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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250502T153000
DTEND;TZID=Europe/Berlin:20250502T170000
DTSTAMP:20260424T113858
CREATED:20250402T112950Z
LAST-MODIFIED:20250402T114256Z
UID:10903-1746199800-1746205200@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Christian Dahlhausen  (Universität Heidelberg): Duality in (perfect) motivic homotopy theory \nThis talk treats a conjectured duality on modules over\nK-theory in the stable homotopy category of a scheme whose dualising\nobject is given by G-theory. I shall explain a proof of the conjecture\nfor quasi-excellent schemes in characteristic zero. In order to approach\nthe conjecture in positive characteristic\, I sketch the construction of\na “perfect motivic homotopy category” and compare it to the classical\nhomotopy category. For this perfect category\, I shall sketch the proof\nof an analogous version of the duality conjecture. This is joint work\nwith Denis-Charles Cisinski\, Jeroen Hekking\, and Storm Wolters. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-23/
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:20250506T160000
DTEND;TZID=Europe/Berlin:20250506T170000
DTSTAMP:20260424T113858
CREATED:20250416T090743Z
LAST-MODIFIED:20250506T091439Z
UID:11085-1746547200-1746550800@crc326gaus.de
SUMMARY:The Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios
DESCRIPTION:International Seminar on Automorphic Forms \nZhiyuan Li (SCMS\, Fudan University) \nThe Shintani–Faddeev modular cocycle: Stark units from q-Pochhammer ratios \nWe give a new interpretation of Stark units associated to real quadratic fields as special “real multiplication values” of a modular cocycle described by complex meromorphic continuation of a simple infinite product. The cocycle encodes the modular transformations of the infinite q-Pochhammer symbol and is related to the Shintani–Barnes double sine funciton and the Faddeev quantum dilogarithm. As a corollary\, we describe some intriguing features of the asymptotic behavior of the infinite q-Pochhammer symbol as the modular parameter approaches a real quadratic number. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits)
URL:https://crc326gaus.de/event/tba-copy-5/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250508T141500
DTEND;TZID=Europe/Berlin:20250508T151500
DTSTAMP:20260424T113858
CREATED:20250423T095325Z
LAST-MODIFIED:20250503T124627Z
UID:11134-1746713700-1746717300@crc326gaus.de
SUMMARY:Duality in (perfect) motivic homotopy theory
DESCRIPTION:Christian Dahlhausen (Uni Heidelberg) \nAbstract: This talk treats a conjectured duality on modules over K-theory in the stable homotopy category of a scheme whose dualising object is given by G-theory. I shall explain a proof of the conjecture for quasi-excellent schemes in characteristic zero. In order to approach the conjecture in positive characteristic\, I sketch the construction of a “perfect motivic homotopy category” and compare it to the classical homotopy category. For this perfect category\, I shall sketch the proof of an analogous version of the duality conjecture. This is joint work with Denis-Charles Cisinski\, Jeroen Hekking\, and Storm Wolters.
URL:https://crc326gaus.de/event/duality-in-perfect-motivic-homotopy-theory/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Tom Bachmann":MAILTO:tom.bachmann@uni-mainz.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250509T133000
DTEND;TZID=Europe/Berlin:20250509T143000
DTSTAMP:20260424T113858
CREATED:20250429T074250Z
LAST-MODIFIED:20250505T124728Z
UID:11177-1746797400-1746801000@crc326gaus.de
SUMMARY:Refined Chabauty–Kim computations for the thrice-punctured line over Z[1/6]
DESCRIPTION:Martin Lüdtke (MPIM Bonn) \nAbstract: If X is a curve of genus at least 2 defined over the rational numbers\, we know by Faltings’s Theorem that the set X(Q) of rational points is finite but we don’t know how to systematically compute this set. In 2005\, Minhyong Kim proposed a new framework for studying rational (or S-integral) points on curves\, called the Chabauty–Kim method. It aims to produce p-adic analytic functions on X(Q_p) containing the rational points X(Q) in their zero locus. We apply this method to solve the S-unit equation for S={2\,3} and computationally verify Kim’s Conjecture for many choices of the auxiliary prime p.
URL:https://crc326gaus.de/event/refined-chabauty-kim-computations-for-the-thrice-punctured-line-over-z1-6/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Marius Leonhardt":MAILTO:mleonhardt@mathi.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250509T153000
DTEND;TZID=Europe/Berlin:20250509T170000
DTSTAMP:20260424T113858
CREATED:20250409T121252Z
LAST-MODIFIED:20250409T121252Z
UID:11010-1746804600-1746810000@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Ferdinand Wagner  (Universität Bonn): q-Hodge filtrations\, Habiro cohomology\, and THH over ku \nThe recent work of Garoufalidis\, Scholze\, Wheeler\, and Zagier on the “Habiro ring of a number field” has sparked the question whether there exists a cohomology theory for smooth schemes over Z with coefficients in the Habiro ring\, the completion of Z[q] at all roots of unity\, and with specialisations to étale and de Rham cohomology. In this talk I’ll explain how this question is intimately related to the question whether the Hodge filtration on de Rham cohomology can be q-deformed to a filtration on q-de Rham cohomology. While such a q-deformed filtration (provably) doesn’t exist in general\, I’ll explain how to construct a filtration (along with the “Habiro cohomology”) in many interesting cases\, using topological Hochschild homology over the complex K-theory spectrum ku. I’ll also explain how a refined version of THH can be used to obtain a completely functorial construction for varieties over Q. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-25/
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:20250513T100000
DTEND;TZID=Europe/Berlin:20250513T110000
DTSTAMP:20260424T113858
CREATED:20250416T090848Z
LAST-MODIFIED:20250513T081214Z
UID:11088-1747130400-1747134000@crc326gaus.de
SUMMARY:Theta series and tautological cycles on orthogonal Shimura varieties
DESCRIPTION:International Seminar on Automorphic Forms \nZhiyuan Li (Fudan university) \nTheta series and tautological cycles on orthogonal Shimura varieties \nIn this talk\, I will explore the fascinating interplay between lattice theory and vector- valued modular forms via theta series\, presenting an elegant connection that bridges these areas. I will discuss its applications in the study of cycle theory on orthogonal Shimura varieties. One of our findings reveal that the Picard group of the Baily-Borel compactification of a broad class of Shimura varieties is isomorphic to ℤ. I will also explain the geometric motivation of this project. Most results are joint work with Huang\, Müller and Ye. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits)
URL:https://crc326gaus.de/event/tba-141/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250515T141500
DTEND;TZID=Europe/Berlin:20250515T151500
DTSTAMP:20260424T113858
CREATED:20250128T082207Z
LAST-MODIFIED:20250508T094212Z
UID:10507-1747318500-1747322100@crc326gaus.de
SUMMARY:On Voevodsky's reconstruction theorem
DESCRIPTION:Sebastian Wolf (Regensburg) \nIn 1990\, Voevodsky proved a conjecture of Grothendieck\, that morphisms of normal schemes of finite type over the rational numbers can be reconstructed from the induced morphism of étale topoi. The goal of this talk is to give an outline of Voevodsky’s proof and explain a generalization of his result: Taking the étale topos is a fully faithful functor from finite type schemes over any finitely generated field to topoi over such a field after inverting univeral homeomorphisms. This is joint work with Magnus Carlson and Peter Haine.
URL:https://crc326gaus.de/event/tba-114/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250516T153000
DTEND;TZID=Europe/Berlin:20250516T170000
DTSTAMP:20260424T113858
CREATED:20250414T115513Z
LAST-MODIFIED:20250414T115513Z
UID:11040-1747409400-1747414800@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Simon Riche  (Université Clermont Auvergne): Semiinfinite sheaves on affine flag varieties \nWe will explain how\, generalizing a construction of Gaitsgory\, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that “models” sheaves on the corresponding semiinfinite flag variety\, with coefficients in a field of positive characteristic\, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application\, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld’s compactification\, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-26/
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:20250522T141500
DTEND;TZID=Europe/Berlin:20250522T151500
DTSTAMP:20260424T113858
CREATED:20250305T094423Z
LAST-MODIFIED:20250516T072330Z
UID:10638-1747923300-1747926900@crc326gaus.de
SUMMARY:Integral Nori Motives
DESCRIPTION:Swann Tubach (ENS Lyon) \nThe classical theory of Nori motives provides a tensor abelian category of motives over a field k of characteristic zero\, with a nice universal property and realisation functors interpolating various cohomology theories. We will construct a commutative algebra N_X in the category of étale motivic sheaves over any scheme X of characteristic zero\, compatible with base change\, such that the category DNgm(X) of geometric objects in modules over N_X has natural t-structures\, the 6 operations\, and conservative realisation functors. Over a field we recover the derived category of Nori motives\, and with rational coefficients we recover the derived category of Ivorra-Morel’s category of perverse Nori motives. This provides abelian categories of motivic sheaves with integral coefficients. This is joint work with Raphaël Ruimy.
URL:https://crc326gaus.de/event/tba-134/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250523T133000
DTEND;TZID=Europe/Berlin:20250523T143000
DTSTAMP:20260424T113858
CREATED:20250320T114638Z
LAST-MODIFIED:20250320T114638Z
UID:10731-1748007000-1748010600@crc326gaus.de
SUMMARY:Berthelot's conjecture via p-adic homotopy theory
DESCRIPTION:Alberto Vezzani (Universitá degli Studi di Milano) \nAbstract: By drawing parallels to classical work by Monsky-Washnitzer\, Elkik\, Arabia and others\, we motivate the study of (non-archimedean) motivic homotopy theory by showing that it can be used to define/re-define rational p-adic cohomology theories and prove new results about them. For example\, we show how to define relative rigid cohomology and deduce finiteness properties for it (joint work with V. Ertl)\, solving a version of a conjecture by Berthelot for coefficients of geometric origin.
URL:https://crc326gaus.de/event/berthelots-conjecture-via-p-adic-homotopy-theory/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250527T160000
DTEND;TZID=Europe/Berlin:20250527T170000
DTSTAMP:20260424T113858
CREATED:20250416T090938Z
LAST-MODIFIED:20250522T080806Z
UID:11090-1748361600-1748365200@crc326gaus.de
SUMMARY:Rigid cocycles for SL(n) and their values at special points
DESCRIPTION:International Seminar on Automorphic Forms \nMarti Roset Julia (McGill University) Rigid cocycles for SL(n) and their values at special points \nThe theory of complex multiplication implies that the values of modular functions at CM points belong to abelian extensions of imaginary quadratic fields. In this talk\, we propose a conjectural extension of this phenomenon to the setting of totally real fields. Generalizing the work of Darmon\, Pozzi\, and Vonk\, we construct rigid cocycles for SL(n)\, which play the role of modular functions\, and define their values at points associated with totally real fields. The construction of these cocycles originates from a topological source: the Eisenstein class of a torus bundle. This is ongoing joint work with Peter Xu. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits)
URL:https://crc326gaus.de/event/tba-142/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20250530T153000
DTEND;TZID=Europe/Berlin:20250530T170000
DTSTAMP:20260424T113858
CREATED:20250507T124915Z
LAST-MODIFIED:20250507T124915Z
UID:11249-1748619000-1748624400@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Guido Bosco (MPI Bonn): On the p-adic monodromy theorem \nI will present a new geometric perspective on the p-adic monodromy theorem of André\, Kedlaya\, and Mebkhout\, which is based on the study of vector bundles on the analytic de Rham stack of the Fargues–Fontaine curve. I will then outline some applications to the p-adic Hodge theory of rigid-analytic varieties. \nThis is based on joint work in progress with Anschütz\, Le Bras\, and Rodriguez Camargo. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-27/
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
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