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SUMMARY:Charlotte Ure (Illinois State University)
DTSTART:20241101T210000Z
DTEND:20241101T220000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/2/">D
 ecomposition of cohomology classes in finite field extensions</a>\nby Char
 lotte Ure (Illinois State University) as part of UBC Number theory seminar
 \n\nLecture held in ESB4133.\n\nAbstract\nRost and Voevodsky proved the Bl
 och-Kato conjecture relating Milnor k-theory and Galois cohomology. It imp
 lies that if a field F contains a primitive pth root of unity\, then the G
 alois cohomology ring of F with coefficients in the trivial F-module 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://researchseminars.org/talk/NT-UBC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Quesada-Herrera (U of Lethbridge)
DTSTART:20241108T220000Z
DTEND:20241108T230000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/3/">O
 n the vertical distribution of the zeros of the Riemann zeta-function</a>\
 nby Emily Quesada-Herrera (U of Lethbridge) as part of UBC Number theory s
 eminar\n\nLecture held in ESB4133.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NT-UBC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (U of Lethbridge)
DTSTART:20241115T220000Z
DTEND:20241115T230000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/4/">T
 he Ostrowski Quotient for a finite extension of number fields</a>\nby Abba
 s Maarefparvar (U of Lethbridge) as part of UBC Number theory seminar\n\nL
 ecture held in ESB4133.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NT-UBC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Didier Lesesvre (U of Lille)
DTSTART:20241122T203000Z
DTEND:20241122T213000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/5/">R
 elation between low-lying zeros and central values</a>\nby Didier Lesesvre
  (U of Lille) as part of UBC Number theory seminar\n\nLecture held in ESB4
 133.\n\nAbstract\nIn practice\, L-functions appear as generating functions
 \nencapsulating information about various objects\, such as Galois\nrepres
 entations\, elliptic curves\, arithmetic functions\, modular forms\,\nMaas
 s forms\, etc. Studying L-functions is therefore of utmost importance\nin 
 number theory at large. Two of their attached data carry critical\ninforma
 tion: their zeros\, which govern the distributional behavior of\nunderlyin
 g objects\; and their central values\, which are related to\ninvariants su
 ch as the class number of a field extension. We discuss a\nconnection betw
 een low-lying zeros and central values of L-functions\, in\nparticular sho
 wing that results about the distribution of low-lying\nzeros (towards the 
 density conjecture of Katz-Sarnak) implies results\nabout the distribution
  of the central values (towards the normal\ndistribution conjecture of Kea
 ting-Snaith). Even though we discuss this\nprinciple in general\, we insta
 nciate it in the case of modular forms in\nthe level aspect to give a stat
 ement and explain the arguments of the proof\n
LOCATION:https://researchseminars.org/talk/NT-UBC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian An Wong (U of Michigan)
DTSTART:20241129T220000Z
DTEND:20241129T230000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/6/">T
 owards a notion of mesoscopy</a>\nby Tian An Wong (U of Michigan) as part 
 of UBC Number theory seminar\n\nLecture held in ESB4133.\n\nAbstract\nWith
 in the Langlands program\, the theory of endoscopy concerns the transfer\n
 of distributions between a reductive group $G$ and $G'$\, an endoscopic\ng
 roup of $G$. At the heart of Langlands' original study on Beyond Endoscopy
 \nis the notion of stable transfer between groups $G$ and $G'$\, where $G'
 $ is\nno longer required to be an endoscopic group. Arthur referred to the
 se as\n'beyond endoscopic groups\,' and which we call mesoscopic groups. I
 n this\ntalk I will introduce these ideas\, the role they play in functori
 ality\, and\nopen problems that arise in their study. Time permitting\, I 
 will explain\nthe role they play in refining the stable trace formula.\n
LOCATION:https://researchseminars.org/talk/NT-UBC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seda Albayrak (U of Calgary)
DTSTART:20241213T220000Z
DTEND:20241213T230000Z
DTSTAMP:20260422T225925Z
UID:NT-UBC/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NT-UBC/8/">M
 ultivariate generalization of Christol's Theorem</a>\nby Seda Albayrak (U 
 of Calgary) as part of UBC Number theory seminar\n\nLecture held in ESB413
 3.\n\nAbstract\nChristol's theorem (1979)\, which sets ground for many int
 eractions\nbetween theoretical computer science and number theory\, charac
 terizes the\ncoefficients of a formal power series over a finite field of 
 positive\ncharacteristic $p>0$ that satisfy an algebraic equation to be th
 e sequences\nthat can be generated by finite automata\, that is\, a finite
 -state machine takes\nthe base-$p$ expansion of $n$ for each coefficient a
 nd gives the coefficient\nitself as output.  Namely\, a formal power serie
 s $\\sum_{n\\ge 0} f(n) t^n$ over\n$\\mathbb{F}_p$ is algebraic over $\\ma
 thbb{F}_p(t)$ if and only if $f(n)$ is a\n$p$-automatic sequence. However\
 , this characterization does not give the full\nalgebraic closure of $\\ma
 thbb{F}_p(t)$. Later it was shown by Kedlaya (2006)\nthat a description of
  the complete algebraic closure of $\\mathbb{F}_p(t)$ can\nbe given in ter
 ms of $p$-quasi-automatic generalized (Laurent) series. In fact\,\nthe alg
 ebraic closure of $\\mathbb{F}_p(t)$ is precisely generalized Laurent\nser
 ies that are $p$-quasi-automatic. We will characterize elements in the\nal
 gebraic closure of function fields over a field of positive characteristic
 \nvia finite automata in the multivariate setting\, extending Kedlaya's re
 sults.\nIn particular\, our aim is to give a description of the \\textit{f
 ull algebraic\nclosure} for \\textit{multivariate} fraction fields of posi
 tive characteristic.\n
LOCATION:https://researchseminars.org/talk/NT-UBC/8/
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