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BEGIN:VEVENT
SUMMARY:Oana Padurariu (Boston University)
DTSTART:20220923T143000Z
DTEND:20220923T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/1/">On Quadratic Analogues of Kenku’s Theorem</a
 >\nby Oana Padurariu (Boston University) as part of Columbia - Automorphic
  forms and arithmetic seminar\n\n\nAbstract\nKenku determined in 1981 all 
 possible cyclic isogenies of elliptic curves\nover $\\mathbb{Q}$\, buildin
 g on Mazur’s 1978 work on prime degree isogenies. Although more than\n40
  years have passed\, the determination of cyclic isogenies of elliptic cur
 ves over a single\nother number field has until now not been realized. In 
 this talk I will present a procedure\nto assist in establishing such a det
 ermination for a given quadratic field. Running this\nprocedure on all qua
 dratic fields $\\mathbb{Q}(\\sqrt{d})$ with $|d| < 104$ we obtain\, condit
 ional on the\nGRH\, the determination of cyclic isogenies of elliptic curv
 es over 19 quadratic fields.\nThis is joint work with Barinder Banwait and
  Filip Najman.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Obus (CUNY-Baruch College)
DTSTART:20221014T143000Z
DTEND:20221014T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/2/">Mac Lane Valuations and applications to conduc
 tor-discriminant inequalities</a>\nby Andrew Obus (CUNY-Baruch College) as
  part of Columbia - Automorphic forms and arithmetic seminar\n\n\nAbstract
 \nMac Lane's technique of "inductive valuations" is over 85 years old\, bu
 t has only recently been used to attack problems in arithmetic geometry. W
 e will give an explicit\, hands-on introduction to inductive valuations. W
 e will then discuss an application to explicit resolutions of singularitie
 s on arithmetic surfaces\, ultimately giving a generalization of a conduct
 or-discriminant inequality of Qing Liu in genus 2 to arbitrary genus. \nTh
 is is joint work with Padmavathi Srinivasan.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacques Tilouine (Universite Paris 13)
DTSTART:20221021T143000Z
DTEND:20221021T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/3/">Iwasawa theory of classical and derived deform
 ation rings</a>\nby Jacques Tilouine (Universite Paris 13) as part of Colu
 mbia - Automorphic forms and arithmetic seminar\n\n\nAbstract\nIn a joint 
 work with E. Urban\, we define Iwasawa-theoretic deformation rings for the
  Galois representation associated to a p-ordinary cusp form on a connected
  reductive group and study their relations to the Iwasawa theory of Selmer
  groups associated to its adjoint representation.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyan Daniel Li-Huerta (Harvard University)
DTSTART:20220909T143000Z
DTEND:20220909T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/4/">The plectic conjecture over local fields</a>\n
 by Siyan Daniel Li-Huerta (Harvard University) as part of Columbia - Autom
 orphic forms and arithmetic seminar\n\n\nAbstract\nThe étale cohomology o
 f varieties over Q enjoys a Galois action. In the case of Hilbert modular 
 varieties\, Nekovář-Scholl observed that this Galois action on the level
  of cohomology extends to a much larger profinite group: the plectic group
 . Motivated by applications to higher-rank Euler systems\, they conjecture
 d that this extension holds even on the level of complexes\, as well as fo
 r more general Shimura varieties.\n\nWe present a proof of the analog of t
 his conjecture for local Shimura varieties. Consequently\, we obtain resul
 ts for the basic locus of global Shimura varieties\, after restricting to 
 a decomposition group. The proof crucially uses a mixed-characteristic ver
 sion of fusion due to Fargues–Scholze.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART:20220930T143000Z
DTEND:20220930T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/5/">The Wiles-Lenstra-Diamond numerical criterion 
 in higher codimensions</a>\nby Chandrashekhar Khare (UCLA) as part of Colu
 mbia - Automorphic forms and arithmetic seminar\n\n\nAbstract\nI will repo
 rt on recent joint work with Srikanth Iyengar and Jeff Manning. We give a 
 development of numerical criterion that was used by Wiles as an essential 
 ingredient in his approach to modularity of elliptic curves over \nQ. The 
 patching method introduced by Wiles and Taylor has been developed consider
 ably while the numerical criterion has lagged behind.\nWe prove new commut
 ative algebra results that lead to a generalisation of the Wiles-Lenstra-D
 iamond numerical criterion in situations of positive defect (as arise when
  proving modularity of elliptic curves over number fields with a complex p
 lace). A key step in our work is the definition of congruence modules in h
 igher codimensions which should be relevant to studying properties of eige
 nvarieties at classical points.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Pollack (Boston University)
DTSTART:20221118T153000Z
DTEND:20221118T170000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/6/">Predicting slopes of modular forms and reducti
 ons of crystalline representations</a>\nby Robert Pollack (Boston Universi
 ty) as part of Columbia - Automorphic forms and arithmetic seminar\n\n\nAb
 stract\nThe ghost conjecture predicts slopes of modular forms whose residu
 al representation is locally reducible.  In this talk\, we'll examine loca
 lly irreducible representations and discuss recent progress on formulating
  a conjecture in this case.  It's a lot trickier and the story remains inc
 omplete\, but we will discuss how an irregular ghost conjecture is intimat
 ely related to reductions of crystalline representations.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART:20221209T153000Z
DTEND:20221209T170000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/7/">Torsion points on abelian surfaces with potent
 ial quaternionic multiplication</a>\nby Ari Shnidman (Hebrew University of
  Jerusalem) as part of Columbia - Automorphic forms and arithmetic seminar
 \n\n\nAbstract\nI'll discuss work in progress with Laga\, Schembri\, and V
 oight\, which aims to classify the finite subgroups that arise inside Mord
 ell-Weil groups of abelian surfaces over Q with geometric endomorphism rin
 g isomorphic to a maximal quaternion order ("potentially QM").\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinbo Ren (Xiamen University)
DTSTART:20220916T143000Z
DTEND:20220916T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/8
DESCRIPTION:by Jinbo Ren (Xiamen University) as part of Columbia - Automor
 phic forms and arithmetic seminar\n\nAbstract: TBA\n\nZoom talk\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Freie Universität Berlin)
DTSTART:20221104T143000Z
DTEND:20221104T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/9/">Integrality of the Betti moduli space</a>\nby 
 Hélène Esnault (Freie Universität Berlin) as part of Columbia - Automor
 phic forms and arithmetic seminar\n\n\nAbstract\nWe show that the Betti mo
 duli space of a smooth complex quasi-projective variety $X$ has a weak int
 egrality property which in particular yields a new obstruction for a finit
 ely presented group to be the topological fundamental group of $X$. We def
 ine weak arithmetic complex points of the Betti moduli space and prove den
 sity of those. Our method relies on the arithmetic (via companions) and th
 e geometric (via de Jong's conjecture solved by Gaitsgory) Langlands corre
 spondence. It also yields other properties of the Betti moduli space which
  we shall mention if time permits.\nJoint work in progress with Johan de J
 ong.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard University)
DTSTART:20221007T143000Z
DTEND:20221007T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/10/">Kolyvagin's Conjecture and Higher Congruences
  of Modular Forms</a>\nby Naomi Sweeting (Harvard University) as part of C
 olumbia - Automorphic forms and arithmetic seminar\n\n\nAbstract\nGiven an
  elliptic curve E\, Kolyvagin used CM points on modular curves to construc
 t a system of classes valued in the Galois cohomology of the torsion point
 s of E. Under the conjecture that not all of these classes vanish\, he ded
 uced remarkable consequences for the Selmer rank of E. For example\, his r
 esults\, combined with work of Gross-Zagier\, implied that a curve with an
 alytic rank one also has algebraic rank one\; a partial converse follows f
 rom his conjecture. \nIn this talk\, I will report on work proving several
  new cases of Kolyvagin's conjecture. The methods follow in the footsteps 
 of Wei Zhang\, who used congruences between modular forms to prove Kolyvag
 in's conjecture under some technical hypotheses. By considering congruence
 s modulo higher powers of p\, we remove many of those hypotheses. The talk
  will provide an introduction to Kolyvagin's conjecture and its applicatio
 ns\, explain an analog of the conjecture in an opposite parity regime\, an
 d give an overview of the proofs\, including the difficulties associated w
 ith higher congruences of modular forms and how they can be overcome via d
 eformation theory.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Chen (Princeton University)
DTSTART:20221111T153000Z
DTEND:20221111T170000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/11/">Duality of singular automorphic periods</a>\n
 by Eric Chen (Princeton University) as part of Columbia - Automorphic form
 s and arithmetic seminar\n\n\nAbstract\nIn the recent framework proposed b
 y Ben-Zvi--Sakellaridis--Venkatesh\, automorphic periods ought to\, very r
 oughly speaking\, come in Langlands dual pairs. I will give a short introd
 uction of this prediction and motivate the need to consider certain singul
 ar automorphic periods. In particular\, I will present an example in joint
  work with Akshay Venkatesh\, where we establish duality using a generaliz
 ation of L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Sheng Lee (Columbia University)
DTSTART:20221028T143000Z
DTEND:20221028T160000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/12/">Arithmetic of theta liftings</a>\nby Yu-Sheng
  Lee (Columbia University) as part of Columbia - Automorphic forms and ari
 thmetic seminar\n\n\nAbstract\nWe discuss the integrality of theta lifting
 s of anti-cyclotomic characters to a definite unitary group $\\mathrm{U}(2
 )$ of two variables. This will allow us to construct a Hida family of the 
 theta liftings and relate the congruence module of which to an anti-cyclot
 omic $p$-adic L-function. The result is an input to Urban's construction o
 f Euler systems.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Hernandez (Université Paris-Saclay)
DTSTART:20221202T153000Z
DTEND:20221202T170000Z
DTSTAMP:20260404T094915Z
UID:Columbia-NumberTheorySeminar/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Colum
 bia-NumberTheorySeminar/13/">The infinite fern in higher dimensions</a>\nb
 y Valentin Hernandez (Université Paris-Saclay) as part of Columbia - Auto
 morphic forms and arithmetic seminar\n\n\nAbstract\nIn full generality def
 ormation spaces of Galois representations are mysterious objects. A natura
 l question to ask is if they contain at least enough modular points in the
 ir generic fiber. In this talk I will explain result about the Zariski den
 sity of such points for conjugate self dual deformations spaces. Such a re
 sult was obtained for GL_2 by Gouvea-Mazur and then generalized by Chenevi
 er in dimension 3. Both strategies uses the Infinite fern\, a fractal-like
  object which is the image of an Eigenvariety. More recently Hellmann-Marg
 erin-Schraen extended Chenevier's result under strong Taylor-Wiles hypothe
 sis\, with main input the local model of the trianguline variety and the p
 atched Eigenvarieties of Breuil-Hellmann-Schraen. Our strategy is to study
  further the geometry of the trianguline variety\, and to use the geometry
  of classical points on the (non-patched) Eigenvariety to remove the Taylo
 r-Wiles hypothesis. \nThis is a joint work with B. Schraen.\n
LOCATION:https://stable.researchseminars.org/talk/Columbia-NumberTheorySem
 inar/13/
END:VEVENT
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