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DTSTART;TZID=Europe/Berlin:20230505T164500
DTEND;TZID=Europe/Berlin:20230505T174500
DTSTAMP:20260601T015326
CREATED:20230403T131339Z
LAST-MODIFIED:20230418T125134Z
UID:5293-1683305100-1683308700@crc326gaus.de
SUMMARY:Tropical functions on skeletons: a finiteness result
DESCRIPTION:TGiF-Seminar: Tropical geometry in Frankfurt (First meeting Summer Semester 2023) \nAntoine Ducros (Sorbonne Université\, Paris) \nAbstract: Skeletons are subsets of non-archimedean spaces (in the sense of Berkovich) that inherit from the ambiant space a natural PL (piecewise-linear) structure\, and if S is such a skeleton\, for every invertible holomorphic function f defined in a neighborhood of S\, the restriction of log |f| to S is PL.\nIn this talk\, I will present a joint work with E.Hrushovski F. Loeser and J. Ye in which we consider an irreducible algebraic variety X over an algebraically closed\, non-trivially valued and complete non-archimedean field k\, and a skeleton S of the analytification of X defined using only algebraic functions\, and consisting of Zariski-generic points. If f is a non-zero rational function on X then log |f| induces a PL function on S\, and if we denote by E the group of all PL functions on S that are of this form\, we  prove the following finiteness result on the group E: it is stable under min and max\, and there exist finitely many non-zero rational functions f_1\,…f_m on X such that E is generated\, as a group equipped with min and max operators\, by the log |f_i| and the constants |a| for a in k^*. Our proof makes a crucial use of Hrushovski-Loeser’s model-theoretic approach of Berkovich spaces. \n 
URL:https://crc326gaus.de/event/tba-36/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230509T140000
DTEND;TZID=Europe/Berlin:20230509T160000
DTSTAMP:20260601T015326
CREATED:20230425T110303Z
LAST-MODIFIED:20230508T084428Z
UID:5619-1683640800-1683648000@crc326gaus.de
SUMMARY:Comparison of tame and log-étale cohomology
DESCRIPTION:Seminar: Non-archimedean geometry \nAmine Koubaa (Universität Frankfurt) \nAbstract:\nGiven a regular scheme $X$ and a normal crossing divisor $D$ one may concider two different cohomology groups.\nThe first one is the log étale cohomology developed by Illusie\, K. Kato and many others: We associate a logarithmic structure $M$ to $X$ and define the log étale site over $(X\,M)$.The second one is the tame cohomology developed by Hübner and Schmidt. Here we consider the tame site over the discretely ringed adic space $Spa(X\backslash D\,X)$. Tame morphisms are those which are étale and induce at most tamely ramified extension on the valuations.We construct a comparison morphism between these cohomology groups and prove that they are equal for schemes over $\mathbb{F}_p$ and locally constant finite sheaves once we assume resolution of singularities.“
URL:https://crc326gaus.de/event/comparison-of-tame-and-log-etale-cohomology-copy/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230509T160000
DTEND;TZID=Europe/Berlin:20230509T170000
DTSTAMP:20260601T015326
CREATED:20230505T150422Z
LAST-MODIFIED:20230505T150422Z
UID:5750-1683648000-1683651600@crc326gaus.de
SUMMARY:p-adic Gross-Zagier and rational points on modular curves
DESCRIPTION:International Seminar on Automorphic Forms \nSachi Hashimoto (MPI Leipzig) \nFaltings’ theorem states that there are finitely many rational points on a nice projective curve defined over the rationals of genus at least 2. The quadratic Chabauty method makes explicit some cases of Faltings’ theorem. Quadratic Chabauty has recent notable success in determining the rational points of some modular curves. In this talk\, I will explain how we can leverage information from p-adic Gross-Zagier formulas to give a new quadratic Chabauty method for certain modular curves. Gross-Zagier formulas relate analytic quantities (special values of p-adic L-functions) to invariants of algebraic cycles (the p-adic height and logarithm of Heegner points). By using p-adic Gross-Zagier formulas\, this new quadratic Chabauty method makes essential use of modular forms to determine rational points.  \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/p-adic-gross-zagier-and-rational-points-on-modular-curves-2/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230510T164500
DTEND;TZID=Europe/Berlin:20230510T180000
DTSTAMP:20260601T015326
CREATED:20230419T065010Z
LAST-MODIFIED:20231115T130317Z
UID:5557-1683737100-1683741600@crc326gaus.de
SUMMARY:Tropical perspectives in enumerative geometry
DESCRIPTION:Frankfurter Seminar – Kolloquium des Instituts für Mathematik \nRenzo Cavalieri (Colorado State University\, Fort Collins) \nAbstract: Enumerative geometry is an ancient branch of mathematics that aims to count the number of geometric objects that satisfy some constrains: the primordial enumerative geometric statement is that there is a unique straight line that passes through two distinct points in a plane. While enumerative geometric questions are often easy to state\, the attempts to answer them have both employed and spurred the development of several mathematical techniques.\nThis talk will be a broad and hopefully friendly survey of how tropical geometry has become an important actor for several enumerative problems especially related to counting curves. I will use Hurwitz theory as the running example\, and show how tropical geometry provides us not only with an interesting approach to classical Hurwitz theory\, but also allows us to define „new“ enumerative problems of Hurwitz type. Much of the work presented has been collaborative work with Paul Johnson\, Hannah Markwig\, Dhruv Ranganathan and Johannes Schmitt.
URL:https://crc326gaus.de/event/tropical-perspectives-in-enumerative-geometry/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230511T140000
DTEND;TZID=Europe/Berlin:20230511T160000
DTSTAMP:20260601T015326
CREATED:20230417T071727Z
LAST-MODIFIED:20230427T120413Z
UID:5436-1683813600-1683820800@crc326gaus.de
SUMMARY:Algebraicity and p-adic interpolation of critical Hecke L-values
DESCRIPTION:Johannes Sprang (Essen) \nAbstract: Euler’s beautiful formula on the values of the Riemann zeta function at the positive even integers can be seen as the starting point of the investigation of special values of L-functions. In particular\, Euler’s result shows that all critical zeta values are rational up to multiplication with a particular period\, here the period is a power of 2πi. Conjecturally this is expected to hold for all critical L-values of motives. In this talk\, I will explain a joint result with Guido Kings on the algebraicity of critical Hecke L-values up to explicit periods for totally imaginary fields. If time permits\, I will discuss the construction of p-adic L-functions for such fields as an application.
URL:https://crc326gaus.de/event/tba-48/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230512T133000
DTEND;TZID=Europe/Berlin:20230512T150000
DTSTAMP:20260601T015326
CREATED:20230505T131942Z
LAST-MODIFIED:20230505T131942Z
UID:5748-1683898200-1683903600@crc326gaus.de
SUMMARY:A quadratically refined tropical Bézout theorem
DESCRIPTION:Sabrina Pauli (Düsseldorf) \nAbstract: Results from motivic homotopy theory allow to study questions in enumerative geometry over an arbitrary field k. In this case the answer to these questions is not a number but a quadratic form carrying arithmetic information about the count. Using tropical geometry one can translate questions from enumerative geometry to questions in combinatorics which are often easier to solve. In my talk I will present one of the first examples of how to use tropical geometry for questions in enumerative geometry over an arbitrary field k\, namely a proof of Bézout’s theorem for tropical curves. This is joint work with Andrés Jaramillo Puentes. \n 
URL:https://crc326gaus.de/event/a-quadratically-refined-tropical-bezout-theorem/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Christian Dahlhausen":MAILTO:cdahlhausen@mathi.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230516T160000
DTEND;TZID=Europe/Berlin:20230516T170000
DTSTAMP:20260601T015326
CREATED:20230414T122931Z
LAST-MODIFIED:20230508T083903Z
UID:5393-1684252800-1684256400@crc326gaus.de
SUMMARY:Endoscopy for GSp(4) and rational points on elliptic curves
DESCRIPTION:International Seminar on Automorphic Forms \nI report on a joint project with M. Bertolini \, M.A. Seveso and R. Venerucci\, aimed at studying the equivariant BSD conjecture for rational elliptic curves twisted by certain self-dual 4-dimensional Artin representations in situations of odd analytic rank. We use the endoscopy for GSp(4) to construct Selmer classes related to the relevant (complex and p-adic) L-values via explicit reciprocity laws.  \nFabrizio Andreatta (University of Milan) \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/tba-40/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230523T140000
DTEND;TZID=Europe/Berlin:20230523T160000
DTSTAMP:20260601T015326
CREATED:20230502T084529Z
LAST-MODIFIED:20230519T150512Z
UID:5705-1684850400-1684857600@crc326gaus.de
SUMMARY:Prismatic F-crystals associated with strongly divisible modules
DESCRIPTION:Seminar: Non-archimedean geometry \nMatti Würthen (Universität Frankfurt) \nAbstract: The talk will be about the relationship between two different categories associated with the category of lattices in crystalline representations with small Hodge-Tate weights. In particular\, I will explain how to attach a prismatic Frobenius crystal to a (crystalline) strongly divisible module.\nTime permitting\, I will also sketch how this can be extended to higher dimensions.
URL:https://crc326gaus.de/event/tba-55/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230524T160000
DTEND;TZID=Europe/Berlin:20230524T170000
DTSTAMP:20260601T015326
CREATED:20230502T084120Z
LAST-MODIFIED:20230502T084120Z
UID:5701-1684944000-1684947600@crc326gaus.de
SUMMARY:Periods\, Power Series\, and Integrated Algebraic Numbers
DESCRIPTION:Oberseminar Algebra und Geometrie \nTobias Kaiser (Universität Passau) \nAbstract:\nPeriods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the polynomial ring over the rationals and evaluate it at a rational number. We follow this path and close these algebraic power series under taking iterated antiderivatives and nearby algebraic and geometric operations. We obtain a system of rings of power series whose coefficients form a countable real closed field. Using techniques from o-minimality we are able to show that every period belongs to this field. In the setting of o-minimality we define exponential integrated algebraic numbers and show that exponential periods and the Euler constant are exponential integrated algebraic number. Hence they are a good candiate for a natural number system extending the period ring and containing important mathematical constants.
URL:https://crc326gaus.de/event/periods-power-series-and-integrated-algebraic-numbers/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230526T133000
DTEND;TZID=Europe/Berlin:20230526T150000
DTSTAMP:20260601T015326
CREATED:20230517T134409Z
LAST-MODIFIED:20230519T185959Z
UID:5864-1685107800-1685113200@crc326gaus.de
SUMMARY:An equivariant local epsilon constant conjecture
DESCRIPTION:Alessandro Cobbe (Universität Heidelberg)\nAbstract: The local epsilon constant conjecture in the formulation by Breuning of 2004 fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected compatibility of the ETNC with the functional equation of Artin-L-functions. It relates local epsilon constants\, which are associated to L-functions\, to some terms which originate from local Galois cohomology groups of Z_p(1). We will also look at more general versions of the conjecture\, obtained by twisting Z_p(1) with unramified representations. This is joint work with Werner Bley.
URL:https://crc326gaus.de/event/tba-56/
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:20230530T090000
DTEND;TZID=Europe/Berlin:20230530T100000
DTSTAMP:20260601T015326
CREATED:20230414T123131Z
LAST-MODIFIED:20230523T085021Z
UID:5395-1685437200-1685440800@crc326gaus.de
SUMMARY:Discontinuity property of a certain Habiro series at roots of unity
DESCRIPTION:International Seminar on Automorphic Forms \nToshiki Matsusaka (Kyushu University) \nThe object of this talk is a family of q-series originating from Habiro’s work on the Witten-Reshetikhin-Turaev invariants. The q-series usually make sense only when q is a root of unity\, but for some instances\, it also determines a holomorphic function on the open unit disc. Such an example is Habiro’s unified WRT invariant H(q) for the Poincaré homology sphere. In 2007\, Hikami observed its discontinuity at roots of unity. More precisely\, the value of H(ζ) at a root of unity is 1/2 times the limit value of H(q) as q tends towards ζ radially within the unit disc. In this talk\, we give an explanation of the appearance of the 1/2 factor and generalize Hikami’s observations by using Bailey’s lemma and the theory of mock/false theta functions. \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/tba-41/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230530T140000
DTEND;TZID=Europe/Berlin:20230530T160000
DTSTAMP:20260601T015326
CREATED:20230508T081909Z
LAST-MODIFIED:20230516T121616Z
UID:5753-1685455200-1685462400@crc326gaus.de
SUMMARY:On Emerton's factorization of completed cohomology
DESCRIPTION:Seminar: Non-archimedean geometry \nPierre Colmez (CNRS\, Sorbonne Université\, Paris) \nAbstract: Emerton has given a factorization of the completed cohomology of the tower of modular curves\, separating the contributions of all the groups that act (i.e.\, the absolute Galois group of ${\mathbb Q}$ and the ${\mathrm GL}_2({\mathbb Q}_\ell)$ for all primes $\ell$).\nI will explain how one can use p-adic Hodge theory to construct a Kirillov model for the completed cohomology and obtain a more direct construction of this factorization.
URL:https://crc326gaus.de/event/tba-57/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230531T161500
DTEND;TZID=Europe/Berlin:20230531T171500
DTSTAMP:20260601T015326
CREATED:20230516T065816Z
LAST-MODIFIED:20230516T121814Z
UID:5835-1685549700-1685553300@crc326gaus.de
SUMMARY:Hidden structures on de Rham cohomology of p-adic analytic varieties
DESCRIPTION:Oberseminar Algebra und Geometrie \nWieslawa Niziol (CNRS\,  Sorbonne Université\, Paris) \nAbstract: I will survey what we know about extra structures (Hodge filtration\, Frobenius\, monodromy) appearing on de Rham cohomology of analytic varieties over local fields of mixed characteristic.
URL:https://crc326gaus.de/event/hidden-structures-on-de-rham-cohomology-of-p-adic-analytic-varieties/
LOCATION:Frankfurt\, Robert-Mayer-Str. 10\, Raum 711 groß
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230601T141500
DTEND;TZID=Europe/Berlin:20230601T151500
DTSTAMP:20260601T015326
CREATED:20230321T082143Z
LAST-MODIFIED:20230519T080320Z
UID:5120-1685628900-1685632500@crc326gaus.de
SUMMARY:Motivic homotopy theory beyond A^1-invariance
DESCRIPTION:Ryomei Iwasa (Paris) \nAbstract: The basic question I’d like to address in this talk is the following: How to do homotopy theory in algebraic geometry while keeping the affine line A^1 non-contractible? I will explain that tensor invertibility of the pointed projective line P^1 supplies homotopies between projective bundle sections in a non-trivial but canonical way. This dramatically expands the scope of motivic homotopy theory\, and non-A^1-invariant theories such as syntomic cohomology\, prismatic cohomology\, algebraic K-theory\, and topological cyclic homology can be studied from this perspective. In particular\, I’ll explain that algebraic and Selmer K-theory are described by Snaith-type formulas. Based on joint work with Toni Annala and Marc Hoyois.
URL:https://crc326gaus.de/event/tba-35/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230602T133000
DTEND;TZID=Europe/Berlin:20230602T150000
DTSTAMP:20260601T015326
CREATED:20230526T132702Z
LAST-MODIFIED:20230526T132702Z
UID:5887-1685712600-1685718000@crc326gaus.de
SUMMARY:Intersections of components of Emerton-Gee stack for GL2
DESCRIPTION:Kalyani Kansal (Johns Hopkins University) \nAbstract: The Emerton-Gee stack for GL2 is a stack of (phi\, Gamma)-modules of rank two. Its reduced part\, X\, is an algebraic stack of finite type over a finite field\, and it can be viewed as a moduli stack of mod p representations of a p-adic Galois group. We compute criteria for codimension one intersections of the irreducible components of X. We interpret these criteria in terms of representation theory of GL2\, motivated by conjectural categorical p-adic and mod p Langlands correspondence. We also give a representation-theoretic cohomological criterion for the number of top-dimensional components in a codimension one intersection.
URL:https://crc326gaus.de/event/intersections-of-components-of-emerton-gee-stack-for-gl2/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230606T140000
DTEND;TZID=Europe/Berlin:20230606T160000
DTSTAMP:20260601T015326
CREATED:20230508T083012Z
LAST-MODIFIED:20230519T151050Z
UID:5759-1686060000-1686067200@crc326gaus.de
SUMMARY:Torsion points of elliptic curves via Berkovich spaces over Z
DESCRIPTION:Seminar: Non-archimedean geometry \nJérôme Poineau \nAbstract: Berkovich spaces over Z may be seen as fibrations containing complex analytic spaces as well as p-adic analytic spaces\, for every prime number p. We will give an introduction to those spaces and explain how they may be used in an arithmetic context to prove height inequalities. As an application\, following a strategy by DeMarco-Krieger-Ye\, we will give a proof of a conjecture of Bogomolov-Fu-Tschinkel on uniform bounds on the number of common images on P^1 of torsion points of two elliptic curves.
URL:https://crc326gaus.de/event/tba-58/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230606T160000
DTEND;TZID=Europe/Berlin:20230606T170000
DTSTAMP:20260601T015326
CREATED:20230414T123320Z
LAST-MODIFIED:20230523T084241Z
UID:5397-1686067200-1686070800@crc326gaus.de
SUMMARY:Artin's primitive root conjecture: classically and over Fq[T]
DESCRIPTION:International Seminar on Automorphic Forms \nIn 1927\, E. Artin proposed a conjecture for the number of primes p ≤ x\, for which g generates (ℤ/pℤ)x. By observing numerical deviations from Artin’s originally predicted asymptotic\, Derrick and Emma Lehmer (1957) identified the need for an additional correction factor; leading to a modified conjecture that was eventually proved correct by Hooley (1967)\, under the assumption of the Generalized Riemann Hypothesis (GRH). In this talk we discuss several variants of Artin’s conjecture: namely an “Artin Twin Primes Conjecture”\, as well as an appropriate analogue of Artin’s primitive root conjecture for algebraic function fields. \nEzra Waxman (University of Haifa) \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/tba-42/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230613T090000
DTEND;TZID=Europe/Berlin:20230613T100000
DTSTAMP:20260601T015326
CREATED:20230414T123441Z
LAST-MODIFIED:20230612T113540Z
UID:5399-1686646800-1686650400@crc326gaus.de
SUMMARY:Indefinite Theta Functions: something old\, something new
DESCRIPTION:International Seminar on Automorphic Forms \nSander Zwegers (University of Cologne) \nIn this talk we give an overview of the theory of indefinite theta functions and discuss some recent results. \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/tba-43/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230613T140000
DTEND;TZID=Europe/Berlin:20230613T160000
DTSTAMP:20260601T015326
CREATED:20230508T082054Z
LAST-MODIFIED:20231114T151118Z
UID:5755-1686664800-1686672000@crc326gaus.de
SUMMARY:Sen Operators and Lie Algebras arising from Galois Representations over p-adic Varieties
DESCRIPTION:Seminar: Non-archimedean geometry \nTongmu He \nAbstract: Any finite-dimensional p-adic representation of the absolute Galois group of a p-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen and Brinon. We generalize their construction to the fundamental group of a p-adic affine variety with a semi-stable chart\, and prove that the module of Sen operators is canonically defined\, independently of the choice of the chart. When the representation comes from a Qp-representation of the fundamental group\, we relate the infinitesimal action of inertia subgroups with Sen operators\, which is a generalization of a result of Sen and Ohkubo. These Sen operators can be extended continuously to certain infinite-dimensional representations. As an application\, we prove that the geometric Sen operators annihilate locally analytic vectors\, generalizing a result of Pan.
URL:https://crc326gaus.de/event/tba-copy-2/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230616T133000
DTEND;TZID=Europe/Berlin:20230616T150000
DTSTAMP:20260601T015326
CREATED:20230606T115957Z
LAST-MODIFIED:20230606T115957Z
UID:5914-1686922200-1686927600@crc326gaus.de
SUMMARY:On the K-theory of Z/p^n
DESCRIPTION:Dr. Achim Krause (Universität Heidelberg) \nAbstract: Algebraic K-theory is an invariant of rings that is notoriously hard to compute\, especially in non-regular situations. For example\, Quillen computed the K-theory of finite fields already in 1972\, but the case of rings of the form Z/p^n for n>1 has been out of reach until now. In joint work with Antieau and Nikolaus\, we apply Prismatic Cohomology to this problem\, leading to both a practical algorithm to compute these groups\, as well as surprising results on their large-degree behaviour.
URL:https://crc326gaus.de/event/on-the-k-theory-of-z-pn/
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:20230620T140000
DTEND;TZID=Europe/Berlin:20230620T160000
DTSTAMP:20260601T015326
CREATED:20230508T083202Z
LAST-MODIFIED:20231114T151522Z
UID:5764-1687269600-1687276800@crc326gaus.de
SUMMARY:Hodge--Tate crystals and p-adic non-abelian Hodge theory
DESCRIPTION:Seminar: Non-archimedean geometry \nYu Min \nAbstract: The coefficient theory of prismatic cohomology has been investigated a lot recently. For example\, Morrow–Tsuji and Tian have discovered the relationship between Hodge–Tate crystals and Higgs bundles (at least in the local case). In this talk\, I will briefly talk about how to get a global correspondence between Hodge–Tate crystals and Higgs bundles after inverting p. Then I will discuss what we can say without inverting p in the geometric case (over Oc) (if time permits\, also in the arithmetic case (over W(k))). This is joint work with Yupeng Wang.
URL:https://crc326gaus.de/event/tba-59/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230620T160000
DTEND;TZID=Europe/Berlin:20230620T170000
DTSTAMP:20260601T015326
CREATED:20230414T123558Z
LAST-MODIFIED:20230614T124617Z
UID:5401-1687276800-1687280400@crc326gaus.de
SUMMARY:Mixed mock modularity of special divisors
DESCRIPTION:International Seminar on Automorphic Forms \nSalim Tayou (Harvard University) \nKudla-Millson and Borcherds have proved some time ago that the generating series of special divisors in orthogonal Shimura varieties are modular forms. In this talk\, I will explain an extension of these results to toroidal compactifications where we prove that the generating series is a mixed mock modular form. More precisely\, we find an explicit completion using theta series associated to rays in the cone decomposition. The proof relies on intersection theory at the boundary of the Shimura variety. This recovers and refines recent results of Bruinier and Zemel. The result of this talk are joint work with Philip Engel and Francois Greer. \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/tba-44/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230622T141500
DTEND;TZID=Europe/Berlin:20230622T151500
DTSTAMP:20260601T015326
CREATED:20230531T074217Z
LAST-MODIFIED:20230531T074217Z
UID:5894-1687443300-1687446900@crc326gaus.de
SUMMARY:Centers of F-purity and their behavior under finite covers
DESCRIPTION:Javier Carvajal-Rojas (Leuven) \nAbstract: Let X be an F -split variety (roughly\, a strong form of ordinary log Calabi—Yau variety) and Y /X be a finite cover such that the F -splitting of X lifts to Y . How do the spectra of centers of F -purity (roughly\, arithmetically tame log-canonical centers) of Y and X relate to one another? This turns out to be a very tricky question due to wild ramification. An optimal answer would look like Cohen—Seidenberg-type theorems for spectra of centers of F-purity. In this talk\, I will report on work in progress with A. Fayolle (U. of Utah) where we address this question. \n 
URL:https://crc326gaus.de/event/centers-of-f-purity-and-their-behavior-under-finite-covers/
LOCATION:Mainz\, Hilbertraum (05-432)
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230623T133000
DTEND;TZID=Europe/Berlin:20230623T150000
DTSTAMP:20260601T015326
CREATED:20230613T110113Z
LAST-MODIFIED:20230613T110113Z
UID:5934-1687527000-1687532400@crc326gaus.de
SUMMARY:Tangent spaces in p-adic geometry
DESCRIPTION:Sean Howe (University of Utah) \nAbstract: In complex geometry\, it is an extremely useful fact that universal covers of complex manifolds have tangent spaces and that period maps arising from the cohomology of families of varieties are differentiable. In p-adic geometry\, unfortunately\, it is known that the covers of rigid analytic varieties trivializing local systems of etale cohomology do not admit a good theory of Kahler differentials. In this talk\, we explain how\, building from first principles and a single clever idea\, one can nonetheless assign tangent spaces to many of the perfectoid spaces and diamonds that arise naturally in the study of rigid analytic varieties and their cohomology and then differentiate period maps. These spaces provide\, in particular\, a natural conceptual framework for predicting when a diamond is a perfectoid space. In this talk we will focus mostly on examples in the theory of local Shimura varieties and explain the relation to work of Johannson\, Ludwig and Hansen on perfectoid quotients of Lubin-Tate space\, Ivanov and Weinstein on cohomological smoothness\, and Pan and Camargo on geometric Sen theory and sheaves of locally analytic functions. This is joint work with Peter Wear.
URL:https://crc326gaus.de/event/tangent-spaces-in-p-adic-geometry/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230627T140000
DTEND;TZID=Europe/Berlin:20230627T160000
DTSTAMP:20260601T015326
CREATED:20231114T152133Z
LAST-MODIFIED:20231114T152133Z
UID:6966-1687874400-1687881600@crc326gaus.de
SUMMARY:Geometric arcs and fundamental groups of rigid spaces
DESCRIPTION:Seminar: Non-archimedean geometry \nMarcin Lara \nAbstract: We introduce a new category of covering spaces in rigid geometry\, called geometric coverings\, and show it is classified by a certain topological fundamental group. Geometric coverings generalize the class of étale coverings\, introduced by de Jong\, and its various natural modifications\, and have certain desirable properties that were missing from those older notions: they are étale local and closed under taking infinite disjoint unions. The definition is based on the property of unique lifting of “geometric arcs.” On the way\, we answer some questions from the foundational paper of de Jong. This is joint work with Piotr Achinger and Alex Youcis.
URL:https://crc326gaus.de/event/geometric-arcs-and-fundamental-groups-of-rigid-spaces/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230627T160000
DTEND;TZID=Europe/Berlin:20230627T170000
DTSTAMP:20260601T015326
CREATED:20230414T123723Z
LAST-MODIFIED:20230627T101601Z
UID:5403-1687881600-1687885200@crc326gaus.de
SUMMARY:Root Number Correlation Bias of Fourier Coefficients of Modular Forms
DESCRIPTION:International Seminar on Automorphic Forms \nNina Zubrilina (Princeton University) \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/tba-45/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230628T140000
DTEND;TZID=Europe/Berlin:20230628T160000
DTSTAMP:20260601T015326
CREATED:20230606T080613Z
LAST-MODIFIED:20230627T145732Z
UID:5907-1687960800-1687968000@crc326gaus.de
SUMMARY:Pell-Abel equations
DESCRIPTION:Quentin Gendron (Universidad Nacional Autónoma de México)
URL:https://crc326gaus.de/event/pell-abel-equations-quentin-gendron/
LOCATION:Frankfurt\, Robert-Mayer-Str.10\, Raum 404
CATEGORIES:GAUS-Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230630T133000
DTEND;TZID=Europe/Berlin:20230630T150000
DTSTAMP:20260601T015326
CREATED:20230621T081700Z
LAST-MODIFIED:20230621T081700Z
UID:5960-1688131800-1688137200@crc326gaus.de
SUMMARY:Motivic monodromy and p-adic cohomology theories
DESCRIPTION:Martin Gallauer (University of Warwick) \nLimit structures in cohomology provide an indispensable tool in the study of varieties in families. This was brought to perfection in complex geometry and attempts have been made to transport it to arithmetic settings. In this talk I will introduce an approach to placing limit structures in all settings on an equal footing. It allows for a sharpening of this tool in p-adic cohomology. (Joint work with Federico Binda and Alberto Vezzani.)
URL:https://crc326gaus.de/event/motivic-monodromy-and-p-adic-cohomology-theories/
LOCATION:Heidelberg\, Mathematikon\, SR A and Livestream
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Christian Dahlhausen":MAILTO:cdahlhausen@mathi.uni-heidelberg.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230704T140000
DTEND;TZID=Europe/Berlin:20230704T160000
DTSTAMP:20260601T015326
CREATED:20231114T152651Z
LAST-MODIFIED:20231114T153537Z
UID:6968-1688479200-1688486400@crc326gaus.de
SUMMARY:Local Weight-Monodromy Conjecture
DESCRIPTION:Seminar: Non-archimedean geometry \nBogdan Zavyalov \nAbstract: Let X be a smooth and proper variety over a local field K. Then the weight-monodromy conjecture predicts that the monodromy and weight filtrations coincide up to a shift. Recently\, P. Scholze proved this conjecture for set-theoretic complete intersections inside the projective space using the theory of perfectoid spaces. Alternatively\, one can formulate a (local) version of the weight-monodromy conjecture for the nearby cycles. We will give a precise formulation of this conjecture and prove it in some cases following the strategy of Scholze in the global case. This is joint work with David Hansen.
URL:https://crc326gaus.de/event/local-weight-monodromy-conjecture-2/
LOCATION:Frankfurt\, Robert-Mayer-Str. 6-8\, Raum 308
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Annette Werner":MAILTO:werner[at]math.uni-frankfurt.de
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230704T160000
DTEND;TZID=Europe/Berlin:20230704T170000
DTSTAMP:20260601T015326
CREATED:20230414T123849Z
LAST-MODIFIED:20230628T070044Z
UID:5405-1688486400-1688490000@crc326gaus.de
SUMMARY:A general view on multiple zeta values\, modular forms and related q-series
DESCRIPTION:International Seminar on Automorphic Forms \nAnnika Burmester (Bielefeld University) \nMultiple zeta values and modular forms have a deep\, partly mysterious\, connection. This can be seen in the Broadhurst-Kreimer conjecture\, which was made partly explicit by Gangl-Kaneko-Zagier in 2006. Further\, multiple zeta values occur in the Fourier expansion of multiple Eisenstein series as computed by Bachmann. We will study this connection in more details on a formal level. This means\, we review formal multiple zeta values and then introduce the algebra G^f\, which should be seen as a formal version of multiple Eisenstein series\, and also multiple q-zeta values and polynomial functions on partitions simultaneously. We will give a surjective algebra morphism from G^f into the algebra of formal multiple zeta values. \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/tba-46/
LOCATION:Zoom
CATEGORIES:GAUS-Seminar
ORGANIZER;CN="Claire Burrin":MAILTO:claire.burrin@math.uzh.ch
END:VEVENT
END:VCALENDAR