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:20260422T225922Z UID:FranceKoreaNT/1 DESCRIPTION:Title: On the Fitting ideals of Selmer groups of modular forms\nby Chan -Ho Kim (KIAS\, Korea) as part of French-Korean webinar in number theory\n \n\nAbstract\nIn 1980's\, Mazur and Tate studied ``Iwasawa theory for elli ptic curves over finite abelian extensions" and formulated various related conjectures. One of their conjectures says that the analytically defined Mazur-Tate element lies in the Fitting ideal of the dual Selmer group of a n elliptic curve. We discuss some cases of the conjecture for modular form s of higher weight.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Riccardo Pengo (ENS de Lyon\, France) DTSTART:20210517T080000Z DTEND:20210517T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/2 DESCRIPTION:Title: Entanglement in the family of division fields of a CM elliptic curve \nby Riccardo Pengo (ENS de Lyon\, France) as part of French-Korean we binar in number theory\n\n\nAbstract\nDivision fields associated to an alg ebraic group defined over a number field\, which are the extensions genera ted by its torsion points\, have been the subject of a great amount of res earch\, at least since the times of Kronecker and Weber. For elliptic curv es without complex multiplication\, Serre's open image theorem shows that the division fields associated to torsion points whose order is a prime po wer are "as big as possible" and pairwise linearly disjoint\, if one remov es a finite set of primes. Explicit versions of this result have recently been featured in the work of Campagna-Stevenhagen and Lombardo-Tronto. 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 co mplex multiplication. Moreover\, I will present a necessary condition to h ave entanglement in the family of division fields\, which is always satisf ied for elliptic curves defined over the rationals. In this last case\, I will describe in detail the entanglement in the family of division fields. \n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Hae-Sang Sun (UNIST\, Korea) DTSTART:20210607T080000Z DTEND:20210607T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/3 DESCRIPTION:Title: Cyclotomic Hecke L-values of a totally real field\nby Hae-Sang S un (UNIST\, Korea) as part of French-Korean webinar in number theory\n\n\n Abstract\nIt is known that any Fourier coefficient of a newform of weight 2 can be expressed as a polynomial with rational coefficients\, of a singl e algebraic critical value of the corresponding L-function twisted by a Di richlet 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-functio n over a totally real field\, twisted by Hecke characters of $p$-power con ductors. The discussion involves new technical challenges that arise from the presence of the unit group\, which are (1) counting lattice points in a cone that $p$-adically close to units and (2) estimating an exponential sum over the unit group. This is joint work with Byungheup Jun and Jungyun Lee.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vlerë Mehmeti (Université Paris-Saclay\, France) DTSTART:20210621T080000Z DTEND:20210621T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/4 DESCRIPTION:Title: Non-Archimedean analytic curves and the local-global principle\n by Vlerë Mehmeti (Université Paris-Saclay\, France) as part of French-Ko rean webinar in number theory\n\n\nAbstract\nIn 2009\, a new technique\, c alled algebraic patching\, was introduced in the study of local-global pri nciples. Under different forms\, patching had in the past been used for th e study of the inverse Galois problem. In this talk\, I will present an ex tension of this technique to non-Archimedean analytic curves. As an applic ation\, we will see various local-global principles for function fields of curves\, ranging from geometric to more classical forms. These results ge neralize those of the previous literature and are applicable to quadratic forms. We will start by a brief introduction of the framework of non-Archi medean analytic curves and will conclude by a presentation of a first step towards such results in higher dimensions.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Seoyoung Kim (Queen's University) DTSTART:20211004T080000Z DTEND:20211004T090000Z DTSTAMP:20260422T225922Z 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\nAbstr act\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} suc h that aiaj+n is a k-th power for any distinct i and j. Define by Mk(n) th e 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 integers. In particular\, we show that for k≥3\, Mk(n) is O(logn) and further assumi ng the Paley graph conjecture\, Mk(n) is O((logn)ϵ). The problem for k=2 was studied by a long list of authors that goes back to Diophantus who stu died 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://researchseminars.org/talk/FranceKoreaNT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Griffon (Université Clermont-Auvergne) DTSTART:20211018T080000Z DTEND:20211018T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/6 DESCRIPTION:Title: Isogenies of elliptic curves over function fields\nby Richard Gr iffon (Université Clermont-Auvergne) as part of French-Korean webinar in number theory\n\n\nAbstract\nI will report on a recent work\, joint with F abien Pazuki\, in which we study elliptic curves over function fields and the isogenies between them. More specifically\, we prove analogues in the function field setting of two famous theorems about isogenous elliptic cur ves 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 spirit of th eorems by Masser—Wüstholz and by Gaudron—Rémond. After stating our r esults and giving quick sketches of their proof\, I will\, time permitting \, mention a few Diophantine applications.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Wansu Kim (KAIST) DTSTART:20211108T080000Z DTEND:20211108T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/7 DESCRIPTION:Title: Equivariant BSD conjecture over global function fields\nby Wansu Kim (KAIST) as part of French-Korean webinar in number theory\n\n\nAbstra ct\nUnder a certain finiteness assumption of Tate-Shafarevich groups\, Kat o and Trihan showed the BSD conjecture for abelian varieties over global f unction fields of positive characteristic. We explain how to generalise th is to semi-stable abelian varieties “twisted by Artin character” over global function field (under some additional technical assumptions)\, and discuss further speculations for generalisations if time permits. This is a joint work with David Burns and Mahesh Kakde.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucile Devin (Université du Littoral\, Calais) DTSTART:20211122T080000Z DTEND:20211122T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/8 DESCRIPTION:Title: Chebyshev’s bias and sums of two squares\nby Lucile Devin (Uni versité du Littoral\, Calais) as part of French-Korean webinar in number theory\n\n\nAbstract\nStudying the secondary terms of the Prime Number The orem in Arithmetic Progressions\, Chebyshev claimed that there are more pr ime numbers congruent to 3 modulo 4 than to 1 modulo 4. We will explain an d qualify this claim following the framework of Rubinstein and Sarnak. The n 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 Chebyshev -like claim : "for more than half of the prime numbers that can be writte n as a sum of two squares\, the odd square is the square of a positive int eger congruent to 1 mod 4".\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Kwangho Choiy (Southern Illinois University) DTSTART:20211220T080000Z DTEND:20211220T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/9 DESCRIPTION:Title: Invariants in restriction of admissible representations of p-adic gr oups\nby Kwangho Choiy (Southern Illinois University) as part of Frenc h-Korean webinar in number theory\n\n\nAbstract\nThe local Langlands corre spondence\, LLC\, of a p-adic group over complex vector spaces has been pr oved for several cases over decades. One of interesting approaches to them is the restriction method which was initiated for SL(2) and its inner for m. It proposes in line with the functoriality principle that the LLC of on e group can be achieved from the LLC of the other group sharing the same d erived group. In this context\, we shall explain how the method is extende d to some other cases of LLC's\, the multiplicity formula in restriction\, and the transfer of the reducibility of parabolic induction.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Gautier Ponsinet (Università degli Studi di Genova) DTSTART:20220207T080000Z DTEND:20220207T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/10 DESCRIPTION:Title: Universal norms of p-adic Galois representations\nby Gautier Po nsinet (Università degli Studi di Genova) as part of French-Korean webina r in number theory\n\n\nAbstract\nIn 1996\, Coates and Greenberg observed that perfectoid fields appear naturally in Iwasawa theory.\nIn particular\ , they have computed the module of universal norms associated with an abel ian variety in a perfectoid field extension.\nA precise description of thi s module is essential in Iwasawa theory\, notably to study Selmer groups o ver infinite algebraic field extensions.\nIn this talk\, I will explain ho w to use properties of the Fargues-Fontaine curve to generalise their resu lts to p-adic representations.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jun-Yong Park (MPIM\, Bonn) DTSTART:20220221T080000Z DTEND:20220221T090000Z DTSTAMP:20260422T225922Z 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\nAbstract\nB y considering the arithmetic geometry of rational orbi-curves on modular c urve $\\overline{\\mathcal{M}}_{1\,1}$ where $\\overline{\\mathcal{M}}_{1\ ,1}$ is the Deligne--Mumford stack of stable elliptic curves\, we formulat e 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 $\\mathrm{Rat}_{n}^{\\gamma}(\\mathbb{P}^1\, \\overline{\\mathcal{ M}}_{1\,1})$ of quasimaps with vanishing constraints $\\gamma$ and $\\math rm{Hom}^{\\Gamma}_n(\\mathcal{C}\, \\overline{\\mathcal{M}}_{1\,1})$ of tw isted maps with cyclotomic twistings $\\Gamma$. Afterward\, we acquire the exact arithmetic invariants of the moduli for each Kodaira--N\\'eron type s which naturally renders new sharp enumerations with a main leading term of order $\\mathcal{B}^{\\frac{5}{6}}$ and secondary \\& tertiary order te rms $\\mathcal{B}^{\\frac{1}{2}} ~\\&~ \\mathcal{B}^{\\frac{1}{3}}$ on $\\ mathcal{Z}_{\\mathbb{F}_q(t)}(\\mathcal{B})$ for counting elliptic curves over $\\mathbb{P}_{\\mathbb{F}_q}^{1}$ with additive reductions ordered by bounded height of discriminant $\\Delta$. The emergence of non-constant l ower order terms are in stark contrast with counting the semistable (i.e.\ , strictly multiplicative reductions) elliptic curves. In the end\, we for mulate an analogous heuristic on $\\mathcal{Z}_{\\mathbb{Q}}(\\mathcal{B}) $ for counting elliptic curves over $\\mathbb{Q}$ through the global field s analogy. This is a joint work with Dori Bejleri (Harvard) and Matthew Sa triano (Waterloo).\n LOCATION:https://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:20260422T225922Z UID:FranceKoreaNT/12 DESCRIPTION:Title: H-minimality (with R. Cluckers\, I. Halupczok)\nby Silvain Ride au-Kikuchi (Institut de Mathématiques de Jussieu-Paris Rive Gauche) as pa rt of French-Korean webinar in number theory\n\n\nAbstract\nThe developmen t and numerous applications of strong minimality and later o-minimality ha s given serious credit to the general model theoretic idea that imposing s trong restrictions on the complexity of arity one sets in a structure can lead to a rich tame geometry in all dimensions. O-minimality (in an ordere d field)\, for example\, requires that subsets of the affine line are fini te 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 min imality for valued fields (C\,V\,P …) that does not\, contrary to previo usly defined notions\, restrict the possible residue fields and value grou ps. By analogy with o-minimality\, this notion requires that definable set s of the affine line are controlled by a finite number of points. Contrary 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-minimality. I will then describe consequences of h-minimality\, among which the jacobi an property that plays a central role in the development of motivic integr ation\, but also various higher degree and arity analogs.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Junho Peter Whang (Seoul National University) DTSTART:20220321T080000Z DTEND:20220321T090000Z DTSTAMP:20260422T225922Z 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://researchseminars.org/talk/FranceKoreaNT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Hernandez (Université d'Orsay) DTSTART:20220404T080000Z DTEND:20220404T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/14 DESCRIPTION:Title: The Infinite Fern in higher dimensions\nby Valentin Hernandez ( Université d'Orsay) as part of French-Korean webinar in number theory\n\n \nAbstract\nIn general\, deformations spaces of residual Galois representa tion are quite mysterious objects. It is natural to ask if there is at lea st enough modular points in their generic fiber X. A related question is t he density of the p-adic modular forms\, which form a fractal-like object called the Infinite Fern. In dimension 2\, in most cases Gouvêa and Mazur proved that this infinite fern is Zariski dense in X. In higher dimension we look at \\emph{polarized} Galois representation\, and the analogous qu estion becomes much more complicated. Chenevier explained a strategy by lo oking for \\emph{good} (called generic) points in Eigenvarieties\, studied the analogous local (p-adic) question and solved the case of dimension 3. Recently Breuil-Hellmann-Schraen studied the local Infinite Fern at well behaved crystalline points\, and Hellmann-Margerin-Schraen\, under strong Taylor-Wiles hypothesis\, managed to prove the density of the (global) Inf inite Fern (in a union of connected components) in all dimensions using th e \\emph{patched} Eigenvariety. In this talk I would like to explain how t o only use the local geometric input to deduce the analogous density resul t without using the Taylor-Wiles hypothesis\, but using another kind of \\ emph{good} points as in Chenevier’s strategy. This is a joint work with Benjamin Schraen.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Seungki Kim (University of Cincinnati) DTSTART:20220502T080000Z DTEND:20220502T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/15 DESCRIPTION:Title: Adelic Rogers integral formula\nby Seungki Kim (University of C incinnati) as part of French-Korean webinar in number theory\n\n\nAbstract \nThe Rogers integral formula\, a natural generalization of the well-known Siegel integral formula\, first appeared in the 1950's as an essential to ol in the geometry of numbers. Very recently\, there has been a surprising resurgence of interest in the formula\, thanks in much part to its useful ness in homogeneous dynamics\, and a number of variants and extensions hav e been proposed. I will introduce the audience to the relevant literature\ , in particular the recently proved formula over an adele of a number fiel d.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Lanard (University of Vienna) DTSTART:20220523T080000Z DTEND:20220523T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/16 DESCRIPTION:Title: Depth zero representations over $\\overline{\\mathbb{Z}}[\\frac{1}{ p}]$\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 coeffi cients in $\\overline{\\mathbb{Z}}[\\frac{1}{p}]$. When the group $\\mathb f{G}$ 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 summands ) of this category are in natural bijection with the connected components of the space of tamely ramified Langlands parameters. In the last part\, I will explain some potential applications to the Fargues-Scholze and Genes tier-Lafforgue semisimple local Langlands correspondences. This is joint w ork with Jean-François Dat.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yeongseoung Jo (University of Maine) DTSTART:20220613T080000Z DTEND:20220613T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/17 DESCRIPTION:Title: Rankin-Selberg integrals in positive characteristic and its connect ion to Langlands functoriality\nby Yeongseoung Jo (University of Maine ) as part of French-Korean webinar in number theory\n\n\nAbstract\nThe pro minent Langlands functoriality conjecture predicts deep relationships amon g representations on different groups. One of the well-understood cases is a local functorial transfer of irreducible generic supercuspidal represen tations 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 charac teristic\, but it is rarely studied. Following the spirit of Cogdell and P iatetski-Shapiro\, the purpose of this talk is to take one more step furth er to investigate the transfer thoroughly. We first consider the image of the map. Somewhat surprisingly\, this is related to poles of local exterio r square $L$-functions via integral representations due to Jacquet and Sha lika. We then discuss whether the map is injective. It turns out that the problem is relevant to what is known as the local converse theorem for ${ \\rm SO}_{2r+1}(F)$.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Baptiste Peaucelle (Université Clermont Auvergne) DTSTART:20220627T080000Z DTEND:20220627T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/18 DESCRIPTION:Title: Exceptional images of modular Galois representations\nby Baptis te Peaucelle (Université Clermont Auvergne) as part of French-Korean webi nar in number theory\n\n\nAbstract\nGiven a modular form $f$ and a prime i deal $\\lambda$ in the coefficient field of $f$\, one can attach a residua l Galois representation of dimension 2 with values in the residue field 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 wil l explain how one can bound explicitly these exceptional ideals\, and how to compute them for some types of small image.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Joachim Koenig (Korea National University of Education) DTSTART:20221017T080000Z DTEND:20221017T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/19 DESCRIPTION:Title: On the arithmetic-geometric complexity of the Grunwald problem\ nby Joachim Koenig (Korea National University of Education) as part of Fre nch-Korean webinar in number theory\n\n\nAbstract\nThe Grunwald problem fo r a group G over a number field k asks whether\, given Galois extensions o f 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 local ext ensions. This question grew naturally out of the Grunwald-Wang theorem\, w hich deals with the case of abelian groups. Following more general concept s 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 problems (f or a given group). In particular\, we determine the groups G for which sol utions to arbitrary Grunwald problems may be obtained via specialization o f a G-cover of {\\it curves}. Joint with D. Neftin.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:François Ballaÿ (Université de Caen Normandie) DTSTART:20221107T080000Z DTEND:20221107T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/20 DESCRIPTION:Title: Positivity in Arakelov geometry and arithmetic Okounkov bodies\ nby François Ballaÿ (Université de Caen Normandie) as part of French-Ko rean webinar in number theory\n\n\nAbstract\nArakelov theory is a powerful approach to Diophantine geometry that develops arithmetic analogues of to ols from algebraic geometry to tackle problems in number theory. It permit s to study the arithmetico-geometric properties of a projective variety ov er a number field by looking at its adelic line bundles\, which are usual line bundles equipped with a suitable collection of metrics. Since the sem inal work of Zhang on arithmetic ampleness\, several notions of positivity for adelic line bundles have been introduced and studied in analogy with the algebro-geometric setting (nefness\, bigness\, pseudo-effectiveness... ). In this talk\, I will present these notions and emphasize their connect ion with the study of height functions in Diophantine geometry. I will the n describe how these positivity properties can be studied through convex a nalysis\, thanks to the theory of arithmetic Okounkov bodies introduced by Boucksom and Chen.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaehyun Cho (UNIST Korea) DTSTART:20221121T080000Z DTEND:20221121T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/21 DESCRIPTION:Title: The average residue of the Dedekind zeta function\nby Jaehyun C ho (UNIST Korea) as part of French-Korean webinar in number theory\n\n\nAb stract\nWe find the explicit formula for the average residue of the Dedeki nd zeta functions over all non-Galois cubic fields. The main tool is a rec ent result of Bhargava\, Taniguchi\, and Thorne's on improving the error t erm in counting cubic fields.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Poëls (University Lyon 1) DTSTART:20221205T080000Z DTEND:20221205T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/22 DESCRIPTION:Title: Rational approximation to real points on quadratic hypersurfaces\nby Anthony Poëls (University Lyon 1) as part of French-Korean webinar in number theory\n\n\nAbstract\nThis is a joint work with Damien Roy. Let Z be a quadratic hypersurface of R^n defined over Q (such as the unit sphe re). We compute the largest exponent of uniform rational approximation of the points belonging to Z whose coordinates together with 1 are linearly i ndependent over Q. We show that it depends only on n and on the Witt index (over Q) of the quadratic form defining Z. This completes a recent work o f Kleinbock and Moshchevitin.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Jungyun Lee (Kangwon University) DTSTART:20221212T080000Z DTEND:20221212T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/23 DESCRIPTION:Title: The mean value of the class numbers of cubic function fields\nb y Jungyun Lee (Kangwon University) as part of French-Korean webinar in num ber theory\n\n\nAbstract\nWe compute the mean value of |L(s\,chi)|^2 evalu ated at s=1 when chi goes through the primitive cubic Dirichlet characters 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 numbers for the cubic function fields K_m=k(\\sqrt[3]{m})\, where k:= F_q(T) is the r ational function field and m in A is a cube-free polynomial.(This is a jo int work with Yoonjin Lee and Jinjoo Yoo.)\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillaume Ricotta (Université de Bordeaux) DTSTART:20230403T080000Z DTEND:20230403T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/24 DESCRIPTION:Title: Kloosterman paths of prime powers moduli\nby Guillaume Ricotta (Université de Bordeaux) as part of French-Korean webinar in number theor y\n\n\nAbstract\nWe prove that the polygonal paths joining the partial sum s of the normalized classical Kloosterman sums of moduli p^n converge in l aw\, 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://researchseminars.org/talk/FranceKoreaNT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaeho Haan (Yeonse University) DTSTART:20230424T080000Z DTEND:20230424T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/25 DESCRIPTION:Title: The local converse theorem for quasi-split SO(2n)\nby Jaeho Haa n (Yeonse University) as part of French-Korean webinar in number theory\n\ n\nAbstract\nLocal converse theorem (LCT) has many interesting application s. For example\, global rigidity theorem and injectivity of global factori al lift of global generic cuspidal representations of classical groups imm ediately follows from it. Starting from the Jiang and Soudry's pioneering 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 qu asi-split SO(2n) by studying the relation of gamma factors between SO(2n) and Sp(2n). If time permits\, we also discuss the positive characteristic cases as well as the characteristic zero cases. This is a joint work with Yeansu Kim and Sanghoon Kwon.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Berger (ENS de Lyon) DTSTART:20230515T080000Z DTEND:20230515T090000Z DTSTAMP:20260422T225922Z 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\nAbstract\nI w ill define super-Hölder functions\, an analogue in characteristic p of lo cally analytic functions. I will give examples of super-Hölder functions in certain situations of arithmetic interest. Joint work with Sandra Rozen sztajn.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Seok Hyeong Lee (Seoul National University) DTSTART:20230522T080000Z DTEND:20230522T090000Z DTSTAMP:20260422T225922Z UID:FranceKoreaNT/27 DESCRIPTION:Title: Explicit construction for Bhargava's "Higher Composition Laws"\ nby Seok Hyeong Lee (Seoul National University) as part of French-Korean w ebinar in number theory\n\n\nAbstract\nBhargava's "Higher Composition Laws " give explicit one-to-one correspondence between rings of low ranks and c ertain integral forms. Generalizing Wood's extension of cubic and quartic ring parametrizations\, we give a general algorithm of constructing rings out of well-posed integral forms which can be applied to all cases of High er Composition Laws.\n LOCATION:https://researchseminars.org/talk/FranceKoreaNT/27/ END:VEVENT END:VCALENDAR