BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lior Yanovski (Max Planck Institute) DTSTART:20210823T140000Z DTEND:20210823T150000Z DTSTAMP:20260423T004755Z UID:MITTop/38 DESCRIPTION:Title: The chromatic discrete Fourier transform\nby Lior Yanovski (Max Planck Institute) as part of MIT topology seminar\n\n\nAbstract\nThe classical d iscrete Fourier transform can be thought of as an isomorphism of rings bet ween the complex group algebra of a finite abelian group A and the algebra of functions on its Pontyagin dual. Hopkins and Lurie have proved an anal ogous result in the chromatic world\, where the field of complex numbers i s replaced by the Lubin-Tate spectrum E_n\, the finite abelian group A is replaced by a suitably finite p-power torsion Z-module spectrum\, and the Pontryagin dual is modified by an n-fold suspension. From this\, they dedu ce a number of structural properties of the infinity-category of K(n)-loca l spectra\, such as affineness and Eilenberg-Moore type formulas for pi-fi nite spaces. In this talk\, I will present a joint work with Barthel\, Car meli\, and Sclank\, in which we develop the notion of a `higher Discrete F ourier transform' for general higher semiadditive infinity-categories. Thi s allows us\, among other things\, to extend the above results of Hopkins and Lurie to the T(n)-local setting. Furthermore\, we study the interactio n of Fourier transforms with categorification suggesting a close relations hip to chromatic redshift phenomena. Finally\, by replacing Pontryagin dua lity with Brown-Comenetz duality\, we can contemplate the notion of Fourie r transform for more general pi-finite spectra than Z-modules\, leading to questions intimately related to the behavior of the `discrepancy spectru m'.\n LOCATION:https://researchseminars.org/talk/MITTop/38/ END:VEVENT END:VCALENDAR