BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michele Fornea (Columbia) DTSTART:20200918T143000Z DTEND:20200918T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/2 DESCRIPTION:Title: Po ints on elliptic curves via p-adic integration\nby Michele Fornea (Col umbia) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nA bstract\nThe work of Bertolini\, Darmon and their schools has shown that p -adic multiplicative integrals can be successfully employed to study the g lobal arithmetic of elliptic curves. Notably\, Guitart\, Masdeu and Sengun have recently constructed and numerically computed Stark-Heegner points i n great generality. Their results strongly support the expectation that St ark-Heegner points completely control the Mordell-Weil group of elliptic c urves of rank 1.\n\nIn our talk\, we will report on work in progress about a conjectural construction of global points on modular elliptic curves\, generalizing the p-adic construction of Heegner points via Cerednik-Drinfe ld uniformization. Inspired by Nekovar and Scholl's plectic conjectures\, we expect the non-triviality of these plectic Heegner points to control th e Morderll-Weil group of higher rank elliptic curves. We provide some evid ence for our conjectures by showing that higher derivatives of anticycloto mic p-adic L-functions compute plectic Heegner points.\n LOCATION:https://researchseminars.org/talk/CAFAS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Dennis Gaitsgory (Harvard) DTSTART:20200925T143000Z DTEND:20200925T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/3 DESCRIPTION:Title: Th e stack of local systems with restricted variation and the passage from ge ometric to classical Langlands theory\nby Dennis Gaitsgory (Harvard) a s part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\ nThe goal of this talk is two explain to closely related phenomena: the ex istence of the categorical geometric Langlands theory for l-adic sheaves a nd the link between geometric to classical Langlands via the operation of categorical trace. A key ingredient is played by a new geometric object: t he stack of local systems with restricted variation.\n LOCATION:https://researchseminars.org/talk/CAFAS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Hector Pasten (PUC Chile) DTSTART:20201002T143000Z DTEND:20201002T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/4 DESCRIPTION:Title: A Chabauty-Coleman estimate for surfaces in abelian threefolds\nby Hecto r Pasten (PUC Chile) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nColeman's explicit version of Chabauty's theorem gi ves a remarkable upper bound for the number of rational points in hyperbol ic curves over number fields\, under a certain rank condition. This result is obtained by p-adic methods. Despite considerable efforts in this topic \, higher dimensional extensions of such a bound have remained elusive. In this talk I will sketch the proof for hyperbolic surfaces contained in ab elian threefolds\, which provides the first case beyond the scope of curve s. This is joint work with Jerson Caro.\n LOCATION:https://researchseminars.org/talk/CAFAS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Wang (MIT) DTSTART:20201009T143000Z DTEND:20201009T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/5 DESCRIPTION:Title: Lo cal L-values and geometric harmonic analysis on spherical varieties\nb y Jonathan Wang (MIT) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nAlmost a decade ago\, Sakellaridis conjectured a v ast generalization of the Rankin-Selberg method to produce integral repres entations of L-functions using affine spherical varieties. The conjecture is still very much unknown\, but generalized Ichino-Ikeda formulas of Sake llaridis-Venkatesh relate the global problem to certain problems in local harmonic analysis. I will explain how we can use techniques from geometric Langlands to compute integrals which give special values of unramified lo cal L-functions over a local function field\, for a large class of spheric al varieties. This is joint work with Yiannis Sakellaridis. Our results gi ve new integral representations of L-functions (in a right half plane)​ over global function fields when the integral "unfolds".\n LOCATION:https://researchseminars.org/talk/CAFAS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:George Boxer (ENS de Lyon) DTSTART:20201016T143000Z DTEND:20201016T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/6 DESCRIPTION:Title: Hi gher Coleman Theory\nby George Boxer (ENS de Lyon) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nWe introduce a hi gher coherent cohomological analog of overconvergent modular forms on Shim ura varieties and explain how to compute the finite slope part of the cohe rent cohomology of Shimura varieties in terms of them. We also discuss ho w they vary p-adically. This is joint work with Vincent Pilloni.\n LOCATION:https://researchseminars.org/talk/CAFAS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Zerbes (UCL) DTSTART:20201023T143000Z DTEND:20201023T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/7 DESCRIPTION:Title: Th e Bloch—Kato conjecture for GSp(4)\nby Sarah Zerbes (UCL) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nIn my ta lk\, I will sketch a proof of new cases of the Bloch—Kato conjecture for the spin Galois representation attached to genus 2 Siegel modular forms. More precisely\, I will show that if the L-function is non-vanishing at so me critical value\, then the corresponding Selmer group is zero\, assuming a number of technical hypotheses. I will also mention work in progress on extending this result to Siegel modular forms of parallel weight 2\, with potential applications to the Birch—Swinnerton-Dyer conjecture for abel ian surfaces. This is joint work with David Loeffler.\n LOCATION:https://researchseminars.org/talk/CAFAS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:David Loeffler (Warwick) DTSTART:20201030T143000Z DTEND:20201030T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/8 DESCRIPTION:Title: P- adic interpolation of Gross--Prasad periods and diagonal cycles\nby Da vid Loeffler (Warwick) as part of Columbia Automorphic Forms and Arithmeti c Seminar\n\n\nAbstract\nThe Gross--Prasad conjecture for orthogonal group s relates special values of L-functions for SO(n) x SO(n+1) to period inte grals of automorphic forms. This conjecture is known for n = 3\, in which case the group SO(3) x SO(4) is essentially GL2 x GL2 x GL2\; and the stud y of these GL2 triple product periods\, and in particular their variation in p-adic families\, has had important arithmetic applications\, such as t he work of Darmon and Rotger on the equivariant BSD conjecture for ellipti c curves.\n\nI'll report on work in progress with Sarah Zerbes studying th ese periods in the n = 4 case\, where the group concerned is isogenous to GSp4 x GL2 x GL2. I'll explain a construction of p-adic L-functions interp olating the Gross--Prasad periods in Hida families\, and an 'explicit reci procity law' relating these p-adic L-functions to diagonal cycle classes i n etale cohomology. These constructions are closely analogous to the Euler system for GSp(4) described in Sarah's talk\, but with cusp forms in plac e of the GL2 Eisenstein series.\n LOCATION:https://researchseminars.org/talk/CAFAS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Chi-Yun Hsu (UCLA) DTSTART:20201106T153000Z DTEND:20201106T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/9 DESCRIPTION:Title: Co nstruction of Euler systems for GSp4×GL2\nby Chi-Yun Hsu (UCLA) as pa rt of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nFol lowing a strategy similar to the work of Loeffler-Skinner-Zerbes\, we cons truct Euler systems for Galois representations coming from automorphic rep resentations of GSp4×GL2. We will explain how the tame norm relations fol low from a local calculation in smooth representation theory\, in which th e integral formula of L-functions\, due to Novodvorsky in our case\, plays an important role. This is a joint work with Zhaorong Jin and Ryotaro Sak amoto.\n LOCATION:https://researchseminars.org/talk/CAFAS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuanqing Cai (Kyoto) DTSTART:20201113T153000Z DTEND:20201113T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/10 DESCRIPTION:Title: C ertain representations with unique models\nby Yuanqing Cai (Kyoto) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nT he uniqueness of Whittaker models is an important ingredient in the study of certain Langlands L-functions. However\, this property fails for groups such as GL(n\,D)\, where D is a central division algebra over a local fie ld. \n\nIn this talk\, we discuss a family of irreducible representations of GL(n\,D) that admit unique models. We also discuss some related local a nd global questions.\n LOCATION:https://researchseminars.org/talk/CAFAS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Takuya Yamauchi (Tohoku) DTSTART:20201120T153000Z DTEND:20201120T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/11 DESCRIPTION:Title: A utomorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials\nby Takuya Yamauchi (Tohoku) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\ nAbstract\nIn this talk\, I will explain my recent work with Tsuzuki Nobuo on computing\nmod $2$ Galois representations $\\overline{\\rho}_{\\psi\,2 }:G_K:={\\rm Gal}(\\overline{K}/K)\\longrightarrow {\\rm GSp}_4(\\F_2)$\na ssociated to the mirror motives of rank 4 with pure weight 3 coming from t he\nDwork quintic family\n$$X^5_0+X^5_1+X^5_2+X^5_3+X^5_4-5\\psi X_0X_1X_2 X_3X_4=0\,\\ \\psi\\in K$$\ndefined over a number field $K$ under the irre ducibility condition of the quintic trinomial\n$f_\\psi(x)=4x^5-5\\psi x^4 +1$.\nIn the course of the computation\, we observe that the image of such a mod $2$ representation is governed by reciprocity of\n$f_\\psi(x)$ whos e decomposition field is generically of type\n5-th symmetric group $S_5$.\ nWhen K=F is totally real field\, we apply the modularity of\n2-dimensiona l\, totally odd Artin representations of ${\\rm Gal}(\\overline{F}/F)$ due to Shu Sasaki\nto obtain automorphy of $\\overline{\\rho}_{\\psi\,2}$ aft er a suitable (at most) quadratic base extension.\n LOCATION:https://researchseminars.org/talk/CAFAS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugen Hellmann (Münster) DTSTART:20201204T153000Z DTEND:20201204T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/12 DESCRIPTION:Title: T owards automorphy lifting for semi-stable Galois representations\nby E ugen Hellmann (Münster) as part of Columbia Automorphic Forms and Arithme tic Seminar\n\n\nAbstract\nAutomorphy lifting theorems aim to show that a p-adic global Galois representation that is unramified almost everywhere a nd de Rham at places dividing p is associated to an automorphic representa tion\, provided its reduction modulo p is. In the past years there has bee n a lot of progress in the case of polarizable representations that are cr ystalline at p. In the semi-stable case much less is known (beyond the ord inary case and the 2-dimensional case).\n\nI will explain recent progress on classicality theorems for p-adic automorphic forms whose associated Gal ois representation is semi-stable at places dividing p. In the context of automorphy lifting problems\, these results can be used to deduce the semi -stable case from the crystalline case.\n LOCATION:https://researchseminars.org/talk/CAFAS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhilin Luo (Minnesota) DTSTART:20201211T153000Z DTEND:20201211T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/13 DESCRIPTION:Title: A local trace formula for the local Gan-Gross-Prasad conjecture for special orthogonal groups\nby Zhilin Luo (Minnesota) as part of Columbia Auto morphic Forms and Arithmetic Seminar\n\n\nAbstract\nThe local Gan-Gross-Pr asad conjecture studies the restriction and branching problems for represe ntations of classical and metaplectic groups. In this talk\, I will talk a bout my proof for the tempered part of the local Gan-Gross-Prasad conjectu re (multiplicity one in Vogan packets) for special orthogonal groups over any local fields of characteristic zero\, which combines the work of Walds purger (for the tempered part of the conjecture for special orthogonal gro ups over $p$-adic fields) and Beuzart-Plessis (for the tempered part of th e conjecture for unitary groups over real field) in a non-trivial way. In the proof\, an indispensable result which is also of independent interest is a formula expressing the regular nilpotent germs of quasi-split reducti ve Lie algebras over any local fields of characteristic zero via endoscopi c invariants\, which was previously proved by Shelstad over $p$-adic field s. We also relate the formula with the Kostant's sections.\n LOCATION:https://researchseminars.org/talk/CAFAS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Amadou Bah (IHES) DTSTART:20201218T153000Z DTEND:20201218T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/14 DESCRIPTION:Title: V ariation of the Swan conductor of an $\\mathbb{F}_{\\ell}$-sheaf on a rigi d disc\nby Amadou Bah (IHES) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nLet $K$ be a complete discrete valuatio n field of residue characteristic $p>0$ and $\\ell\\neq p$ a prime number. To a finite dimensional $\\mathbb{F}_{\\ell}$-representation $M$ of the a bsolute Galois group $G_K$\, the ramification theory of Abbes and Saito at taches a Swan conductor ${\\rm sw}(M)$ and a characteristic cycle ${\\rm C C}(M)$. Let $D$ be the rigid unit disc over $K$ and $\\mathcal{F}$ a lisse sheaf of $\\mathbb{F}_{\\ell}$-modules on $D$. For $t\\in \\mathbb{Q}_{\\ geq 0}$\, the normalized integral model $\\mathcal{D}^{(t)}$ of the subdis c $D^{(t)}$ of radius $t$ is defined over some finite extension of $K$. Th e restriction $\\mathcal{F}_{\\lvert D^{(t)}}$ defines\, at the generic po int $\\mathfrak{p}^{(t)}$ of the special fiber of $\\mathcal{D}^{(t)}$\, a Galois representation $M_t$ over a complete discrete valuation field\, th us yielding a Swan conductor ${\\rm sw}(M_t)$ and a characteristic cycle $ {\\rm CC}(M_t)$. The goal of the talk is to explain how we connect earlier works\, of Lütkebohmert on a discriminant function attached to a cover o f $D$\, and of Kato on the ramification of valuation rings of height $2$\, and prove that the function $t\\mapsto {\\rm sw}(M_t)$ is continuous and piecewise linear with finitely many slopes which are all integers\, and th at its right derivative is $t\\mapsto -{\\rm ord}_{\\mathfrak{p}^{(t)}}({\ \rm CC}(M_t)) + \\dim_{\\mathbb{F}_{\\ell}}(M_t/M_t^{(0)})$\, where ${\\rm ord}_{\\mathfrak{p}^{(t)}}$ is a normalized discrete valuation at $\\math frak{p}^{(t)}$ extended to differentials and $M_t^{(0)}$ is the tame part of $M_t$.\n LOCATION:https://researchseminars.org/talk/CAFAS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Nelson (ETH Zurich) DTSTART:20210129T153000Z DTEND:20210129T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/15 DESCRIPTION:Title: T he orbit method\, microlocal analysis and applications to L-functions\ nby Paul Nelson (ETH Zurich) as part of Columbia Automorphic Forms and Ari thmetic Seminar\n\n\nAbstract\nI will describe how the orbit method can be developed in a quantitative form\, along the lines of microlocal analysis \, and applied to local problems in representation theory and global probl ems concerning automorphic forms. The local applications include asymptot ic expansions of relative characters. The global applications include mom ent estimates and subconvex bounds for L-functions. These results are the subject of two papers\, the first joint with Akshay Venkatesh:\n\nhttps:/ /arxiv.org/abs/1805.07750\nhttps://arxiv.org/abs/2012.02187\n LOCATION:https://researchseminars.org/talk/CAFAS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Shizhang Li (Michigan) DTSTART:20210205T153000Z DTEND:20210205T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/16 DESCRIPTION:Title: O n the boundary case of Breuil--Caruso's theory\nby Shizhang Li (Michig an) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbst ract\nIn the talk I shall report on recent joint work with Tong Liu on int egral p-adic Hodge theory. Using newly developed cohomology theory we exte nd a result of Caruso\, stating roughly that\, in nice situations\, certai n natural structure on the crystalline cohomology of a variety is a Breuil module related to its étale cohomology.\n LOCATION:https://researchseminars.org/talk/CAFAS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yingkun Li (TU Darmstadt) DTSTART:20210212T153000Z DTEND:20210212T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/17 DESCRIPTION:Title: I ntegrality of regularized Petersson inner product\nby Yingkun Li (TU D armstadt) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n \nAbstract\nPetersson inner products of classical cusp forms contain\nimpo rtant arithmetic information\, such as congruences of modular forms.\nWhen the cusp forms are replaced by meromorphic modular form\, the\nPetersson inner product can still be defined and calculated after suitable\nregulari zation. It turns out these regularized inner product also carry\ninteresti ng arithmetic information\, such as special values of derivatives\nof L-fu nction. In this talk\, we will recall some of these results\, and\ndiscuss a joint work with Markus Schwagenscheidt from ETH\, where we\nobtained an integrality result of such regularized inner products\ninvolving unary th eta functions.\n LOCATION:https://researchseminars.org/talk/CAFAS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ashay Burungale (Caltech) DTSTART:20210226T160000Z DTEND:20210226T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/18 DESCRIPTION:Title: A n even parity instance of the Goldfeld conjecture\nby Ashay Burungale (Caltech) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n \nAbstract\nIn 1979 D. Goldfeld conjectured: 50% of the quadratic twists o f an elliptic curve over the rationals have analytic rank zero. We present the first instance - the congruent number elliptic curves (joint with Y. Tian).\n LOCATION:https://researchseminars.org/talk/CAFAS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhiwei Yun (MIT) DTSTART:20210312T153000Z DTEND:20210312T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/19 DESCRIPTION:Title: T owards a higher arithmetic Siegel-Weil formula for unitary groups\nby Zhiwei Yun (MIT) as part of Columbia Automorphic Forms and Arithmetic Semi nar\n\n\nAbstract\nThe classical Siegel-Weil formula relates an integral o f a theta function along one classical group H to special values of the Si egel-Eisenstein series on another classical group G. Kudla proposed an ari thmetic analogue of it that relates a generating series of algebraic cycle s on the Shimura variety for H to the first derivative of the Siegel-Eisen stein series for G\, which has become a very active program. We propose to go further in the function field case\, relating a generating series of a lgebraic cycles on the moduli of H-Shtukas with multiple legs to higher de rivatives of the Siegel-Eisenstein series for G\, when H and G are unitary groups. We prove such a formula for nonsingular Fourier coefficients\, re lating their higher derivatives to degrees of zero cycles on the moduli of unitary Shtukas. The proof ultimately relies on an argument from Springer theory. This is joint work with Tony Feng and Wei Zhang.\n LOCATION:https://researchseminars.org/talk/CAFAS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Cong Xue (CNRS/IMJ-PRG) DTSTART:20210319T143000Z DTEND:20210319T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/20 DESCRIPTION:Title: C ohomology sheaves of stacks of shtukas\nby Cong Xue (CNRS/IMJ-PRG) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nT he stacks of shtukas play an important role in the Langlands correspondenc e for function fields. In this talk\, we will recall the definition of coh omology sheaves of stacks of shtukas and review the partial Frobenius morp hisms and Drinfeld's lemma. Then we will talk about the smoothness propert y of the cohomology sheaves and some applications.\n LOCATION:https://researchseminars.org/talk/CAFAS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Lei Zhang (NUS) DTSTART:20210326T143000Z DTEND:20210326T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/21 DESCRIPTION:Title: T wisted Automorphic Descent and Gan-Gross-Prasad Conjecture\nby Lei Zha ng (NUS) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\ nAbstract\nIn this talk\, we will discuss the theory of twisted automorphi c descents\, which is an extension of the automorphic descent of Ginzburg- Rallis-Soudry.\nOne of our goals is to construct cuspidate automorphic mod ules in the generic global Arthur packets by using Fourier coefficients of automorphic representations.\nMoreover\, we will discuss our approach for one direction of Gan-Gross-Prasad Conjecture for the Bessel-Fourier model s and some connections between Fourier coefficients and spherical varietie s.\nThis is a joint work with Dihua Jiang.\n LOCATION:https://researchseminars.org/talk/CAFAS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Litt (Georgia) DTSTART:20210409T143000Z DTEND:20210409T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/23 DESCRIPTION:Title: S ingle-valued Hodge\, p-adic^2\, and tropical integration\nby Daniel Li tt (Georgia) as part of Columbia Automorphic Forms and Arithmetic Seminar\ n\n\nAbstract\nI'll discuss 4 different types of single-valued integration on algebraic varieties -- one in the complex setting\, one in the tropica l setting\, and two in the p-adic setting\, and the relationships between them. In particular\, I'll explain how to compute Vologodsky's "single-val ued" iterated integrals on curves of bad reduction in terms of Berkovich i ntegrals\, and how to give a single-valued integration theory on complex v arieties. Time permitting\, I'll explain some potential arithmetic applica tions. This is a report on joint work in progress with Sasha Shmakov (in t he complex setting) and Eric Katz (in the p-adic setting).\n LOCATION:https://researchseminars.org/talk/CAFAS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Robin Zhang (Columbia) DTSTART:20210917T143000Z DTEND:20210917T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/24 DESCRIPTION:Title: M odular Gelfand pairs and multiplicity-free triples\nby Robin Zhang (Co lumbia) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\n Abstract\nThe classical theory of Gelfand pairs and its generalizations ov er the complex numbers has many applications to number theory and automorp hic forms\, such as the uniqueness of Whittaker models and the non-vanishi ng of the central value of a triple product L-function. With an eye toward s similar applications in the modular setting\, this talk presents an exte nsion of the classical theory to representations of finite groups over alg ebraically closed fields whose characteristics possibly divide the orders of the groups.\n LOCATION:https://researchseminars.org/talk/CAFAS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Linus Hamann (Princeton) DTSTART:20211001T143000Z DTEND:20211001T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/25 DESCRIPTION:Title: C ompatibility of the Fargues-Scholze and Gan-Takeda Local Langlands\nby Linus Hamann (Princeton) as part of Columbia Automorphic Forms and Arithm etic Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/CAFAS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Lawrence (UCLA) DTSTART:20211008T143000Z DTEND:20211008T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/26 DESCRIPTION:Title: S parsity of Integral Points on Moduli Spaces of Varieties\nby Brian Law rence (UCLA) as part of Columbia Automorphic Forms and Arithmetic Seminar\ n\n\nAbstract\nInteresting moduli spaces don't have many integral points. More precisely\, if $X$ is a variety over a number field\, admitting a va riation of Hodge structure whose associate period map is injective\, then the number of $S$-integral points on $X$ of height at most $H$ grows more slowly than $H^{\\epsilon}$\, for any positive $\\epsilon$. This is a sor t of weak generalization of the Shafarevich conjecture\; it is a consequen ce of a point-counting theorem of Broberg\, and the largeness of the funda mental group of $X$. Joint with Ellenberg and Venkatesh.\n LOCATION:https://researchseminars.org/talk/CAFAS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Disegni (BGU) DTSTART:20211015T143000Z DTEND:20211015T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/27 DESCRIPTION:Title: E uler systems for conjugate-symplectic motives\nby Daniel Disegni (BGU) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstrac t\nKolyvagin's original Euler system (1990)\, based on Heegner points\, co mplemented the height formula of Gross and Zagier to prove a key case of t he Birch and Swinnerton-Dyer conjecture. I will introduce some new Euler s ystems. They are of a species theorized by Jetchev--Nekovar--Skinner\, and pertain to those representations of the Galois group of a CM field that a re automorphic\, carry a conjugate-symplectic form\, and have the simplest Hodge--Tate type. \n\nThe construction is based on Kudla's special cycles on unitary Shimura varieties\, under an assumption of modularity for thei r generating series. Together with a recent height formula by Li--Liu and the forthcoming theory of JNS\, this reduces some cases of the Beilinson-- Bloch--Kato conjecture to the injectivity of Abel--Jacobi maps.\n LOCATION:https://researchseminars.org/talk/CAFAS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunqing Tang (Princeton) DTSTART:20211022T143000Z DTEND:20211022T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/28 DESCRIPTION:Title: T he unbounded denominators conjecture\nby Yunqing Tang (Princeton) as p art of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\n(J oint work with Frank Calegari and Vesselin Dimitrov.) The unbounded denomi nators conjecture\, first raised by Atkin and Swinnerton-Dyer\, asserts th at a modular form for a finite index subgroup of SL_2(Z) whose Fourier coe fficients have bounded denominators must be a modular form for some congru ence subgroup. In this talk\, we will give a sketch of the proof of this c onjecture based on a new arithmetic algebraization theorem.\n LOCATION:https://researchseminars.org/talk/CAFAS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Elena Mantovan (Caltech) DTSTART:20211029T170000Z DTEND:20211029T183000Z DTSTAMP:20260422T212711Z UID:CAFAS/29 DESCRIPTION:Title: I nfinitely many primes of basic reduction\nby Elena Mantovan (Caltech) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract \nIn 1987\, Elkies proved that an elliptic curve defined over the field of rational numbers has infinitely many primes of supersingular reduction. I will discuss a generalization of this result to the case of special cycli c covers of the projective line ramified at 4 points. This talk is based o n joint work in progress with Wanlin Li\, Rachel Pries and Yunqing Tang.\n LOCATION:https://researchseminars.org/talk/CAFAS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Ming-Lun Hsieh (Academia Sinica) DTSTART:20211105T143000Z DTEND:20211105T160000Z DTSTAMP:20260422T212711Z UID:CAFAS/30 DESCRIPTION:Title: O n the first derivatives of the cyclotomic Katz p-adic L-functions for CM f ields\nby Ming-Lun Hsieh (Academia Sinica) as part of Columbia Automor phic Forms and Arithmetic Seminar\n\n\nAbstract\nBuyukboduk and Sakamoto i n 2019 proposed a precise conjectural formula relating the leading coeffic ient at the trivial zero s=0 of the cyclotomic Katz p-adic L-functions ass ociated with ray class characters of a CM field K to suitable L-invariants /regulators of K. They were able to prove this formula in most cases when K is an imaginary quadratic field thanks to the existence of the Euler sys tem of elliptic units/Rubin-Stark elements. In this talk\, we will present a formula relating the first derivative of the cyclotomic Katz p-adic L-f unctions for general CM fields attached to ring class characters to the pr oduct of the L-invariant and the value of the improved Katz p-adic L-funct ion at s=0. In particular\, when the trivial zero occurs at s=0\, we prove that the Katz p-adic L-function has a simple zero at s=0 if certain L-inv ariant is non-vanishing. Our method uses the congruence of Hilbert CM form s and does reply on the existence of the conjectural Rubin-Stark elements. This is a joint work with Adel Betina.\n LOCATION:https://researchseminars.org/talk/CAFAS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Yujie Xu (Harvard) DTSTART:20211112T153000Z DTEND:20211112T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/31 DESCRIPTION:Title: O n normalization in the integral models of Shimura varieties of Hodge type< /a>\nby Yujie Xu (Harvard) as part of Columbia Automorphic Forms and Arith metic Seminar\n\n\nAbstract\nShimura varieties are moduli spaces of abelia n varieties with extra structures. Over the decades\, various mathematicia ns (e.g. Rapoport\, Kottwitz\, etc.) have constructed integral models of S himura varieties. In this talk\, I will discuss some motivic aspects of in tegral models of Hodge type constructed by Kisin (resp. Kisin-Pappas). I w ill talk about recent work on removing the normalization step in the const ruction of such integral models\, which gives closed embeddings of Hodge t ype integral models into Siegel integral models under some assumption. I w ill explain how this question is related to the Grothendieck Standard Conj ecture D for abelian varieties\, and sketch a proof of this type of questi ons if time permits. I will also mention an application to toroidal compac tifications of Hodge type integral models.\n LOCATION:https://researchseminars.org/talk/CAFAS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Fox (Oregon) DTSTART:20211119T153000Z DTEND:20211119T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/32 DESCRIPTION:Title: S upersingular Loci of Unitary (2\,m-2) Shimura Varieties\nby Maria Fox (Oregon) as part of Columbia Automorphic Forms and Arithmetic Seminar\n\n\ nAbstract\nThe supersingular locus of a Unitary (2\,m-2) Shimura variety p arametrizes supersingular abelian varieties of dimension m\, with an actio n of a quadratic imaginary field meeting the "signature (2\,m-2)" conditio n. In some cases\, for example when m=3 or m=4\, every irreducible compone nt of the supersingular locus is isomorphic to a Deligne-Lusztig variety\, and the intersection combinatorics are governed by a Bruhat-Tits building . We'll consider these cases for motivation\, and then see how the structu re of the supersingular locus becomes very different for m>4. (The new res ult in this talk is joint with Naoki Imai.)\n LOCATION:https://researchseminars.org/talk/CAFAS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Lei (Laval) DTSTART:20211203T153000Z DTEND:20211203T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/33 DESCRIPTION:Title: I wasawa theory over imaginary quadratic fields for inert primes\nby Ant onio Lei (Laval) as part of Columbia Automorphic Forms and Arithmetic Semi nar\n\n\nAbstract\nLet $p$ be a fixed odd prime and $K$ an imaginary quadr atic field where $p$ is inert. Let $f$ be an elliptic modular form with go od ordinary reduction at $p$. We discuss how the cyclotomic Iwasawa theory of the Rankin-Selberg product of $f$ and a $p$-non-ordinary CM form allow s us to study the Iwasawa theory of $f$ over the $\\mathbf{Z}_p^2$-extensi on of $K$. We make use of the plus and minus theory of Kobayashi and Polla ck as well as Euler systems built out of Beilinson--Flach elements. This i s joint work with Kazim Buyukboduk.\n LOCATION:https://researchseminars.org/talk/CAFAS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Shaul Zemel (Einstein Institute of Mathematics) DTSTART:20211210T153000Z DTEND:20211210T170000Z DTSTAMP:20260422T212711Z UID:CAFAS/34 DESCRIPTION:Title: S pecial cycles on toroidal compactifications of orthogonal Shimura varietie s\nby Shaul Zemel (Einstein Institute of Mathematics) as part of Colum bia Automorphic Forms and Arithmetic Seminar\n\n\nAbstract\nWe determine t he behavior of automorphic Green functions along the boundary components o f toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating series of the resulting special divisors on a toroidal comp actification is modular. This is joint work with Jan Bruinier.\n LOCATION:https://researchseminars.org/talk/CAFAS/34/ END:VEVENT END:VCALENDAR