 11 |
| Shunsuke Usuki | University: Keio University | Country: Japan | Arrival and Departure: Oct 1 - Dec 12 |
| Sanju Velani | University: York University | Country: Canada | Arrival and Departure: Nov 22 - Dec 5 |
| Hong Wang | University: Courant Institute of Mathematical Sciences, Institut des Hautes Études Scientifiques | Country: United States | Arrival and Departure: Sep 16 - Sep 25 (1st visit) |
| Hong Wang | University: Courant Institute of Mathematical Sciences, Institut des Hautes Études Scientifiques | Country: United States | Arrival and Departure: Nov 15 - Nov 28 (2nd visit) |
| Barak Weiss | University: Tel Aviv University | Country: Israel | Arrival and Departure: Oct 6 - Oct 21 |
| Meng Wu | University: Hunan University | Country: China | Arrival and Departure: Sep 18 - Oct 12 |
| Shukun Wu | University: Indiana University | Country: United States | Arrival and Departure: Nov 14 - Nov 29 |
| Lei Yang | University: National University of Singapore | Country: Singapore | Arrival and Departure: Nov 15 - Nov 21 |
| Alexia Yavicoli | University: University of British Columbia | Country: Canada | Arrival and Departure: Sep 2 - Sep 13 |
| Guangzeng Yi | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Oct 5 - Oct 11 |
| Joshua Zahl | University: Chern Institute, Nankai University | Country: China | Arrival and Departure: Sep 10 - Nov 29 |
| Dmitrii Zakharov | University: Massachusetts Institute of Technology | Country: United States | Arrival and Departure: Sep 28 - Dec 6 |
| Ruixiang Zhang | University: University of California, Berkeley | Country: United States | Arrival and Departure: Sep 21 - Sep 25 (1st visit) |
| Ruixiang Zhang | University: UC Berkeley | Country: USA | Arrival and Departure: Nov 15 - Nov 21 (2nd visit) |
| Zhiyuan Zhang | University: Imperial College London | Country: United Kingdom | Arrival and Departure: Nov 3 - Nov 5 |
| Tamar Ziegler | University: The Hebrew University of Jerusalem | Country: Israel | Arrival and Departure: Nov 15 - Nov 21 |