BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chan-Ho Kim (KIAS\, Korea) DTSTART:20210503T080000Z DTEND:20210503T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/1 DESCRIPTION:Title: On the Fitting ideals of Selmer groups of modular forms\n by Chan-Ho Kim (KIAS\, Korea) as part of French-Korean webinar in number t heory\n\n\nAbstract\nIn 1980's\, Mazur and Tate studied ``Iwasawa theory f or elliptic curves over finite abelian extensions" and formulated various related conjectures. One of their conjectures says that the analytically d efined Mazur-Tate element lies in the Fitting ideal of the dual Selmer gro up of an elliptic curve. We discuss some cases of the conjecture for modul ar forms of higher weight.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Pengo (ENS de Lyon\, France) DTSTART:20210517T080000Z DTEND:20210517T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/2 DESCRIPTION:Title: Entanglement in the family of division fields of a CM ellipti c curve\nby Riccardo Pengo (ENS de Lyon\, France) as part of French-Ko rean webinar in number theory\n\n\nAbstract\nDivision fields associated to an algebraic group defined over a number field\, which are the extensions generated by its torsion points\, have been the subject of a great amount of research\, at least since the times of Kronecker and Weber. For ellipt ic curves without complex multiplication\, Serre's open image theorem show s that the division fields associated to torsion points whose order is a p rime power are "as big as possible" and pairwise linearly disjoint\, if on e removes a finite set of primes. Explicit versions of this result have re cently been featured in the work of Campagna-Stevenhagen and Lombardo-Tron to. In this talk\, based on joint work with Francesco Campagna (arXiv:2006 .00883)\, I will present an analogue of these results for elliptic curves with complex multiplication. Moreover\, I will present a necessary conditi on to have entanglement in the family of division fields\, which is always satisfied for elliptic curves defined over the rationals. In this last ca se\, I will describe in detail the entanglement in the family of division fields.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Hae-Sang Sun (UNIST\, Korea) DTSTART:20210607T080000Z DTEND:20210607T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/3 DESCRIPTION:Title: Cyclotomic Hecke L-values of a totally real field\nby Hae -Sang Sun (UNIST\, Korea) as part of French-Korean webinar in number theor y\n\n\nAbstract\nIt is known that any Fourier coefficient of a newform of weight 2 can be expressed as a polynomial with rational coefficients\, of a single algebraic critical value of the corresponding L-function twisted by a Dirichlet character of $p$-power conductor for a rational prime $p$. In the talk\, I will discuss a version of this result in terms of Hecke L- function over a totally real field\, twisted by Hecke characters of $p$-po wer conductors. The discussion involves new technical challenges that aris e from the presence of the unit group\, which are (1) counting lattice poi nts in a cone that $p$-adically close to units and (2) estimating an expon ential sum over the unit group. This is joint work with Byungheup Jun and Jungyun Lee.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vlerë Mehmeti (Université Paris-Saclay\, France) DTSTART:20210621T080000Z DTEND:20210621T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/4 DESCRIPTION:Title: Non-Archimedean analytic curves and the local-global principl e\nby Vlerë Mehmeti (Université Paris-Saclay\, France) as part of Fr ench-Korean webinar in number theory\n\n\nAbstract\nIn 2009\, a new techni que\, called algebraic patching\, was introduced in the study of local-glo bal principles. Under different forms\, patching had in the past been used for the study of the inverse Galois problem. In this talk\, I will presen t an extension of this technique to non-Archimedean analytic curves. As an application\, we will see various local-global principles for function fi elds of curves\, ranging from geometric to more classical forms. These res ults generalize those of the previous literature and are applicable to qua dratic forms. We will start by a brief introduction of the framework of no n-Archimedean analytic curves and will conclude by a presentation of a fir st step towards such results in higher dimensions.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Seoyoung Kim (Queen's University) DTSTART:20211004T080000Z DTEND:20211004T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/5 DESCRIPTION:Title: On the generalized Diophantine m-tuples\nby Seoyoung Kim (Queen's University) as part of French-Korean webinar in number theory\n\n \nAbstract\nFor non-zero integers n and k≥2\, a generalized Diophantine m-tuple with property Dk(n) is a set of m positive integers {a1\,a2\,…\, am} such that aiaj+n is a k-th power for any distinct i and j. Define by M k(n) the supremum of the size of the set which has property Dk(n). In this paper\, we study upper bounds on Mk(n)\, as we vary n over positive integ ers. In particular\, we show that for k≥3\, Mk(n) is O(logn) and further assuming the Paley graph conjecture\, Mk(n) is O((logn)ϵ). The problem f or k=2 was studied by a long list of authors that goes back to Diophantus who studied the quadruple {1\,33\,68\,105} with property D(256). This is a joint work with A. Dixit and M. R. Murty.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Griffon (Université Clermont-Auvergne) DTSTART:20211018T080000Z DTEND:20211018T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/6 DESCRIPTION:Title: Isogenies of elliptic curves over function fields\nby Ric hard Griffon (Université Clermont-Auvergne) as part of French-Korean webi nar in number theory\n\n\nAbstract\nI will report on a recent work\, joint with Fabien Pazuki\, in which we study elliptic curves over function fiel ds and the isogenies between them. More specifically\, we prove analogues in the function field setting of two famous theorems about isogenous ellip tic curves over number fields. The first of these describes the variation of the Weil height of the j-invariant of elliptic curves within an isogeny class. Our second main result is an ``isogeny estimate’’ in the spiri t of theorems by Masser—Wüstholz and by Gaudron—Rémond. After statin g our results and giving quick sketches of their proof\, I will\, time per mitting\, mention a few Diophantine applications.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Wansu Kim (KAIST) DTSTART:20211108T080000Z DTEND:20211108T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/7 DESCRIPTION:Title: Equivariant BSD conjecture over global function fields\nb y Wansu Kim (KAIST) as part of French-Korean webinar in number theory\n\n\ nAbstract\nUnder a certain finiteness assumption of Tate-Shafarevich group s\, Kato and Trihan showed the BSD conjecture for abelian varieties over g lobal function fields of positive characteristic. We explain how to genera lise this to semi-stable abelian varieties “twisted by Artin character ” over global function field (under some additional technical assumption s)\, and discuss further speculations for generalisations if time permits. This is a joint work with David Burns and Mahesh Kakde.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucile Devin (Université du Littoral\, Calais) DTSTART:20211122T080000Z DTEND:20211122T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/8 DESCRIPTION:Title: Chebyshev’s bias and sums of two squares\nby Lucile Dev in (Université du Littoral\, Calais) as part of French-Korean webinar in number theory\n\n\nAbstract\nStudying the secondary terms of the Prime Num ber Theorem in Arithmetic Progressions\, Chebyshev claimed that there are more prime numbers congruent to 3 modulo 4 than to 1 modulo 4. We will exp lain and qualify this claim following the framework of Rubinstein and Sarn ak. Then we will see how this framework can be adapted to other questions on the distribution of prime numbers. This will be illustrated by a new Ch ebyshev-like claim : "for more than half of the prime numbers that can be written as a sum of two squares\, the odd square is the square of a posit ive integer congruent to 1 mod 4".\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Kwangho Choiy (Southern Illinois University) DTSTART:20211220T080000Z DTEND:20211220T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/9 DESCRIPTION:Title: Invariants in restriction of admissible representations of p- adic groups\nby Kwangho Choiy (Southern Illinois University) as part o f French-Korean webinar in number theory\n\n\nAbstract\nThe local Langland s correspondence\, LLC\, of a p-adic group over complex vector spaces has been proved for several cases over decades. One of interesting approaches to them is the restriction method which was initiated for SL(2) and its in ner form. It proposes in line with the functoriality principle that the LL C of one group can be achieved from the LLC of the other group sharing the same derived group. In this context\, we shall explain how the method is extended to some other cases of LLC's\, the multiplicity formula in restri ction\, and the transfer of the reducibility of parabolic induction.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Gautier Ponsinet (Università degli Studi di Genova) DTSTART:20220207T080000Z DTEND:20220207T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/10 DESCRIPTION:Title: Universal norms of p-adic Galois representations\nby Gau tier Ponsinet (Università degli Studi di Genova) as part of French-Korean webinar in number theory\n\n\nAbstract\nIn 1996\, Coates and Greenberg ob served that perfectoid fields appear naturally in Iwasawa theory.\nIn part icular\, they have computed the module of universal norms associated with an abelian variety in a perfectoid field extension.\nA precise description of this module is essential in Iwasawa theory\, notably to study Selmer g roups over infinite algebraic field extensions.\nIn this talk\, I will exp lain how to use properties of the Fargues-Fontaine curve to generalise the ir results to p-adic representations.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jun-Yong Park (MPIM\, Bonn) DTSTART:20220221T080000Z DTEND:20220221T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/11 DESCRIPTION:Title: Arithmetic Moduli of Elliptic Surfaces\nby Jun-Yong Park (MPIM\, Bonn) as part of French-Korean webinar in number theory\n\n\nAbst ract\nBy considering the arithmetic geometry of rational orbi-curves on mo dular curve $\\overline{\\mathcal{M}}_{1\,1}$ where $\\overline{\\mathcal{ M}}_{1\,1}$ is the Deligne--Mumford stack of stable elliptic curves\, we f ormulate the moduli stack of minimal elliptic fibrations over $\\mathbb{P} ^{1}$\, also known as minimal elliptic surfaces with section over any base field $K$ with $\\mathrm{char}(K) \\neq 2\,3$. Inspired by the classical work of [Tate] which allows us to determine the Kodaira--N\\'eron type of fibers over global fields\, we establish Tate's correspondence between the moduli stacks $\\mathrm{Rat}_{n}^{\\gamma}(\\mathbb{P}^1\, \\overline{\\m athcal{M}}_{1\,1})$ of quasimaps with vanishing constraints $\\gamma$ and $\\mathrm{Hom}^{\\Gamma}_n(\\mathcal{C}\, \\overline{\\mathcal{M}}_{1\,1}) $ of twisted maps with cyclotomic twistings $\\Gamma$. Afterward\, we acqu ire the exact arithmetic invariants of the moduli for each Kodaira--N\\'er on types which naturally renders new sharp enumerations with a main leadin g term of order $\\mathcal{B}^{\\frac{5}{6}}$ and secondary \\& tertiary o rder terms $\\mathcal{B}^{\\frac{1}{2}} ~\\&~ \\mathcal{B}^{\\frac{1}{3}}$ on $\\mathcal{Z}_{\\mathbb{F}_q(t)}(\\mathcal{B})$ for counting elliptic curves over $\\mathbb{P}_{\\mathbb{F}_q}^{1}$ with additive reductions ord ered by bounded height of discriminant $\\Delta$. The emergence of non-con stant lower order terms are in stark contrast with counting the semistable (i.e.\, strictly multiplicative reductions) elliptic curves. In the end\, we formulate an analogous heuristic on $\\mathcal{Z}_{\\mathbb{Q}}(\\math cal{B})$ for counting elliptic curves over $\\mathbb{Q}$ through the globa l fields analogy. This is a joint work with Dori Bejleri (Harvard) and Mat thew Satriano (Waterloo).\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Silvain Rideau-Kikuchi (Institut de Mathématiques de Jussieu-Pari s Rive Gauche) DTSTART:20220307T080000Z DTEND:20220307T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/12 DESCRIPTION:Title: H-minimality (with R. Cluckers\, I. Halupczok)\nby Silva in Rideau-Kikuchi (Institut de Mathématiques de Jussieu-Paris Rive Gauche ) as part of French-Korean webinar in number theory\n\n\nAbstract\nThe dev elopment and numerous applications of strong minimality and later o-minima lity has given serious credit to the general model theoretic idea that imp osing strong restrictions on the complexity of arity one sets in a structu re can lead to a rich tame geometry in all dimensions. O-minimality (in an ordered field)\, for example\, requires that subsets of the affine line a re finite unions of points and intervals.\n\nIn this talk\, I will present a new minimality notion (h-minimality)\, geared towards henselian valued fields of characteristic zero\, generalising previously considered notions of minimality for valued fields (C\,V\,P …) that does not\, contrary to previously defined notions\, restrict the possible residue fields and val ue groups. By analogy with o-minimality\, this notion requires that defina ble sets of the affine line are controlled by a finite number of points. C ontrary to o-minimality though\, one has to take special care of how this finite set is defined\, leading us to a whole family of notions of h-minim ality. I will then describe consequences of h-minimality\, among which the jacobian property that plays a central role in the development of motivic integration\, but also various higher degree and arity analogs.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Junho Peter Whang (Seoul National University) DTSTART:20220321T080000Z DTEND:20220321T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/13 DESCRIPTION:by Junho Peter Whang (Seoul National University) as part of Fr ench-Korean webinar in number theory\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Hernandez (Université d'Orsay) DTSTART:20220404T080000Z DTEND:20220404T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/14 DESCRIPTION:Title: The Infinite Fern in higher dimensions\nby Valentin Hern andez (Université d'Orsay) as part of French-Korean webinar in number the ory\n\n\nAbstract\nIn general\, deformations spaces of residual Galois rep resentation are quite mysterious objects. It is natural to ask if there is at least enough modular points in their generic fiber X. A related questi on is the density of the p-adic modular forms\, which form a fractal-like object called the Infinite Fern. In dimension 2\, in most cases Gouvêa an d Mazur proved that this infinite fern is Zariski dense in X. In higher di mension we look at \\emph{polarized} Galois representation\, and the analo gous question becomes much more complicated. Chenevier explained a strateg y by looking for \\emph{good} (called generic) points in Eigenvarieties\, studied the analogous local (p-adic) question and solved the case of dimen sion 3. Recently Breuil-Hellmann-Schraen studied the local Infinite Fern a t well behaved crystalline points\, and Hellmann-Margerin-Schraen\, under strong Taylor-Wiles hypothesis\, managed to prove the density of the (glob al) Infinite Fern (in a union of connected components) in all dimensions u sing the \\emph{patched} Eigenvariety. In this talk I would like to explai n how to only use the local geometric input to deduce the analogous densit y result without using the Taylor-Wiles hypothesis\, but using another kin d of \\emph{good} points as in Chenevier’s strategy. This is a joint wor k with Benjamin Schraen.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Seungki Kim (University of Cincinnati) DTSTART:20220502T080000Z DTEND:20220502T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/15 DESCRIPTION:Title: Adelic Rogers integral formula\nby Seungki Kim (Universi ty of Cincinnati) as part of French-Korean webinar in number theory\n\n\nA bstract\nThe Rogers integral formula\, a natural generalization of the wel l-known Siegel integral formula\, first appeared in the 1950's as an essen tial tool in the geometry of numbers. Very recently\, there has been a sur prising resurgence of interest in the formula\, thanks in much part to its usefulness in homogeneous dynamics\, and a number of variants and extensi ons have been proposed. I will introduce the audience to the relevant lite rature\, in particular the recently proved formula over an adele of a numb er field.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Lanard (University of Vienna) DTSTART:20220523T080000Z DTEND:20220523T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/16 DESCRIPTION:Title: Depth zero representations over $\\overline{\\mathbb{Z}}[\\f rac{1}{p}]$\nby Thomas Lanard (University of Vienna) as part of French -Korean webinar in number theory\n\n\nAbstract\nIn this talk\, I will talk about the category of depth zero representations of a $p$-adic group with coefficients in $\\overline{\\mathbb{Z}}[\\frac{1}{p}]$. When the group $ \\mathbf{G}$ is quasi-split and tamely ramified\, the depth zero category over $\\overline{\\mathbb{Z}}[\\frac{1}{p}]$ is indecomposable. In general \, for a quasi-split group\, we will see that the blocks (indecomposable s ummands) of this category are in natural bijection with the connected comp onents of the space of tamely ramified Langlands parameters. In the last p art\, I will explain some potential applications to the Fargues-Scholze an d Genestier-Lafforgue semisimple local Langlands correspondences. This is joint work with Jean-François Dat.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yeongseoung Jo (University of Maine) DTSTART:20220613T080000Z DTEND:20220613T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/17 DESCRIPTION:Title: Rankin-Selberg integrals in positive characteristic and its connection to Langlands functoriality\nby Yeongseoung Jo (University o f Maine) as part of French-Korean webinar in number theory\n\n\nAbstract\n The prominent Langlands functoriality conjecture predicts deep relationshi ps among representations on different groups. One of the well-understood c ases is a local functorial transfer of irreducible generic supercuspidal r epresentations of ${\\rm SO}_{2r+1}(F)$ to irreducible supercuspidal ones of ${\\rm GL}_{2r}(F)$ over $p$-adic fields $F$. This functorial lift is defined by Lomel\\'{\\i} over non-archimedean local fields $F$ of positive characteristic\, but it is rarely studied. Following the spirit of Cogdel l and Piatetski-Shapiro\, the purpose of this talk is to take one more ste p further to investigate the transfer thoroughly. We first consider the im age of the map. Somewhat surprisingly\, this is related to poles of local exterior square $L$-functions via integral representations due to Jacquet and Shalika. We then discuss whether the map is injective. It turns out th at the problem is relevant to what is known as the local converse theorem for ${\\rm SO}_{2r+1}(F)$.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Peaucelle (Université Clermont Auvergne) DTSTART:20220627T080000Z DTEND:20220627T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/18 DESCRIPTION:Title: Exceptional images of modular Galois representations\nby Baptiste Peaucelle (Université Clermont Auvergne) as part of French-Kore an webinar in number theory\n\n\nAbstract\nGiven a modular form $f$ and a prime ideal $\\lambda$ in the coefficient field of $f$\, one can attach a residual Galois representation of dimension 2 with values in the residue f ield of $\\lambda$. A theorem of Ribet states that this representation has small image for a finite number of prime ideals $\\lambda$. In this talk\ , I will explain how one can bound explicitly these exceptional ideals\, a nd how to compute them for some types of small image.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Joachim Koenig (Korea National University of Education) DTSTART:20221017T080000Z DTEND:20221017T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/19 DESCRIPTION:Title: On the arithmetic-geometric complexity of the Grunwald probl em\nby Joachim Koenig (Korea National University of Education) as part of French-Korean webinar in number theory\n\n\nAbstract\nThe Grunwald pro blem for a group G over a number field k asks whether\, given Galois exten sions of kp of Galois group embedding into G at finitely many completions kp of k (possibly away from some finite set of primes depending only on G and k)\, there always exists a G-extension of k approximating all these lo cal extensions. This question grew naturally out of the Grunwald-Wang theo rem\, which deals with the case of abelian groups. Following more general concepts of arithmetic-geometric complexity in inverse Galois theory\, we develop a notion of complexity of Grunwald problems by looking for Galois covers of varieties which encapsulate solutions to arbitrary Grunwald prob lems (for a given group). In particular\, we determine the groups G for wh ich solutions to arbitrary Grunwald problems may be obtained via specializ ation of a G-cover of {\\it curves}. Joint with D. Neftin.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:François Ballaÿ (Université de Caen Normandie) DTSTART:20221107T080000Z DTEND:20221107T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/20 DESCRIPTION:Title: Positivity in Arakelov geometry and arithmetic Okounkov bodi es\nby François Ballaÿ (Université de Caen Normandie) as part of Fr ench-Korean webinar in number theory\n\n\nAbstract\nArakelov theory is a p owerful approach to Diophantine geometry that develops arithmetic analogue s of tools from algebraic geometry to tackle problems in number theory. It permits to study the arithmetico-geometric properties of a projective var iety over a number field by looking at its adelic line bundles\, which are usual line bundles equipped with a suitable collection of metrics. Since the seminal work of Zhang on arithmetic ampleness\, several notions of pos itivity for adelic line bundles have been introduced and studied in analog y with the algebro-geometric setting (nefness\, bigness\, pseudo-effective ness...). In this talk\, I will present these notions and emphasize their connection with the study of height functions in Diophantine geometry. I w ill then describe how these positivity properties can be studied through c onvex analysis\, thanks to the theory of arithmetic Okounkov bodies introd uced by Boucksom and Chen.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaehyun Cho (UNIST Korea) DTSTART:20221121T080000Z DTEND:20221121T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/21 DESCRIPTION:Title: The average residue of the Dedekind zeta function\nby Ja ehyun Cho (UNIST Korea) as part of French-Korean webinar in number theory\ n\n\nAbstract\nWe find the explicit formula for the average residue of the Dedekind zeta functions over all non-Galois cubic fields. The main tool i s a recent result of Bhargava\, Taniguchi\, and Thorne's on improving the error term in counting cubic fields.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Poëls (University Lyon 1) DTSTART:20221205T080000Z DTEND:20221205T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/22 DESCRIPTION:Title: Rational approximation to real points on quadratic hypersurf aces\nby Anthony Poëls (University Lyon 1) as part of French-Korean w ebinar in number theory\n\n\nAbstract\nThis is a joint work with Damien Ro y. Let Z be a quadratic hypersurface of R^n defined over Q (such as the un it sphere). We compute the largest exponent of uniform rational approximat ion of the points belonging to Z whose coordinates together with 1 are lin early independent over Q. We show that it depends only on n and on the Wit t index (over Q) of the quadratic form defining Z. This completes a recent work of Kleinbock and Moshchevitin.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Jungyun Lee (Kangwon University) DTSTART:20221212T080000Z DTEND:20221212T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/23 DESCRIPTION:Title: The mean value of the class numbers of cubic function fields \nby Jungyun Lee (Kangwon University) as part of French-Korean webinar in number theory\n\n\nAbstract\nWe compute the mean value of |L(s\,chi)|^ 2 evaluated at s=1 when chi goes through the primitive cubic Dirichlet cha racters of A:=F_q[T]\, where F_q is a finite field with q elements and q \ \equiv 1 \\p mod 3. Furthermore\, we find the mean value of the class numb ers for the cubic function fields K_m=k(\\sqrt[3]{m})\, where k:= F_q(T) i s the rational function field and m in A is a cube-free polynomial.(This is a joint work with Yoonjin Lee and Jinjoo Yoo.)\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Ricotta (Université de Bordeaux) DTSTART:20230403T080000Z DTEND:20230403T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/24 DESCRIPTION:Title: Kloosterman paths of prime powers moduli\nby Guillaume R icotta (Université de Bordeaux) as part of French-Korean webinar in numbe r theory\n\n\nAbstract\nWe prove that the polygonal paths joining the part ial sums of the normalized classical Kloosterman sums of moduli p^n conver ge in law\, as p tends to infinity\, to an explicit random Fourier series in the Banach space of complex-valued continuous function on [0\,1].\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaeho Haan (Yeonse University) DTSTART:20230424T080000Z DTEND:20230424T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/25 DESCRIPTION:Title: The local converse theorem for quasi-split SO(2n)\nby Ja eho Haan (Yeonse University) as part of French-Korean webinar in number th eory\n\n\nAbstract\nLocal converse theorem (LCT) has many interesting appl ications. For example\, global rigidity theorem and injectivity of global factorial lift of global generic cuspidal representations of classical gro ups immediately follows from it. Starting from the Jiang and Soudry's pion eering work for SO(2n+1)\, the LCT has now proved for almost all classical groups but quasi-split SO(2n). In this talk\, we discuss the proof of LCT for quasi-split SO(2n) by studying the relation of gamma factors between SO(2n) and Sp(2n). If time permits\, we also discuss the positive characte ristic cases as well as the characteristic zero cases. This is a joint wor k with Yeansu Kim and Sanghoon Kwon.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Berger (ENS de Lyon) DTSTART:20230515T080000Z DTEND:20230515T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/26 DESCRIPTION:Title: Super-Hölder functions and vectors\nby Laurent Berger ( ENS de Lyon) as part of French-Korean webinar in number theory\n\n\nAbstra ct\nI will define super-Hölder functions\, an analogue in characteristic p of locally analytic functions. I will give examples of super-Hölder fun ctions in certain situations of arithmetic interest. Joint work with Sandr a Rozensztajn.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Seok Hyeong Lee (Seoul National University) DTSTART:20230522T080000Z DTEND:20230522T090000Z DTSTAMP:20260424T235139Z UID:FranceKoreaNT/27 DESCRIPTION:Title: Explicit construction for Bhargava's "Higher Composition Law s"\nby Seok Hyeong Lee (Seoul National University) as part of French-K orean webinar in number theory\n\n\nAbstract\nBhargava's "Higher Compositi on Laws" give explicit one-to-one correspondence between rings of low rank s and certain integral forms. Generalizing Wood's extension of cubic and q uartic ring parametrizations\, we give a general algorithm of constructing rings out of well-posed integral forms which can be applied to all cases of Higher Composition Laws.\n LOCATION:https://stable.researchseminars.org/talk/FranceKoreaNT/27/ END:VEVENT END:VCALENDAR