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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230202T140000
DTEND;TZID=Europe/Berlin:20230202T160000
DTSTAMP:20260531T201417
CREATED:20221116T085643Z
LAST-MODIFIED:20230116T081424Z
UID:4326-1675346400-1675353600@crc326gaus.de
SUMMARY:Toroidal b-divisors and applications in differential and arithmetic geometry
DESCRIPTION:Ana Botero (Regensburg) \nWe define toroidal b-divisors on a quasi projective variety over a field. These can be seen as conical functions on a balanced polyhedral space. We show the existence of an intersection pairing for so called nef toroidal b-divisors\, which gives rise to a Monge-Ampére type measure on the polyhedral space. Moreover\, using the theory of Okounkov bodies\, we show that a Hilbert-Samuel type formula holds in this setting. We then show some applications of this theory. First\, we show some Chern-Weil type formulae for singular semi-positive metrics on line bundles. Then\, using the Hilbert-Samuel formula\, we compute asymptotic dimension formulae of spaces of automorphic forms on mixed Shimura varieties.
URL:https://crc326gaus.de/event/tba-30/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230203T133000
DTEND;TZID=Europe/Berlin:20230203T150000
DTSTAMP:20260531T201417
CREATED:20221214T130418Z
LAST-MODIFIED:20221214T130418Z
UID:4629-1675431000-1675436400@crc326gaus.de
SUMMARY:Integrality of smoothed p-adic Artin L-functions
DESCRIPTION:Bence Forrás (Universität Duisburg-Essen) \nAbstract: We introduce a smoothed version of the equivariant S-truncated p-adic Artin L-function for one-dimensional admissible p-adic Lie extensions of number fields. Integrality of this smoothed p-adic L-function\, conjectured by Greenberg\, has been verified for pro-p extensions (assuming the Equivariant Iwasawa Main Conjecture) as well as p-abelian extensions (unconditionally). Integrality in the general case is also expected to hold\, and is the subject of ongoing research.
URL:https://crc326gaus.de/event/integrality-of-smoothed-p-adic-artin-l-functions/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230203T140000
DTEND;TZID=Europe/Berlin:20230203T150000
DTSTAMP:20260531T201417
CREATED:20221205T120737Z
LAST-MODIFIED:20230123T134644Z
UID:4484-1675432800-1675436400@crc326gaus.de
SUMMARY:Linear degenerate tropical flag matroids
DESCRIPTION:TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2022/23) \nVictoria Schleis (Universität Tübingen) \nAbstract: Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Their linear degenerations arise in representation theory as they describe quiver representations and their irreducible modules. As linear degenerations of flag varieties are difficult to analyze algebraically\, we describe them in a combinatorial setting and further investigate their tropical counterparts. \nIn this talk\, I will introduce matroidal\, polyhedral and tropical analoga and descriptions of linear degenerate flags and their varieties obtained in joint work with Alessio Borzì. To this end\, we introduce and study morphisms of valuated matroids. Using techniques from matroid theory\, polyhedral geometry and linear tropical geometry\, we use the correspondences between the different descriptions to gain insight on the structure of linear degeneration. Further\, we analyze the structure of linear degenerate flag varieties in all three settings\, and provide some cover relations on the poset of degenerations. For small examples\, we relate the observations on cover relations to the flat irreducible locus studied in representation theory.
URL:https://crc326gaus.de/event/tba-32/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230203T153000
DTEND;TZID=Europe/Berlin:20230203T163000
DTSTAMP:20260531T201417
CREATED:20221205T120951Z
LAST-MODIFIED:20230125T132340Z
UID:4496-1675438200-1675441800@crc326gaus.de
SUMMARY:Polyhedral models for K-theory
DESCRIPTION:TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2022/23) \nLeonid Monin (Universität Leipzig) \nAbstract: One can associate a commutative\, graded algebra which satisfies Poincare duality to a homogeneous polynomial f on a vector space V. One particularly interesting example of this construction is when f is the volume polynomial on a suitable space of (virtual) polytopes. In this case the algebra A_f recovers cohomology rings of toric or flag varieties. \nIn my talk I will explain these results and present their recent generalizations. In particular\, I will explain how to associate an algebra with Gorenstein duality to any function g on a lattice L. In the case when g is the Ehrhart function on a lattice of integer (virtual) polytopes\, this construction recovers K-theory of toric and full flag varieties.
URL:https://crc326gaus.de/event/tba-33/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230203T164500
DTEND;TZID=Europe/Berlin:20230203T174500
DTSTAMP:20260531T201417
CREATED:20221205T121408Z
LAST-MODIFIED:20230124T140817Z
UID:4503-1675442700-1675446300@crc326gaus.de
SUMMARY:Universality for tropical maps
DESCRIPTION:TGiF-Seminar: Tropical geometry in Frankfurt (Second meeting Winter Semester 2022/23) \nNavid Nabijou (University of Cambridge) \nAbstract: I will discuss recent work concerning maps from tropical curves to orthants. A “combinatorial type” of such map is the data of an abstract graph together with slope vectors along the edges. To each such combinatorial type there is an associated moduli space\, which parametrises metric enhancements of the graph compatible with the given slopes. This moduli space is a rational polyhedral cone\, giving rise to an affine toric variety.\nOur main result shows that every rational polyhedral cone appears as the moduli space associated to some combinatorial type of tropical map. This establishes universality (also known as Murphy’s law) for tropical maps. The proof is constructive and extremely concrete\, as I will demonstrate. Combined with insights from logarithmic geometry\, our result implies that every toric singularity appears as a virtual singularity on a moduli space of stable logarithmic maps. \n\n\nThis is joint work with Gabriel Corrigan and Dan Simms.
URL:https://crc326gaus.de/event/tba-34/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230206T150000
DTEND;TZID=Europe/Berlin:20230206T173000
DTSTAMP:20260531T201417
CREATED:20230131T145759Z
LAST-MODIFIED:20230201T124708Z
UID:4821-1675695600-1675704600@crc326gaus.de
SUMMARY:The geometry of coherent sheaves: From derived categories to Higgs bundles
DESCRIPTION:GAUS-Workshop: “Invariants and curve counting” \n15:00-16:00: Luca Battistella (Frankfurt):\nLogarithmic and orbifold Gromov-Witten invariants\nAbstract: Logarithmic Gromov-Witten theory can be thought of as the study of curves in open manifolds\, or\, in other words\, curves with tangency conditions to a boundary divisor. When the divisor is smooth\, several techniques have been developed to compute the invariants\, most notably orbifold stable maps. When the divisor is normal crossings\, on the other hand\, the logarithmic theory remains hardly accessible. The strategy of rank reduction\, i.e. looking at the components of the boundary one at a time\, is more directly applicable to other theories than the logarithmic one (as shown in Nabijou-Ranganathan and B.-Nabijou-Tseng-You) due to tropical obstructions. Inspired by one of the distinguishing features of the logarithmic theory – namely\, birational invariance [Abramovich-Wise] – in joint work with Nabijou and Ranganathan we show that\, when the genus is zero\, tropical obstructions can be disposed of by blowing up the target sufficiently. The slogan is that the logarithmic theory is the limit orbifold theory under birational modifications along the boundary divisor. If time permits I will discuss work in progress towards understanding negative contact. \n16:20-17:20: Georg Oberdieck (Stockholm):\nPandharipande-Thomas theory of elliptic threefolds and Jacobi forms\nAbstract: Pandharipande-Thomas theory is the study of the intersection theory of the moduli space of stable pairs of a threefold. The intersection numbers\, called Pandharipande-Thomas invariants\, may be viewed as counting curves on the threefold subject to given incidence conditions. In this talk we explore the properties of the generating series of Pandharipande-Thomas invariants of elliptically fibered threefolds. There will be two main conjectures: Quasi-Jacobi Property and Holomorphic Anomaly Equations. Together these essentially determine the modular properties of the generating series. The conjectures are motivated by the case of Calabi-Yau threefolds where by mirror symmetry computations Huang-Katz-Klemm conjectured that the series of PT invariants are Jacobi forms. I discuss several examples\, in particular the equivariant geometry of K3xA^1. Here the conjectures lead to explicit new formulas for the invariants. Based on joint work with Maximilian Schimpf.
URL:https://crc326gaus.de/event/invariants-and-curve-counting/
LOCATION:Frankfurt\, Hilbertraum\, Rober-Mayer-Str. 6-8\, Raum 302
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230207T160000
DTEND;TZID=Europe/Berlin:20230207T170000
DTSTAMP:20260531T201417
CREATED:20221108T132317Z
LAST-MODIFIED:20230130T121438Z
UID:4216-1675785600-1675789200@crc326gaus.de
SUMMARY:Asymptotic equidistribution for partition statistics and topological invariants
DESCRIPTION:International Seminar on Automorphic Forms \nThroughout mathematics\, the equidistribution properties of certain objects are a central  theme studied by many authors. In my talk I am going to speak about a joint project with William Craig and Joshua Males\, where we provide a general framework for proving asymptotic equidistribution\, convexity\, and log-concavity of coefficients of generating functions on arithmetic progressions. \nGiulia Cesana (University of Cologne) \nYou can join the Zoom meeting at https://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/international-seminar-on-automorphic-forms-tba-11/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230210T153000
DTEND;TZID=Europe/Berlin:20230210T170000
DTSTAMP:20260531T201417
CREATED:20230130T121955Z
LAST-MODIFIED:20230130T121955Z
UID:4814-1676043000-1676048400@crc326gaus.de
SUMMARY:Revisiting derived crystalline cohomology
DESCRIPTION:Seminar Arithmetic Geometry \nZhouhang Mao (Paris) \nProjectively generated ∞-categories and left derived functors turn out to be important in derived geometry. In this talk\, we will present the result of the ∞-category of surjections  of animated rings being projectively generated\, the notion of animated PD-pairs —  surjections of animated rings with a “derived” PD-structure\, and how to use these tools to study the crystalline and prismatic cohomology. In particular\, we will deduce various comparison theorems without finiteness conditions. \nZoom (Meeting-ID: 635 7328 0984\, Password: smallest six digit prime)
URL:https://crc326gaus.de/event/revisiting-derived-crystalline-cohomology/
LOCATION:Darmstadt\, Room 401 and Zoom\, Schlossgartenstraße 7\, Darmstadt\, 64289\, Germany
CATEGORIES:GAUS-Seminar
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