BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Sebastian Eterovic (UC Berkeley)
DTSTART:20200609T181500Z
DTEND:20200609T193000Z
DTSTAMP:20260404T092655Z
UID:BerkeleyModelTheory/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyModelTheory/1/">Differential existential closedness for the $j$-functio
 n</a>\nby Sebastian Eterovic (UC Berkeley) as part of Berkeley model theor
 y seminar\n\n\nAbstract\nI will give a proof of the Existential Closedness
  conjecture for the differential equation of the $j$-function and its deri
 vatives. It states that in a differentially closed field certain equations
  involving the differential equation of the $j$-function have solutions. I
 ts consequences include a complete axiomatisation of $j$-reducts of differ
 entially closed fields\, a dichotomy result for strongly minimal sets in t
 hose reducts\, and a functional analogue of the Modular Zilber-Pink with D
 erivatives conjecture. This is joint work with Vahagn Aslanyan and Jonatha
 n Kirby.\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyModelTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vahagn Aslanyan (University of East Anglia)
DTSTART:20200616T181500Z
DTEND:20200616T193000Z
DTSTAMP:20260404T092655Z
UID:BerkeleyModelTheory/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Berke
 leyModelTheory/2/">Blurrings of the $j$-Function</a>\nby Vahagn Aslanyan (
 University of East Anglia) as part of Berkeley model theory seminar\n\n\nA
 bstract\nI will define blurred variants of the $j$-function and its deriva
 tives\, where blurring is given by the action of a subgroup of $\\GL_2(\\C
 )$. For a dense subgroup (in the complex topology) I will prove an Existen
 tial Closedness theorem which states that all systems of equations in term
 s of the corresponding blurred $j$ with derivatives have complex solutions
 \,  except where there is a functional transcendence reason why they shoul
 d not. The proof is based on the Ax-Schanuel theorem and Remmert’s open 
 mapping theorem from complex geometry. For the $j$-function without deriva
 tives a stronger theorem holds\, namely\, Existential Closedness for $j$ b
 lurred by the action of a subgroup which is dense in $\\GL_2^+(\\R)$\, but
  not necessarily in $\\GL_2(\\C)$. In this case apart from the Ax-Schanuel
  theorem and some basic complex geometry we also use o-minimality in the p
 roof. If time permits\, I will also discuss some model theoretic propertie
 s of the blurred $j$-function such as stability and quasiminimality. This 
 is joint work with Jonathan Kirby.\n
LOCATION:https://stable.researchseminars.org/talk/BerkeleyModelTheory/2/
END:VEVENT
END:VCALENDAR