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BEGIN:VEVENT
SUMMARY:Oana Padurariu (Boston University)
DTSTART:20220923T143000Z
DTEND:20220923T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/1/">On Quadratic Analogues of Kenku’s Theorem</a>\nby O
 ana Padurariu (Boston University) as part of Columbia - Automorphic forms 
 and arithmetic seminar\n\n\nAbstract\nKenku determined in 1981 all possibl
 e cyclic isogenies of elliptic curves\nover $\\mathbb{Q}$\, building on Ma
 zur’s 1978 work on prime degree isogenies. Although more than\n40 years 
 have passed\, the determination of cyclic isogenies of elliptic curves ove
 r a single\nother number field has until now not been realized. In this ta
 lk I will present a procedure\nto assist in establishing such a determinat
 ion for a given quadratic field. Running this\nprocedure on all quadratic 
 fields $\\mathbb{Q}(\\sqrt{d})$ with $|d| < 104$ we obtain\, conditional o
 n the\nGRH\, the determination of cyclic isogenies of elliptic curves over
  19 quadratic fields.\nThis is joint work with Barinder Banwait and Filip 
 Najman.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Obus (CUNY-Baruch College)
DTSTART:20221014T143000Z
DTEND:20221014T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/2/">Mac Lane Valuations and applications to conductor-dis
 criminant inequalities</a>\nby Andrew Obus (CUNY-Baruch College) as part o
 f Columbia - Automorphic forms and arithmetic seminar\n\n\nAbstract\nMac L
 ane's technique of "inductive valuations" is over 85 years old\, but has o
 nly recently been used to attack problems in arithmetic geometry. We will 
 give an explicit\, hands-on introduction to inductive valuations. We will 
 then discuss an application to explicit resolutions of singularities on ar
 ithmetic surfaces\, ultimately giving a generalization of a conductor-disc
 riminant inequality of Qing Liu in genus 2 to arbitrary genus. \nThis is j
 oint work with Padmavathi Srinivasan.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacques Tilouine (Universite Paris 13)
DTSTART:20221021T143000Z
DTEND:20221021T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/3/">Iwasawa theory of classical and derived deformation r
 ings</a>\nby Jacques Tilouine (Universite Paris 13) as part of Columbia - 
 Automorphic forms and arithmetic seminar\n\n\nAbstract\nIn a joint work wi
 th E. Urban\, we define Iwasawa-theoretic deformation rings for the Galois
  representation associated to a p-ordinary cusp form on a connected reduct
 ive group and study their relations to the Iwasawa theory of Selmer groups
  associated to its adjoint representation.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyan Daniel Li-Huerta (Harvard University)
DTSTART:20220909T143000Z
DTEND:20220909T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/4/">The plectic conjecture over local fields</a>\nby Siya
 n Daniel Li-Huerta (Harvard University) as part of Columbia - Automorphic 
 forms and arithmetic seminar\n\n\nAbstract\nThe étale cohomology of varie
 ties over Q enjoys a Galois action. In the case of Hilbert modular varieti
 es\, Nekovář-Scholl observed that this Galois action on the level of coh
 omology extends to a much larger profinite group: the plectic group. Motiv
 ated by applications to higher-rank Euler systems\, they conjectured that 
 this extension holds even on the level of complexes\, as well as for more 
 general Shimura varieties.\n\nWe present a proof of the analog of this con
 jecture for local Shimura varieties. Consequently\, we obtain results for 
 the basic locus of global Shimura varieties\, after restricting to a decom
 position group. The proof crucially uses a mixed-characteristic version of
  fusion due to Fargues–Scholze.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandrashekhar Khare (UCLA)
DTSTART:20220930T143000Z
DTEND:20220930T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/5/">The Wiles-Lenstra-Diamond numerical criterion in high
 er codimensions</a>\nby Chandrashekhar Khare (UCLA) as part of Columbia - 
 Automorphic forms and arithmetic seminar\n\n\nAbstract\nI will report on r
 ecent joint work with Srikanth Iyengar and Jeff Manning. We give a develop
 ment of numerical criterion that was used by Wiles as an essential ingredi
 ent in his approach to modularity of elliptic curves over \nQ. The patchin
 g method introduced by Wiles and Taylor has been developed considerably wh
 ile the numerical criterion has lagged behind.\nWe prove new commutative a
 lgebra results that lead to a generalisation of the Wiles-Lenstra-Diamond 
 numerical criterion in situations of positive defect (as arise when provin
 g modularity of elliptic curves over number fields with a complex place). 
 A key step in our work is the definition of congruence modules in higher c
 odimensions which should be relevant to studying properties of eigenvariet
 ies at classical points.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Pollack (Boston University)
DTSTART:20221118T153000Z
DTEND:20221118T170000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/6/">Predicting slopes of modular forms and reductions of 
 crystalline representations</a>\nby Robert Pollack (Boston University) as 
 part of Columbia - Automorphic forms and arithmetic seminar\n\n\nAbstract\
 nThe ghost conjecture predicts slopes of modular forms whose residual repr
 esentation is locally reducible.  In this talk\, we'll examine locally irr
 educible representations and discuss recent progress on formulating a conj
 ecture in this case.  It's a lot trickier and the story remains incomplete
 \, but we will discuss how an irregular ghost conjecture is intimately rel
 ated to reductions of crystalline representations.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART:20221209T153000Z
DTEND:20221209T170000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/7/">Torsion points on abelian surfaces with potential qua
 ternionic multiplication</a>\nby Ari Shnidman (Hebrew University of Jerusa
 lem) as part of Columbia - Automorphic forms and arithmetic seminar\n\n\nA
 bstract\nI'll discuss work in progress with Laga\, Schembri\, and Voight\,
  which aims to classify the finite subgroups that arise inside Mordell-Wei
 l groups of abelian surfaces over Q with geometric endomorphism ring isomo
 rphic to a maximal quaternion order ("potentially QM").\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinbo Ren (Xiamen University)
DTSTART:20220916T143000Z
DTEND:20220916T160000Z
DTSTAMP:20260422T230721Z
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://researchseminars.org/talk/Columbia-NumberTheorySeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Freie Universität Berlin)
DTSTART:20221104T143000Z
DTEND:20221104T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/9/">Integrality of the Betti moduli space</a>\nby Hélèn
 e Esnault (Freie Universität Berlin) as part of Columbia - Automorphic fo
 rms and arithmetic seminar\n\n\nAbstract\nWe show that the Betti moduli sp
 ace of a smooth complex quasi-projective variety $X$ has a weak integralit
 y property which in particular yields a new obstruction for a finitely pre
 sented group to be the topological fundamental group of $X$. We define wea
 k arithmetic complex points of the Betti moduli space and prove density of
  those. Our method relies on the arithmetic (via companions) and the geome
 tric (via de Jong's conjecture solved by Gaitsgory) Langlands corresponden
 ce. It also yields other properties of the Betti moduli space which we sha
 ll mention if time permits.\nJoint work in progress with Johan de Jong.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard University)
DTSTART:20221007T143000Z
DTEND:20221007T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/10/">Kolyvagin's Conjecture and Higher Congruences of Mod
 ular Forms</a>\nby Naomi Sweeting (Harvard University) as part of Columbia
  - Automorphic forms and arithmetic seminar\n\n\nAbstract\nGiven an ellipt
 ic curve E\, Kolyvagin used CM points on modular curves to construct a sys
 tem of classes valued in the Galois cohomology of the torsion points of E.
  Under the conjecture that not all of these classes vanish\, he deduced re
 markable consequences for the Selmer rank of E. For example\, his results\
 , combined with work of Gross-Zagier\, implied that a curve with analytic 
 rank one also has algebraic rank one\; a partial converse follows from his
  conjecture. \nIn this talk\, I will report on work proving several new ca
 ses of Kolyvagin's conjecture. The methods follow in the footsteps of Wei 
 Zhang\, who used congruences between modular forms to prove Kolyvagin's co
 njecture under some technical hypotheses. By considering congruences modul
 o higher powers of p\, we remove many of those hypotheses. The talk will p
 rovide an introduction to Kolyvagin's conjecture and its applications\, ex
 plain an analog of the conjecture in an opposite parity regime\, and give 
 an overview of the proofs\, including the difficulties associated with hig
 her congruences of modular forms and how they can be overcome via deformat
 ion theory.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/10
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Chen (Princeton University)
DTSTART:20221111T153000Z
DTEND:20221111T170000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/11/">Duality of singular automorphic periods</a>\nby Eric
  Chen (Princeton University) as part of Columbia - Automorphic forms and a
 rithmetic seminar\n\n\nAbstract\nIn the recent framework proposed by Ben-Z
 vi--Sakellaridis--Venkatesh\, automorphic periods ought to\, very roughly 
 speaking\, come in Langlands dual pairs. I will give a short introduction 
 of this prediction and motivate the need to consider certain singular auto
 morphic periods. In particular\, I will present an example in joint work w
 ith Akshay Venkatesh\, where we establish duality using a generalization o
 f L-functions.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/11
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu-Sheng Lee (Columbia University)
DTSTART:20221028T143000Z
DTEND:20221028T160000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/12/">Arithmetic of theta liftings</a>\nby Yu-Sheng Lee (C
 olumbia University) as part of Columbia - Automorphic forms and arithmetic
  seminar\n\n\nAbstract\nWe discuss the integrality of theta liftings of an
 ti-cyclotomic characters to a definite unitary group $\\mathrm{U}(2)$ of t
 wo variables. This will allow us to construct a Hida family of the theta l
 iftings and relate the congruence module of which to an anti-cyclotomic $p
 $-adic L-function. The result is an input to Urban's construction of Euler
  systems.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/12
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Hernandez (Université Paris-Saclay)
DTSTART:20221202T153000Z
DTEND:20221202T170000Z
DTSTAMP:20260422T230721Z
UID:Columbia-NumberTheorySeminar/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Columbia-Num
 berTheorySeminar/13/">The infinite fern in higher dimensions</a>\nby Valen
 tin Hernandez (Université Paris-Saclay) as part of Columbia - Automorphic
  forms and arithmetic seminar\n\n\nAbstract\nIn full generality deformatio
 n spaces of Galois representations are mysterious objects. A natural quest
 ion to ask is if they contain at least enough modular points in their gene
 ric fiber. In this talk I will explain result about the Zariski density of
  such points for conjugate self dual deformations spaces. Such a result wa
 s obtained for GL_2 by Gouvea-Mazur and then generalized by Chenevier in d
 imension 3. Both strategies uses the Infinite fern\, a fractal-like object
  which is the image of an Eigenvariety. More recently Hellmann-Margerin-Sc
 hraen extended Chenevier's result under strong Taylor-Wiles hypothesis\, w
 ith main input the local model of the trianguline variety and the patched 
 Eigenvarieties of Breuil-Hellmann-Schraen. Our strategy is to study furthe
 r the geometry of the trianguline variety\, and to use the geometry of cla
 ssical points on the (non-patched) Eigenvariety to remove the Taylor-Wiles
  hypothesis. \nThis is a joint work with B. Schraen.\n
LOCATION:https://researchseminars.org/talk/Columbia-NumberTheorySeminar/13
 /
END:VEVENT
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