I will discuss recent developments around the theme of bubble
towers in the context of critical wave equations. Solutions of this type
figure prominently in the so-called soliton resolution results\, and they
also play a role in the classification of dynamics around certain ground s
tate solutions. In particular\, I will discuss recent work joint with Jend
rej and with Palacios.
\;
The Obukhov--Corrsin spectrum predicts the distribution of Fo urier mass for a passive scalar field advected by a "turbulent" velocity f ield with spatial regularity C^\\alpha_x for \\alpha \\in (0\,1) and subje ct to a time-stationary forcing. We prove the Obukhov--Corrsin spectrum ho lds after summing over geometric annuli in Fourier space -- up to logarith mic corrections -- as a consequence of a sharp anomalous regularization re sult. We then prove this anomalous regularization for a broad class of Kra ichnan-type models. The proof of anomalous regularization relies on a Four ier space \\ell^p energy equality and a weighted lattice Poincaré inequal ity.
DTEND;TZID=Europe/Zurich:20260522T181500 END:VEVENT BEGIN:VEVENT UID:news2027@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260416T140828 DTSTART;TZID=Europe/Zurich:20260602T161500 SUMMARY:PhD Defense Mathematics: Florian Lanz DESCRIPTION:Tales From the Fractional Gelfand Equation X-ALT-DESC:Tales From the Fractional Gelfand Equation\n\n END:VEVENT BEGIN:VEVENT UID:news1976@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20260129T123017 DTSTART;VALUE=DATE:20260831 SUMMARY:Cremona Conference 2026 DESCRIPTION:31.8. - 4.9.2026 in Basel\, Switzerland\\r\\n7.9. - 11.9.2026 i n Neuchâtel\, Switzerland\\r\\nThe first week will feature a summer schoo l at the University of Basel\, offering five introductory mini-courses des igned to introduce junior researchers to this rich and beautiful area of m athematics. The second week will host a research conference at the Univers ity of Neuchâtel\, bringing together leading experts to share recent brea kthroughs\, exchange ideas\, and provide opportunities for new collaborati ons. The aim of the event is to bring together diverse perspectives on Cre mona groups—from birational geometry and dynamics to geometric group the ory and beyond. The program will also include poster sessions and short ta lks by young participants.\\r\\n\\r\\nFor updates and more information\, p lease visit the Cremona Conference 2026 website [https://www.cremonaconfer ence.ch/index.html]. X-ALT-DESC:31.8. - 4.9.2026 in Basel\, Switzerland
\ n7.9. - 11.9.2026 in Neuchâtel\, Switzerland
\nThe first week will feature a summer school at the University of Basel\, o ffering five introductory mini-courses designed to introduce junior resear chers to this rich and beautiful area of mathematics. The second week will host a research conference at the University of Neuchâtel\, bringing tog ether leading experts to share recent breakthroughs\, exchange ideas\, and provide opportunities for new collaborations. The aim of the event is to bring together diverse perspectives on Cremona groups—from birational ge ometry and dynamics to geometric group theory and beyond. The program will also include poster sessions and short talks by young participants.
\n \nFor updates and more information\, please visit the Cremona Conference 2026 website.< /p> DTEND;VALUE=DATE:20260911 END:VEVENT END:VCALENDAR