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DTSTART;TZID=Europe/Berlin:20241018T153000
DTEND;TZID=Europe/Berlin:20241018T170000
DTSTAMP:20260424T231257
CREATED:20240909T081154Z
LAST-MODIFIED:20240912T122506Z
UID:9170-1729265400-1729270800@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Joakim Faergeman (Yale University): Motivicity of rigid G-local systems on curves \nAbstract: A natural problem in the study of local systems on complex varieties is to characterize those that arise in a family of varieties. We refer to such local systems as motivic. While a classification of motivic local systems is evidently out of reach\, Simpson conjectured that for a reductive group G\, rigid G-local systems with suitable finiteness conditions at infinity are motivic. This was proven for curves when G=GL_n by Katz who classified such rigid local systems. In this talk\, we discuss our generalization of Katz’ theorem to a general reductive group. Our proof goes through the (tamely ramified) categorical geometric Langlands program in characteristic zero. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-8/
LOCATION:Darmstadt\, Room 401 and Zoom\, Schlossgartenstraße 7\, Darmstadt\, 64289\, Germany
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Sabrina Pauli":MAILTO:pauli@mathematik.tu-darmstadt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241022T160000
DTEND;TZID=Europe/Berlin:20241022T170000
DTSTAMP:20260424T231257
CREATED:20241016T113803Z
LAST-MODIFIED:20241121T133311Z
UID:9376-1729612800-1729616400@crc326gaus.de
SUMMARY:On the cohomology of $SL(n\,\mathbb Z)$ beyond the "stable range"
DESCRIPTION:International Seminar on Automorphic Forms \nHarald Grobner (University of Vienna): On the cohomology of $SL(n\,\mathbb Z)$ beyond the “stable range” \nThe cohomology of the group $SL(n\,\mathbb{Z})\, n>1$\, plays a fundamental role in geometry\, topology and representation theory\, while yielding many number theoretical applications: For instance\, Borel used his description of $H^*(SL(n\,\mathbb Z))$ to compute the algebraic K-theory of the integers; whereas the (non-)vanishing of $H^*(SL(n\,\mathbb Z))$ tells a lot about the existence of certain automorphic forms. In this talk we will study the cohomology of $SL(n\,\mathbb Z)$\, „right outside“ of what one calls the stable range. More precisely\, we will show new non-vanishing results in degrees n−1 and n. As a byproduct\, we will also answer a question\, recently asked by F. Brown for n=6 and explain a phenomenon for n=8\, which has been considered by A. Ash. (This is joint work with N. Grbac.) \nhttps://tu-darmstadt.zoom.us/j/68048280736 \n 
URL:https://crc326gaus.de/event/tba-115/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241023T160000
DTEND;TZID=Europe/Berlin:20241023T170000
DTSTAMP:20260424T231257
CREATED:20241023T073421Z
LAST-MODIFIED:20241025T150227Z
UID:9455-1729699200-1729702800@crc326gaus.de
SUMMARY:Oberseminar Algebra und Geometrie
DESCRIPTION:Marius Leonhardt (Universität Frankfurt): Affine abelian non-abelian Chabauty \nAbstract: The central question of this talk is how to find all integral points on affine hyperbolic curves. For example\, which integers x\,y satisfy y^2 = x^3 + x^2 + x + 1?\nWe approach this problem by introducing Kim’s non-abelian Chabauty method\, which constructs p-adic analytic functions that have the integral points among their zeroes. In joint work with M. Lütdke and J.S. Müller\, we showed that the abelian version of this method succeeds if the curve satisfies a certain inequality involving its genus and the Mordell-Weil rank of its Jacobian.\nThis talk is an introduction to the Chabauty–Kim method. I will present the above result and report on work in progress with M. Lüdtke that turns it into an algorithm determining the integral points on the curve.
URL:https://crc326gaus.de/event/affine-abelian-non-abelian-chabauty-2/
LOCATION:Frankfurt\, RM-Str. 6-8\, R. 308
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241024T141500
DTEND;TZID=Europe/Berlin:20241024T151500
DTSTAMP:20260424T231257
CREATED:20241002T100703Z
LAST-MODIFIED:20241017T113423Z
UID:9271-1729779300-1729782900@crc326gaus.de
SUMMARY:On the algebraic K-theory of algebraic tori
DESCRIPTION:Florian Riedel (Kopenhagen) \nAbstract:\nI will describe work in progress joint with Bai\, Carmeli and Juran. A classical computation by Quillen expresses the algebraic K-theory spectrum of the ring of Laurent polynomials as the group ring of S^1 over the K-theory of the base field. We generalize this by showing that the algebraic K-theory spectrum of a not-necessarily split algebraic torus is given by the group ring of the delooping of the character lattice of the torus\, thus showing that a version of Cartier duality between algebraic and topological tori holds on the level of K-theory. We do this by constructing a motivic Fourier transform which is of independent interest and also recover an explicit formula of Merkujev-Panin for K_0 in a straightforward way.
URL:https://crc326gaus.de/event/tba-111/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241025T133000
DTEND;TZID=Europe/Berlin:20241025T150000
DTSTAMP:20260424T231257
CREATED:20241018T115611Z
LAST-MODIFIED:20241018T115611Z
UID:9434-1729863000-1729868400@crc326gaus.de
SUMMARY:A moduli-theoretic approach to Sen theory
DESCRIPTION:Ben Heuer (Universität Frankfurt) \nClassical Sen theory describes C_p-semilinear representations of Galois groups of p-adic fields in terms of linear algebra data called Sen modules. I will first explain how this theory can be reinterpreted geometrically in terms of v-vector bundles\, creating a relation to the p-adic Simpson correspondence. I will then explain how one can use this to upgrade Sen’s Theorem to a comparison of moduli spaces of Galois representations and Sen modules: This explains known subtleties in classical Sen theory in a geometric fashion. Finally\, I will describe how we can use this to study moduli spaces of (phi\,Gamma)-modules. This is joint work-in-progress with Eugen Hellmann.
URL:https://crc326gaus.de/event/a-moduli-theoretic-approach-to-sen-theory/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241029T160000
DTEND;TZID=Europe/Berlin:20241029T170000
DTSTAMP:20260424T231257
CREATED:20241016T114245Z
LAST-MODIFIED:20241022T114634Z
UID:9379-1730217600-1730221200@crc326gaus.de
SUMMARY:Exact formulae for ranks of partitions
DESCRIPTION:International Seminar on Automorphic Forms \nQihang Sun (University of Lille): Exact formulae for ranks of partitions \nDyson’s ranks provided a new understanding of the integer partition function\, especially of its congruence properties. In 2009\, Bringmann used the circle method to prove an asymptotic formula for the Fourier coefficients of rank generating functions. In this talk\, we will prove that the asymptotic formula\, when summing up to infinity\, converges and becomes a Rademacher-type exact formula for the rank of partitions. \n\nhttps://tu-darmstadt.zoom.us/j/68048280736 \n 
URL:https://crc326gaus.de/event/tba-116/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241029T161500
DTEND;TZID=Europe/Berlin:20241029T171500
DTSTAMP:20260424T231257
CREATED:20241025T131302Z
LAST-MODIFIED:20241025T134639Z
UID:9558-1730218500-1730222100@crc326gaus.de
SUMMARY:Moduli of twisted maps to smooth pairs
DESCRIPTION:Robert Crumplin (Heidelberg)
URL:https://crc326gaus.de/event/moduli-of-twisted-maps-to-smooth-pairs/
LOCATION:Heidelberg\, MATHEMATIKON\, SR 5\, INF 205\, Heidelberg\, Germany
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Georg Bernhard Oberdieck":MAILTO:georgo@uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241031T141500
DTEND;TZID=Europe/Berlin:20241031T151500
DTSTAMP:20260424T231257
CREATED:20241002T100932Z
LAST-MODIFIED:20241022T104135Z
UID:9273-1730384100-1730387700@crc326gaus.de
SUMMARY:On the K-theory of curves over number fields.
DESCRIPTION:Rob de Jeu (Amsterdam) \nAbstract: Borel defined regulators for the odd degree higher K-groups of a number field k and proved a relation between these and the values of the zeta-function of k at 2\, 3\, 4\, …\, generalising the classical relation between its residue at s=1 and the regulator of the unit group of the ring of integers. Similar results were proved and/or conjectured by Bloch and Beilinson for the K-groups of varieties over number fields. After a review of the background\, we discuss some recent joint work with François Brunault\, Liu Hang\, and Fernando Rodriguez Villegas on K_2 of elliptic curves over certain cubic or quartic number fields\, and\, time permitting\, how one can try to describe the K_4 of curves over number fields.
URL:https://crc326gaus.de/event/tba-112/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
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