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 Favard length decay of random Cantor sets September 15 14:00 - 15:00 Ville Suomala: Sharp Favard length decay of random Cantor sets
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Paige Bright: Radial Projections and Beck-type Problems September 17 11:00 - 12:00 Paige Bright: Radial Projections and Beck-type Problems
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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]: Fourier decay from L^2-flattening September 21 11:15 - 12:15 Amlan Banaji [WS1]: Fourier decay from L^2-flattening
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Ana de Orellana [WS1]: Finding 3APs in fractal sets September 21 14:00 - 15:00 Ana de Orellana [WS1]: Finding 3APs in fractal sets
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Jonathan Fraser [WS1]: Quantitative flatness and Fourier decay September 21 15:45 - 16:45 Jonathan Fraser [WS1]: Quantitative flatness and Fourier decay
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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]: Estimates of Brascamp-Lieb constants September 22 11:15 - 12:15 Weikun He [WS1]: Estimates of Brascamp-Lieb constants
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Mike Hochman [WS1]: Transverse orbits in dimension zero September 22 14:00 - 15:00 Mike Hochman [WS1]: Transverse orbits in dimension zero
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Joel Moreira [WS1]: Transversality for fractal sets of integers September 23 09:30 - 10:30 Joel Moreira [WS1]: Transversality for fractal sets of integers
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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]: Dimensions of surface repellers and attractors of non-linear planar IFSs September 23 14:00 - 15:00 Jialun Li [WS1]: Dimensions of surface repellers and attractors of non-linear planar IFSs
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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]: Curved Kakeya sets and maximal estimates September 24 09:30 - 10:30 Ruixiang Zhang [WS1]: Curved Kakeya sets and maximal estimates
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Meng Wu [WS1]: Projections of Regular Fractal Sets September 24 11:15 - 12:15 Meng Wu [WS1]: Projections of Regular Fractal Sets
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Florian Richter [WS1]: Local Fourier analysis in the integers September 24 14:00 - 15:00 Florian Richter [WS1]: Local Fourier analysis in the integers
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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]: Subspaces, angles and Diophantine approximation September 25 11:15 - 12:15 Nicolas de Saxcé [WS1]: Subspaces, angles and Diophantine approximation
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Damian Dabrowski: Favard length of non-homogeneous random Cantor sets September 29 14:00 - 15:00 Damian Dabrowski: Favard length of non-homogeneous random Cantor sets
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Gaétan Leclerc: The Fractal Van Der Corput Lemma October 01 11:00 - 12:00 Gaétan Leclerc: The Fractal Van Der Corput Lemma
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Félix Lequen: Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than 1/2 October 01 14:00 - 15:00 Félix Lequen: Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than 1/2
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Barak Weiss: Recent progress on Minkowski’s conjecture October 08 11:00 - 12:00 Barak Weiss: Recent progress on Minkowski’s conjecture
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Don Stull: Incidence bounds in higher dimensions, and their applications to distance sets in R^3 and R^4 October 08 14:00 - 15:00 Don Stull: Incidence bounds in higher dimensions, and their applications to distance sets in R^3 and R^4
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Yotam Smilansky: Patterns and Projections of Zeros of Exponential Polynomials October 13 11:00 - 12:00 Yotam Smilansky: Patterns and Projections of Zeros of Exponential Polynomials
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Kenneth Falconer: TBA October 15 11:00 - 12:00 Kenneth Falconer: TBA
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Emilio Corso: TBA October 15 14:00 - 15:00 Emilio Corso: TBA
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Antti Käenmäki: Exponential separation of self-conformal systems October 20 11:00 - 12:00 Antti Käenmäki: Exponential separation of self-conformal systems
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Itamar Oliveira: TBA October 20 14:00 - 15:00 Itamar Oliveira: TBA
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Will O’Regan: TBA October 22 14:00 - 15:00 Will O’Regan: TBA
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Pär Kurlberg: Quantum ergodicity for higher dimensional cat maps October 27 11:00 - 12:00 Pär Kurlberg: Quantum ergodicity for higher dimensional cat maps
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Vincent Ferrari-Dominguez: TBA October 27 14:00 - 15:00 Vincent Ferrari-Dominguez: TBA
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Elena Kim: TBA October 29 11:00 - 12:00 Elena Kim: TBA
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Tamás Keleti: TBA November 03 11:00 - 12:00 Tamás Keleti: TBA
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Alex Rutar: TBA November 03 14:00 - 15:00 Alex Rutar: TBA
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Lauritz Streck: TBA November 05 11:00 - 12:00 Lauritz Streck: TBA
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Zhiyuan Zhang: TBA November 05 14:00 - 15:00 Zhiyuan Zhang: TBA
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Xiong Jin: TBA November 10 11:00 - 12:00 Xiong Jin: TBA
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Sascha Troscheit: TBA November 10 14:00 - 15:00 Sascha Troscheit: 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 |
| Riku Anttila | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Dec 6 - Dec 11 |
| 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: Nov 15 - Nov 27 |
| 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) |
| Ryan Bushling | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Oct 5 - Oct 15 |
| 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 |
| Leonardo Franchi | University: University of Cambridge | Country: United Kingdom | Arrival and Departure: Nov 21 - Nov 29 |
| 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 |
| Attila Gáspár | University: Eötvös Loránd University | Country: Hungary | Arrival and Departure: Oct 18 - Nov 7 |
| 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) |
| Xiong Jin | University: University of Manchester | Country: United Kingdom | Arrival and Departure: Oct 24 - Nov 11 |
| 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: Oct 21 - 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 26 |
| 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 15 - 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 17 - Nov 28 |
| Dominique Maldague | University: University of Cambridge & University of California, Los Angeles | Country: United States | Arrival and Departure: Oct 25 - Nov 24 |
| Mirmuhsin Maxmud | University: University of Oulu | Country: Finland | Arrival and Departure: Oct 10 - Nov 8 |
| 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 |
| Markus Myllyoja | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Nov 24 - Dec 9 |
| Arian Nadjimzadah | 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 |
| Itamar Oliveira | University: University of Birmingham | Country: United Kingdom | Arrival and Departure: Oct 3 - Nov 7 |
| Vilma Orgovanyi | University: Budapest University of Technology and Economics | Country: Hungary | Arrival and Departure: Oct 4 - Nov 23 |
| 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 (1st visit) |
| Mark Pollicott | University: University of Warwick | Country: United Kingdom | Arrival and Departure: Oct 10 - Oct 17 (2nd visit) |
| Aleksi Pyörälä | University: University of Oulu | Country: Finland | Arrival and Departure: Nov 29 - Dec 5 |
| Firdavs Rakhmonov | University: University of St Andrews | Country: United Kingdom | Arrival and Departure: Nov 20 - Nov 27 |
| 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 (1st visit) |
| Hrit Roy | University: University of Jyväskylä | Country: Finland | Arrival and Departure: Oct 15 - Nov 15 (2nd visit) |
| 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 21 - Sep 22 (2nd visit) |
| Pablo Shmerkin | University: University of British Columbia | Country: Canada | Arrival and Departure: Sep 27 - Oct 17 (3rd visit) |
| Pablo Shmerkin | University: University of British Columbia | Country: Canada | Arrival and Departure: Oct 31 - Nov 20 (4th 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 |
| Adam Śpiewak | University: Institute of Mathematics of the Polish Academy of Sciences | Country: Poland | Arrival and Departure: Oct 12 - Oct 31 |
| 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) |
| 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 19 - Sep 22 (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 |
| Charlie Wilson | University: University of Exeter | Country: United Kingdom | Arrival and Departure: Oct 25 - Nov 7 |
| 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 |
| 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 |