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DTSTART;TZID=Europe/Berlin:20251017T133000
DTEND;TZID=Europe/Berlin:20251017T150000
DTSTAMP:20260424T030750
CREATED:20250916T124552Z
LAST-MODIFIED:20250916T124552Z
UID:11688-1760707800-1760713200@crc326gaus.de
SUMMARY:Solid Locally Analytic Representations in Mixed Characteristic
DESCRIPTION:Dr. Gal Porat (Einstein Institute of Mathematics\, Hebrew University of Jerusalem) \nAbstract:\nLocally analytic representations of p-adic Lie groups with Q_p coefficients are powerful tools in p-adic Hodge theory and the p-adic Langlands program. This perspective reveals important differential structures\, such as the Sen and Casimir operators.\nA few years ago\, Rodrigues Jacinto and Rodriguez Camargo developed a “solid” version of this theory using the language of condensed mathematics\, which provides more robust homological tools (comparison theorems\, spectral sequences…) for studying these representations.\nThis talk will present ongoing work that extends this solid theory to a much broader class of mixed characteristic coefficients\, such as F_p((X)) or Z_p[[X]]<p/x>\, as well as semilinear representations. I will conclude by exploring how these ideas relate to mixed characteristic phenomena in p-adic Hodge theory and the Langlands program.
URL:https://crc326gaus.de/event/solid-locally-analytic-representations-in-mixed-characteristic/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
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DTSTART;TZID=Europe/Berlin:20251024T133000
DTEND;TZID=Europe/Berlin:20251024T150000
DTSTAMP:20260424T030750
CREATED:20251017T131844Z
LAST-MODIFIED:20251017T133629Z
UID:11957-1761312600-1761318000@crc326gaus.de
SUMMARY:Some cases of cube sum problem
DESCRIPTION:Dipramit Majumdar (IIT Madras / Universität Heidelberg) \nAbstract: An integer n is said to be a rational cube sum or simply a cube sum if n can be written as a sum of cubes of two rational numbers. For example\, 6 = (17/21)^3+ (37/21)^3. A cube-free integer n > 2 is a cube sum if and only if the elliptic curve y^2=x^3-432n^2 has infinitely many solutions over the rational numbers. A recent result of Alpöge-Bhargava-Shnidman-Burungale-Skinner shows that a positive proportion of integers are cube sums and a positive proportion of integers are not. \nWe will discuss the cube sum problem for some special family of integers. This talk is based on joint works with De\, Jha\, Mondal\, Shingavekar and Sury.
URL:https://crc326gaus.de/event/some-cases-of-cube-sum-problem/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20251024T153000
DTEND;TZID=Europe/Berlin:20251024T170000
DTSTAMP:20260424T030750
CREATED:20250915T102833Z
LAST-MODIFIED:20250915T102833Z
UID:11619-1761319800-1761325200@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Michael Rapoport (University Bonn): Toric schemes and integral models of Shimura varieties \nThe modular curve with Gamma0(p)$-level structure has a beautiful integral model over BZp\, and generalizations of this model to any Shimura variety with p-parahoric level have been constructed in the last 30 years. When passing from Gamma0(p)-level to Gamma1(p)-level\, the situation changes drastically. In the talk I will explain a general method that potentially allows to deal with such level structures. The method is based on the construction of torus embeddings of the maximal torus of a reductive group scheme. Joint work with G. Pappas. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl)
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-241025/
LOCATION:Darmstadt\, Room 401 and Zoom\, Schlossgartenstraße 7\, Darmstadt\, 64289\, Germany
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Sabrina Pauli":MAILTO:pauli@mathematik.tu-darmstadt.de
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