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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240705T140000
DTEND;TZID=Europe/Berlin:20240705T170000
DTSTAMP:20260531T160251
CREATED:20240405T092944Z
LAST-MODIFIED:20240620T121924Z
UID:8085-1720188000-1720198800@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Fabio Tanania (TU Darmstadt): Isotropic motivic fundamental groups \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-7/
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:20240709T170000
DTEND;TZID=Europe/Berlin:20240709T180000
DTSTAMP:20260531T160251
CREATED:20240702T121736Z
LAST-MODIFIED:20240709T102934Z
UID:8929-1720544400-1720548000@crc326gaus.de
SUMMARY:Fourier-Jacobi periods on unitary groups
DESCRIPTION:International Seminar on Automorphic Forms \nHang Xue (Arizona University): Fourier-Jacobi periods on unitary groups \nAbstract: We prove the Gan-Gross-Prasad conjecture for Fourier-Jacobi periods on unitary groups via relative trace formulae. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \n 
URL:https://crc326gaus.de/event/tba-110/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240711T140000
DTEND;TZID=Europe/Berlin:20240711T160000
DTSTAMP:20260531T160251
CREATED:20240704T070018Z
LAST-MODIFIED:20240704T070131Z
UID:8938-1720706400-1720713600@crc326gaus.de
SUMMARY:On DGAs with polynomial homology
DESCRIPTION:Julius Frank (Bielefeld) \nAbstract: It is surprisingly hard to find non-trivial examples of DGAs whose homology is polynomial in one generator. I will discuss one such example\, which is a derived quotient of a discrete ring by an odd prime. I will also give one reason why it is hard to find examples: If the homology of a DGA A is polynomial over a perfect F_p-algebra and the underlying ring spectrum of A refines to an E_3-ring spectrum\, then A must already be trivial in a certain sense.
URL:https://crc326gaus.de/event/on-dgas-with-polynomial-homology/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240712T133000
DTEND;TZID=Europe/Berlin:20240712T150000
DTSTAMP:20260531T160251
CREATED:20240705T091804Z
LAST-MODIFIED:20240705T091804Z
UID:8945-1720791000-1720796400@crc326gaus.de
SUMMARY:On a characterisation of perfectoid fields by Iwasawa theory
DESCRIPTION:Gautier Ponsinet (IHES\, Université Paris Saclay) \nWith a p-adic representation of the Galois group of a p-adic field are associated the Bloch-Kato groups defined via p-adic Hodge theory.\nIwasawa theory motivates the study of these Bloch-Kato groups over infinite algebraic extensions of the field of p-adic numbers. \nOver perfectoid fields\, several results (by Coates-Greenberg\, Perrin-Riou\, Berger\, P. …) state that the Bloch-Kato groups admit a simple description. \nIn this talk\, we will present a reciprocal statement: the structure of the Bloch-Kato groups associated with certain crystalline representations characterises the algebraic extensions of the field of p-adic numbers whose completion are perfectoid fields. In particular\, we will recover\, via a different method\, results by Coates and Greenberg for abelian varieties\, and by Bondarko for p-divisible groups. \n 
URL:https://crc326gaus.de/event/on-a-characterisation-of-perfectoid-fields-by-iwasawa-theory/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Rustam Steingart":MAILTO:rsteingart@mathi.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240716T160000
DTEND;TZID=Europe/Berlin:20240716T170000
DTSTAMP:20260531T160251
CREATED:20240702T121840Z
LAST-MODIFIED:20240709T102846Z
UID:8931-1721145600-1721149200@crc326gaus.de
SUMMARY:Theta correspondence via C*-algebras
DESCRIPTION:International Seminar on Automorphic Forms \nHaluk Sengun (University of Sheffield):Theta correspondence via C*-algebras \nAbstract: The local theta correspondence sets up a bijection between certain subsets of admissible duals of suitable pairs of reductive groups. There are two special cases in which the correspondence is known to enjoy extra features\, the ‘equal rank’ case where temperedness is preserved and the ‘stable range’ case where unitarity is preserved. In joint work with Bram Mesland (Leiden)\, we show that in these special cases\, the local theta correspondence is actually given by a Morita equivalence of suitable\nC*-algebras. I will try to expose this result and\, time permitting\, some applications. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \n 
URL:https://crc326gaus.de/event/tba-copy-4/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240718T141500
DTEND;TZID=Europe/Berlin:20240718T151500
DTSTAMP:20260531T160251
CREATED:20240710T070747Z
LAST-MODIFIED:20240710T070747Z
UID:8980-1721312100-1721315700@crc326gaus.de
SUMMARY:Certain families of K3 surfaces and their modularity
DESCRIPTION:Yui\, Noriko (Queen’s University) \nAbstract: We start with a double sextic family of K3 surfaces with four parameters with Picard number 16 defined over Q. Then by geometric reduction (top-to-bottom) processes\, we obtain three\, two and one parameter families of K3 surfaces of Picard number 17\, 18\, and 19 respectively. All these families turn out to be of hypergeometric type in the sense that their Picard–Fuch differential equations are given by hypergeometric or Heun functions. We will study the geometry of two parameter families in detail. \nWe will then prove\, after suitable specializations of parameters\, these K3 surfaces will have CM (complex multiplication)\, and will become modular\, i.e.\, the Galois representations of dimensions less than or equal to 6 associated to the transcendental lattices are all induced from 1-dimensional representations. Thus\, these K3 surfaces will be determined by modular forms of various weights. This is done starting with one-parameter family and then applying arithmetic induction (bottom-to-top) processes. \nOur final goal is to determine explicit modular forms that determine the L-functions of these K3 families\nat special fibers. \nThis is a joint work with A. Clingher\, S. Kim and A. Malmendier.
URL:https://crc326gaus.de/event/certain-families-of-k3-surfaces-and-their-modularity/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20240719T153000
DTEND;TZID=Europe/Berlin:20240719T170000
DTSTAMP:20260531T160251
CREATED:20240701T093526Z
LAST-MODIFIED:20240718T143756Z
UID:8909-1721403000-1721408400@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Konstantin Jakob (TU Darmstadt): Counting absolutely indecomposable G-bundles \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-copy/
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:20240917T160000
DTEND;TZID=Europe/Berlin:20240917T180000
DTSTAMP:20260531T160251
CREATED:20240906T074613Z
LAST-MODIFIED:20240916T120512Z
UID:9151-1726588800-1726596000@crc326gaus.de
SUMMARY:Initial degenerations of homogeneous varieties
DESCRIPTION:Victoria Schleis (Durham University): \nAbstract: We study the geometry of initial degenerations of homogeneous subvarieties of (multi-)projective space using polyhedral geometry. In 2017\, Corey characterized initial degenerations of the Grassmannian through limits of strata in a matroid stratification of the Grassmannian corresponding to the weight vector of the initial degeneration. Since then\, similar results have been proven for the flag variety and Spinor varieties. In my talk\, I will discuss recent work in progress extending this study beyond specific examples to homogeneous subvarieties of (multi)-projective space. The talk is based on joint work in progress with George Balla\, Dan Corey\, and Igor Mahklin.
URL:https://crc326gaus.de/event/initial-degenerations-of-homogeneous-varieties/
LOCATION:Frankfurt\, Rober-Mayer-Str. 10\, Raum 711 klein
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241018T153000
DTEND;TZID=Europe/Berlin:20241018T170000
DTSTAMP:20260531T160251
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:20260531T160251
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:20260531T160251
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:20260531T160251
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:20260531T160251
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:20260531T160251
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:20260531T160251
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:20260531T160251
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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241101T153000
DTEND;TZID=Europe/Berlin:20241101T170000
DTSTAMP:20260531T160251
CREATED:20240909T081328Z
LAST-MODIFIED:20241028T095457Z
UID:9172-1730475000-1730480400@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Pol van Hoften (VU Amsterdam): Igusa stacks and the cohomology of Shimura varieties \nAssociated to a modular form f is a two-dimensional Galois representation whose Frobenius eigenvalues can be expressed in terms of the Fourier coefficients of f\, using a formula known as the Eichler–Shimura congruence relation. This relation was proved by Eichler–Shimura and Deligne by analyzing the mod p (bad) reduction of the modular curve of level ?0(p). In this talk\, I will discuss joint work with Patrick Daniels\, Dongryul Kim and Mingjia Zhang\, where we give a new proof of this congruence relation that happens “entirely on the generic fibre”. More precisely\, we prove a compatibility result between the cohomology of Shimura varieties of Hodge type and the Fargues?Scholze semisimple local Langlands correspondence\, generalizing the Eichler–Shimura relation of Blasius–Rogawski. Our proof makes crucial use of the Igusa stacks that we construct\, generalizing earlier work of Zhang in the PEL case. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-11/
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:20241105T160000
DTEND;TZID=Europe/Berlin:20241105T170000
DTSTAMP:20260531T160251
CREATED:20241016T114401Z
LAST-MODIFIED:20241101T075704Z
UID:9380-1730822400-1730826000@crc326gaus.de
SUMMARY:Counting characters on algebraic tori according to their Langlands L-functions
DESCRIPTION:International Seminar on Automorphic Forms \nIan Petrow (UCL): Counting characters on algebraic tori according to their Langlands L-functions \nGiven a connected reductive group G over a global field\, Langlands introduced the automorphic L-function L(s\, π\, r) of a cuspidal automorphic representation π of G and a complex representation r of the L-group of G. While in general very little is known about Langlands L-functions\, if G = T is a torus the properties of these L-functions can be obtained from class field theory and one can attempt to study analytic problems pertaining to them. In this talk I will describe some analytic results on automorphic characters of tori with respect to the analytic conductor of L(s\, π\, r)\, attempting to focus on the interplay of analytic and algebraic ideas that arise in the proofs. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits) \n 
URL:https://crc326gaus.de/event/tba-117/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241108T111500
DTEND;TZID=Europe/Berlin:20241108T121500
DTSTAMP:20260531T160251
CREATED:20241025T135236Z
LAST-MODIFIED:20241025T135236Z
UID:9566-1731064500-1731068100@crc326gaus.de
SUMMARY:From SL(2) to SO(2): Rank-2 Vafa-Witten invariants
DESCRIPTION:Simon Schirren (Rom)
URL:https://crc326gaus.de/event/from-sl2-to-so2-rank-2-vafa-witten-invariants/
LOCATION:Heidelberg\, MATHEMATIKON\, SR 11\, 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:20241108T133000
DTEND;TZID=Europe/Berlin:20241108T143000
DTSTAMP:20260531T160251
CREATED:20241030T102418Z
LAST-MODIFIED:20241030T102805Z
UID:9587-1731072600-1731076200@crc326gaus.de
SUMMARY:Rigid cocycles and geodesics on Shimura curves
DESCRIPTION:Håvard Damm-Johnsen (University of Oxford /MPIM Bonn) \nDarmon and Vonk’s theory of rigid meromorphic cocycles gives a conjectural description of abelian extensions of real quadratic fields akin to the classical theory of complex multiplication. While their conjectures currently seem out of reach\, the work of Darmon-Pozzi-Vonk uses p-adic families of Hilbert modular forms to give unconditional results in this direction. I will explain how a reinterpretation in terms of the so-called Kudla programme suggests an approach to extending their results. This point of view also gives a new proof of a theorem of Rickards on intersections of geodesics on Shimura curves\, which is related to forthcoming work of Darmon-Vonk.
URL:https://crc326gaus.de/event/rigid-cocycles-and-geodesics-on-shimura-curves/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241108T153000
DTEND;TZID=Europe/Berlin:20241108T170000
DTSTAMP:20260531T160251
CREATED:20240909T081457Z
LAST-MODIFIED:20241021T103300Z
UID:9174-1731079800-1731085200@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Siyan Daniel Li-Huerta (MPIM Bonn): Close fields and the local Langlands correspondence \nThere is a heuristic that\, as ramification goes to infinity\, p-adic fields tend to function fields. For Galois representations\, this was made precise by Deligne\, and for representations of p-adic groups\, a similar result was shown by Kazhdan and Ganapathy. We present a proof that this is compatible with Fargues–Scholze’s local Langlands correspondence. The proof relies on carrying out Fargues–Scholze’s construction over the one-point compactification of the natural numbers. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-12/
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:20241112T160000
DTEND;TZID=Europe/Berlin:20241112T170000
DTSTAMP:20260531T160251
CREATED:20241016T114448Z
LAST-MODIFIED:20241105T091814Z
UID:9381-1731427200-1731430800@crc326gaus.de
SUMMARY:On an extension of the Rohrlich-Jensen formula
DESCRIPTION:International Seminar on Automorphic Forms \nLeila Smajlovic (University of Sarajevo): On an extension of the Rohrlich-Jensen formula \nWe revisit the Rohrlich-Jensen formula and prove that\, in the case of any Fuchsian group of the first kind with one cusp it can be viewed as a regularized inner product of special values of two Poincaré series\, one of which is the Niebur-Poincaré series and the other is the resolvent kernel of the Laplacian. The regularized inner product can be seen as a type of Maass-Selberg relation. In this form\, we develop a Rohrlich-Jensen formula associated to any Fuchsian group Γ of the first kind with one cusp by employing a type of Kronecker limit formula associated to the resolvent kernel. We present two examples of our main result: First\, when Γ is the full modular group; and second when Γ is an Atkin-Lehner group Γ0(N)+. This work is joint with James Cogdell and Jay Jorgenson. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits) \n 
URL:https://crc326gaus.de/event/tba-118/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241115T111500
DTEND;TZID=Europe/Berlin:20241115T121500
DTSTAMP:20260531T160251
CREATED:20241108T101412Z
LAST-MODIFIED:20241126T101943Z
UID:9752-1731669300-1731672900@crc326gaus.de
SUMMARY:Jacobi forms\, mock modular forms and qMZVs in enumerative geometry
DESCRIPTION:Jan-Willem van Ittersum (Cologne) \nAbstract: There are several instances where Gromov-Witten invariants can be expressed in terms of (quasi)Jacobi forms. In other examples in enumerative geometry\, one also encounters mock modular forms or even q-analogues of multiple zeta values. We explain the origin and properties of these series and provide examples of their occurrences as generating series of geometrical invariants.\n\nhttps://sites.google.com/view/heidelbergag/algebraic-geometry-seminar
URL:https://crc326gaus.de/event/jacobi-forms-mock-modular-forms-and-qmzvs-in-enumerative-geometry/
LOCATION:Heidelberg\, MATHEMATIKON\, SR 11\, 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:20241115T133000
DTEND;TZID=Europe/Berlin:20241115T150000
DTSTAMP:20260531T160251
CREATED:20241106T133148Z
LAST-MODIFIED:20241126T102031Z
UID:9724-1731677400-1731682800@crc326gaus.de
SUMMARY:Antisymmetry in the theory of rigid meromorphic cocycles
DESCRIPTION:Sören Sprehe (Universität Bielefeld) \nAround six years ago Darmon and Vonk initiated the theory of p-adic singular moduli for real quadratic fields by defining “rigid meromorphic cocycles”. These are elements of the first cohomology group of Ihara’s group SL2(Z[1/p]) with values in the group of rigid meromorphic functions on Drinfeld’s upper half-plane. Using rigid meromorphic cocycles\, Darmon and Vonk assign to each pair of real quadratic irrationalities a p-adic number. The two irrationalities play a vastly different role in the construction of this assignment. However\, it is expected to behave like the difference of two classical singular moduli – in particular\, it should be anti-symmetric in the argument. We will use the recent work of Darmon\, Gehrmann and Lipnowski on rigid meromorphic cocycles for higher dimensional orthogonal groups to give a new\, symmetric construction of this function.
URL:https://crc326gaus.de/event/antisymmetry-in-the-theory-of-rigid-meromorphic-cocycles/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Gebhard B%C3%B6ckle":MAILTO:gebhard.boeckle iwr.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241115T153000
DTEND;TZID=Europe/Berlin:20241115T170000
DTSTAMP:20260531T160251
CREATED:20241016T112344Z
LAST-MODIFIED:20241104T123602Z
UID:9353-1731684600-1731690000@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Ludwig Modin (Leibniz Universität Hannover): Moduli spaces for Theta-strata and non-reductive quotients \nThe U-hat theorem of Bérczi\, Doran\, Hawes and Kirwan gives conditions for when a linear action of a complex graded unipotent group admits a geometric quotient\, it is one of the key results non-reductive geometric invariant theory is built on.\nWe give a stacky re-interpretation of this theorem in terms of Theta-strata\, as introduced by Halpern-Leistner\, of algebraic stacks. As a corollary we generalize the U-hat theorem to not necessarily linear actions of graded unipotent groups over a Noetherian base scheme. \nZoom (635 7328 0984)\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-13/
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:20241119T160000
DTEND;TZID=Europe/Berlin:20241119T170000
DTSTAMP:20260531T160251
CREATED:20241016T114537Z
LAST-MODIFIED:20241108T080337Z
UID:9382-1732032000-1732035600@crc326gaus.de
SUMMARY:Cones of Noether-Lefschetz divisors and moduli of hyperkähler manifolds
DESCRIPTION:International Seminar on Automorphic Forms \nLaure Flapan (Michigan State University): Cones of Noether-Lefschetz divisors and moduli of hyperkähler manifolds \nWe describe how to compute cones of Noether-Lefshetz divisors on orthogonal modular varieties with a particular view towards moduli spaces of polarized K3 surfaces and hyperkähler manifolds. We then describe some geometric applications of these cone computations for these moduli spaces. This is joint work with I. Barros\, P. Beri\, and B. Williams. \nhttps://tu-darmstadt.zoom.us/j/68048280736 \nThe password is the first Fourier coefficient of the modular j-function (as digits) \n 
URL:https://crc326gaus.de/event/tba-119/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241122T103000
DTEND;TZID=Europe/Berlin:20241122T113000
DTSTAMP:20260531T160251
CREATED:20241111T132603Z
LAST-MODIFIED:20241126T102342Z
UID:9817-1732271400-1732275000@crc326gaus.de
SUMMARY:Differential operators on automorphic forms\, special functions\, and arithmetic applications
DESCRIPTION:Tomoyoshi Ibukiyama\, Professor Emeritus Department of Mathematics Graduate School of Science\, Osaka University \nA theory of differential operators on automorphic forms\nwhich preserve automorphy after restrictions of\nthe domains have a long history and turned out\nto include a nice theory of special functions.\nWe will give rough outline on results\nsince 1990 (partly a joint work with D. Zagier) and\nexplain several arithmetic applications.
URL:https://crc326gaus.de/event/differential-operators-on-automorphic-forms-special-functions-and-arithmetic-applications/
LOCATION:Heidelberg\, MATHEMATIKON\, SR 11\, 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:20241122T133000
DTEND;TZID=Europe/Berlin:20241122T143000
DTSTAMP:20260531T160251
CREATED:20241113T101011Z
LAST-MODIFIED:20241126T102149Z
UID:9829-1732282200-1732285800@crc326gaus.de
SUMMARY:Heights of modular polynomials
DESCRIPTION:Prof. Dr. Florian Breuer (University of Newcastle) \nFor every positive integer $N$\, the modular polynomial $\Phi_N(X\,Y)$ has integer coefficients and vanishes precisely at pairs of $j$-invariants of elliptic curves linked by a cyclic isogeny of order $N$. These polynomials have applications in cryptography and define integral (but singular) models for the modular curves $X_0(N)$. Their coefficients grow rapidly with $N$. In this talk\, I will explain recent joint work with Fabien Pazuki and Desir\’ee Gij\’on G\’omez obtaining explicit upper and lower bounds on the size of these coefficients. Our methods also lead to explicit bounds on the heights of Hecke images. If time allows\, I can also outline analogous results for Drinfeld modular polynomials.
URL:https://crc326gaus.de/event/heights-of-modular-polynomials/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Gebhard B%C3%B6ckle":MAILTO:gebhard.boeckle iwr.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241122T141500
DTEND;TZID=Europe/Berlin:20241122T151500
DTSTAMP:20260531T160251
CREATED:20241115T214100Z
LAST-MODIFIED:20241126T102247Z
UID:9870-1732284900-1732288500@crc326gaus.de
SUMMARY:Tropical refined curve counting and mirror symmetry
DESCRIPTION:Qaasim Shafi (Heidelberg) \nAn old theorem\, due to Mikhalkin\, says that the number of\nrational plane curves of degree d through 3d-1 points is equal to a\ncount of tropical curves (combinatorial objects which are more amenable\nto computations). There are two natural directions for generalising this\nresult: extending to higher genus curves and allowing for more general\nconditions than passing through points. I’ll discuss a generalisation\nwhich does both\, as well as recent work connecting it to mirror symmetry\nfor log Calabi-Yau surfaces. This is joint work with Patrick\nKennedy-Hunt and Ajith Urundolil Kumaran. \nhttps://sites.google.com/view/heidelbergag/algebraic-geometry-seminar
URL:https://crc326gaus.de/event/tropical-refined-curve-counting-and-mirror-symmetry/
LOCATION:Heidelberg
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Georg Bernhard Oberdieck":MAILTO:georgo@uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20241122T153000
DTEND;TZID=Europe/Berlin:20241122T170000
DTSTAMP:20260531T160251
CREATED:20241016T112540Z
LAST-MODIFIED:20241114T073128Z
UID:9355-1732289400-1732294800@crc326gaus.de
SUMMARY:Seminar on Arithmetic Geometry
DESCRIPTION:Andrés Jaramillo Puentes (Universität Tübngen): A Wall-Crossing Formula for Motivic Gromov-Witten Invariants \nIn enumerative geometry\, Gromov-Witten invariants play a central role in counting curves on algebraic varieties\, and their variations under different conditions provide a rich framework for understanding moduli spaces. In recent years\, there has been significant progress in developing enriched versions of these invariants within the framework of motivic homotopy theory\, leading to what we now call motivic Gromov-Witten invariants. Motivic invariants encode additional algebraic structure over the Grothendieck-Witt ring of a base field\, allowing for finer distinctions in curve counts\, particularly over fields with nontrivial real structure. \nIn this talk\, we discuss a wall-crossing formula for motivic Gromov-Witten invariants. Specifically\, we explore how variations in point conditions and configurations influence the values of these invariants\, and demonstrate how these changes can be systematically tracked using a motivic analogue of classical wall-crossing phenomena. We will illustrate how this formula provides a mechanism to relate invariants associated with distinct configurations by tracking contributions along certain “walls” in the parameter space\, which play an analogous role to wall-crossing in real enumerative geometry. \nAdditionally\, we will present applications of this formula to specific enumerative problems\, showcasing how the motivic perspective not only recovers known real and complex cases but also opens new pathways for counting problems over arbitrary fields. This development lays the groundwork for future research\, providing a powerful tool to bridge combinatorial and motivic techniques in tropical and algebraic geometry. \nZoom (635 7328 0984\, Kenncode: kleinste sechsstellige Primzahl
URL:https://crc326gaus.de/event/seminar-on-arithmetic-geometry-14/
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
END:VCALENDAR