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SUMMARY:Charlotte Ure (Illinois State University)
DTSTART:20241101T210000Z
DTEND:20241101T220000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/2/">Decomposition of cohomology classes in finite field extensions</a>\n
 by Charlotte Ure (Illinois State University) as part of UBC Number theory 
 seminar\n\nLecture held in ESB4133.\n\nAbstract\nRost and Voevodsky proved
  the Bloch-Kato conjecture relating Milnor k-theory and Galois cohomology.
  It implies that if a field F contains a primitive pth root of unity\, the
 n the Galois cohomology ring of F with coefficients in the trivial F-modul
 e with p elements is generated\nby elements of degree one. In this talk\, 
 I will discuss a systematic approach to studying this phenomenon in finite
  field extensions via decomposition fields. This is joint work with Sunil 
 Chebolu\, Jan Minac\, Cihan Okay\, and Andrew Schultz.\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Quesada-Herrera (U of Lethbridge)
DTSTART:20241108T220000Z
DTEND:20241108T230000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/3/">On the vertical distribution of the zeros of the Riemann zeta-functi
 on</a>\nby Emily Quesada-Herrera (U of Lethbridge) as part of UBC Number t
 heory seminar\n\nLecture held in ESB4133.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (U of Lethbridge)
DTSTART:20241115T220000Z
DTEND:20241115T230000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/4/">The Ostrowski Quotient for a finite extension of number fields</a>\n
 by Abbas Maarefparvar (U of Lethbridge) as part of UBC Number theory semin
 ar\n\nLecture held in ESB4133.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Didier Lesesvre (U of Lille)
DTSTART:20241122T203000Z
DTEND:20241122T213000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/5/">Relation between low-lying zeros and central values</a>\nby Didier L
 esesvre (U of Lille) as part of UBC Number theory seminar\n\nLecture held 
 in ESB4133.\n\nAbstract\nIn practice\, L-functions appear as generating fu
 nctions\nencapsulating information about various objects\, such as Galois\
 nrepresentations\, elliptic curves\, arithmetic functions\, modular forms\
 ,\nMaass forms\, etc. Studying L-functions is therefore of utmost importan
 ce\nin number theory at large. Two of their attached data carry critical\n
 information: their zeros\, which govern the distributional behavior of\nun
 derlying objects\; and their central values\, which are related to\ninvari
 ants such as the class number of a field extension. We discuss a\nconnecti
 on between low-lying zeros and central values of L-functions\, in\nparticu
 lar showing that results about the distribution of low-lying\nzeros (towar
 ds the density conjecture of Katz-Sarnak) implies results\nabout the distr
 ibution of the central values (towards the normal\ndistribution conjecture
  of Keating-Snaith). Even though we discuss this\nprinciple in general\, w
 e instanciate it in the case of modular forms in\nthe level aspect to give
  a statement and explain the arguments of the proof\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian An Wong (U of Michigan)
DTSTART:20241129T220000Z
DTEND:20241129T230000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/6/">Towards a notion of mesoscopy</a>\nby Tian An Wong (U of Michigan) a
 s part of UBC Number theory seminar\n\nLecture held in ESB4133.\n\nAbstrac
 t\nWithin the Langlands program\, the theory of endoscopy concerns the tra
 nsfer\nof distributions between a reductive group $G$ and $G'$\, an endosc
 opic\ngroup of $G$. At the heart of Langlands' original study on Beyond En
 doscopy\nis the notion of stable transfer between groups $G$ and $G'$\, wh
 ere $G'$ is\nno longer required to be an endoscopic group. Arthur referred
  to these as\n'beyond endoscopic groups\,' and which we call mesoscopic gr
 oups. In this\ntalk I will introduce these ideas\, the role they play in f
 unctoriality\, and\nopen problems that arise in their study. Time permitti
 ng\, I will explain\nthe role they play in refining the stable trace formu
 la.\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seda Albayrak (U of Calgary)
DTSTART:20241213T220000Z
DTEND:20241213T230000Z
DTSTAMP:20260404T094914Z
UID:NT-UBC/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NT-UB
 C/8/">Multivariate generalization of Christol's Theorem</a>\nby Seda Albay
 rak (U of Calgary) as part of UBC Number theory seminar\n\nLecture held in
  ESB4133.\n\nAbstract\nChristol's theorem (1979)\, which sets ground for m
 any interactions\nbetween theoretical computer science and number theory\,
  characterizes the\ncoefficients of a formal power series over a finite fi
 eld of positive\ncharacteristic $p>0$ that satisfy an algebraic equation t
 o be the sequences\nthat can be generated by finite automata\, that is\, a
  finite-state machine takes\nthe base-$p$ expansion of $n$ for each coeffi
 cient and gives the coefficient\nitself as output.  Namely\, a formal powe
 r series $\\sum_{n\\ge 0} f(n) t^n$ over\n$\\mathbb{F}_p$ is algebraic ove
 r $\\mathbb{F}_p(t)$ if and only if $f(n)$ is a\n$p$-automatic sequence. H
 owever\, this characterization does not give the full\nalgebraic closure o
 f $\\mathbb{F}_p(t)$. Later it was shown by Kedlaya (2006)\nthat a descrip
 tion of the complete algebraic closure of $\\mathbb{F}_p(t)$ can\nbe given
  in terms of $p$-quasi-automatic generalized (Laurent) series. In fact\,\n
 the algebraic closure of $\\mathbb{F}_p(t)$ is precisely generalized Laure
 nt\nseries that are $p$-quasi-automatic. We will characterize elements in 
 the\nalgebraic closure of function fields over a field of positive charact
 eristic\nvia finite automata in the multivariate setting\, extending Kedla
 ya's results.\nIn particular\, our aim is to give a description of the \\t
 extit{full algebraic\nclosure} for \\textit{multivariate} fraction fields 
 of positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/NT-UBC/8/
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