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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Ramin Takloo-Bighash (Department of Math\, Stat\, and Computer Sci
ence\, UIC Chicago\, IL)
DTSTART;VALUE=DATE-TIME:20210928T150000Z
DTEND;VALUE=DATE-TIME:20210928T170000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/1
DESCRIPTION:Title:
The distribution of rational points on some spherical varieties.\nby R
amin Takloo-Bighash (Department of Math\, Stat\, and Computer Science\, UI
C Chicago\, IL) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac
t\nIn this talk I will discuss a work in progress in which\, together with
Sho Tanimoto and Yuri Tschinkel\, we study the distribution of rational p
oints on some anisotropic spherical varieties of rank 1 over an arbitrary
number field. Our work is the non-split analogue of the results of Valenti
n Blomer\, Jörg Brüdern\, Ulrich Derenthal\, and Giuliano Gagliardi wher
e they consider split spherical varieties of rank 1 over the rational numb
ers\, though our methods are completely different. In our proof we use the
theory of automorphic forms\, especially Waldspurger's celebrated theorem
on toric periods\, to analyse the height zeta function. Once this analysi
s is done\, the result on the distribution of rational points follows from
a standard Tauberian theorem. We hope to address split spherical varietie
s of rank 1 over an arbitrary number field using similar methods in a futu
re work.\n\nMeeting ID: 908 611 6889\nPasscode: ''the order of the symmetr
ic group on 9 elements (type the 6-digit number)''\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kisin (Harvard University)
DTSTART;VALUE=DATE-TIME:20211012T140000Z
DTEND;VALUE=DATE-TIME:20211012T160000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/2
DESCRIPTION:Title:
Essential dimension via prismatic cohomology\nby Mark Kisin (Harvard U
niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nLe
t $f:Y \\rightarrow X$ be a finite covering map of complex algebraic varie
ties. The essential dimension of $f$ is the smallest integer $e$ such that
\, birationally\, $f$ arises as the pullback of a covering $Y'\\rightarrow
X'$ of dimension $e$\, via a map $X \\rightarrow X'$. This invariant goes
back to classical questions about reducing the number of parameters in a
solution to a general $n$-th degree polynomial\, and appeared in work of K
ronecker and Klein on solutions of the quintic. \n\nI will report on joint
work with Benson Farb and Jesse Wolfson\, where we introduce a new techni
que\, using prismatic cohomology\, to obtain lower bounds on the essential
dimension of certain coverings. For example\, we show that for an abelian
variety $A$ of dimension $g$ the multiplication by $p$ map $A \\rightarr
ow A$ has essential dimension $g$ for almost all primes $p$.\n\nMeeting ID
: 908 611 6889 \,\nPasscode: order of the symmetric group on 9 letters (ty
pe the 6-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reza Taleb (Shahid Beheshti University)
DTSTART;VALUE=DATE-TIME:20211026T140000Z
DTEND;VALUE=DATE-TIME:20211026T160000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/3
DESCRIPTION:Title:
The Coates-Sinnott Conjecture\nby Reza Taleb (Shahid Beheshti Universi
ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe Coate
s-Sinnott Conjecture was formulated in 1974 as a K-theory analogue of Stic
kelberger's Theorem. For a finite abelian extension $E/F$ of number fields
and any integer $n\\geq 2$\, this conjecture constructs an element in ter
ms of special values of the (equivariant) L-function of $E/F$ at $1-n$ to
annihilate the even Quillen K-group $K_{2n-2}(O_E)$ of associated ring of
integers $O_E$ over the group ring $\\mathbb{Z}[Gal(E/F)]$. In this talk a
fter describing the precise formulation of the conjecture we present the r
ecent results. Part of this is a joint work with Manfred Kolster.\n\nMeet
ing ID: 908 611 6889 \,\nPasscode: Order of the symmetric group on 9 lette
rs (Type the 6-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shabnam Akhatri (University of Oregon)
DTSTART;VALUE=DATE-TIME:20211109T140000Z
DTEND;VALUE=DATE-TIME:20211109T160000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/4
DESCRIPTION:Title:
Monogenic cubic rings and Thue equations\nby Shabnam Akhatri (Universi
ty of Oregon) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\
nLet K be a cubic number field. We give an absolute upper bound for the nu
mber of monogenic orders which have small index (compared to the discrimin
ant of K) in the ring of integers of K. This is done by counting the numb
er of integral solutions of some cubic Thue equations. This reduction to t
he resolution of Thue equations will also allow us to count the number of
monogenic orders with a fixed index in the ring of integers of K.\n\nMeeti
ng ID: 908 611 6889\, \nPasscode: The order of the symmetric group on 9 el
ements (Type the 6-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Mohammadi (IPM)
DTSTART;VALUE=DATE-TIME:20211123T113000Z
DTEND;VALUE=DATE-TIME:20211123T133000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/5
DESCRIPTION:Title:
Bounds on point-conic incidences over finite fields and applications\n
by Ali Mohammadi (IPM) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n
Abstract\nI will begin with a brief overview of some well-known results in
incidence geometry and go on to discuss a recent joint work with Thang Ph
am and Audie Warren\, in which we prove upper bounds on the number of inci
dences between sets of points and conics over finite fields. I will conclu
de the talk by considering applications to certain finite field variants o
f Erd\\H{o}s type problems on the number of distinct algebraic distances f
ormed by point sets\, including improvements to results of Koh and Sun (20
14) and Shparlinski (2006).\n\nMeeting ID: 908 611 6889\,\nPasscode: The o
rder of the symmetric group on 9 elements (Type the 6-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Dabrowski (University of Szczecin)
DTSTART;VALUE=DATE-TIME:20211207T113000Z
DTEND;VALUE=DATE-TIME:20211207T133000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/6
DESCRIPTION:Title:
On a class of generalized Fermat equations of signature $(2\,2n\,3)$\n
by Andrzej Dabrowski (University of Szczecin) as part of FGC-HRI-IPM Numbe
r Theory Webinars\n\n\nAbstract\nWe will discuss the generalized Fermat eq
uations\n$Ax^2 + By^{2n} = 4z^3$\, assuming (for simplicity) that\nthe cl
ass number of the imaginary quadratic field\n$\\mathbb Q(\\sqrt{-AB})$ is
one. The methods use techniques\ncoming from Galois representations and mo
dular forms\; for\nsmall $n$'s one needs Chabauty type methods. Our result
s\,\nconjectures (and methods) extend those given by Bruin\, Chen\net al.
in the case $x^2 + y^{2n} = z^3$. This is a joint work\nwith K. Chałupka
and G. Soydan.\n\nMeeting ID: 989 8485 8471\, \nPasscode: 039129\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Ghadermarzi (University of Tehran)
DTSTART;VALUE=DATE-TIME:20211221T140000Z
DTEND;VALUE=DATE-TIME:20211221T160000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/7
DESCRIPTION:Title:
Integral points on Mordell curves of rank 1\nby Amir Ghadermarzi (Univ
ersity of Tehran) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
act\nA well-known theorem of Siegel states that any elliptic curve $E/\\ma
thbb{Q}$ has only finitely many integral points. Lang conjectured that the
number of integral points on a quasi-minimal model of an elliptic curve s
hould be bounded solely in terms of the rank of the group of rational poin
ts. Silverman proved Lang's conjecture for the curves with at most a fixed
number of primes dividing the denominator of the $j$-invariant. Using mor
e explicit methods\, Silverman and Gross compute the dependence of the bou
nds on the various constants. In the case of curves of rank 1\, techniques
of Ingram on multiples of integral points enable one to prove much better
bounds for special families of elliptic curves. In this talk\, we investi
gate the integral points on Mordell curves of rank 1.\n\nMeeting ID: 908 6
11 6889\, \nPasscode: the order of the symmetric group on 9 letters (Type
the 6-digit number).\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IITGandhinagar)
DTSTART;VALUE=DATE-TIME:20210104T113000Z
DTEND;VALUE=DATE-TIME:20210104T133000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/8
DESCRIPTION:Title:
Selberg’s Central Limit Theorem\nby Fatma Cicek (IITGandhinagar) as
part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IIT Gandhinagar)
DTSTART;VALUE=DATE-TIME:20210104T113000Z
DTEND;VALUE=DATE-TIME:20210104T133000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/9
DESCRIPTION:Title:
Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhinagar) as
part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IIT Gandhinagar)
DTSTART;VALUE=DATE-TIME:20220104T113000Z
DTEND;VALUE=DATE-TIME:20220104T133000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/10
DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhinagar) a
s part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nSelberg's c
entral limit theorem is an influential probabilistic result in analytic nu
mber theory which roughly states that the logarithm of the Riemann zeta-fu
nction $\\zeta(s)$ on the half-line\, that is $\\Re s = \\frac12$
\, has an approximate two-dimensional Gaussian distribution as $\\Im s
\\to \\infty$. We will carefully review the important ideas in the p
roof of Selberg's theorem and then will mention some variants of it.
Towards the end of the talk\, we will also see some of its applic
ations.\n\nMeeting ID: 922 2650 4686 \; Passcode: 645549\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian David Gonzalez Aviles (Universidad de La Serena)
DTSTART;VALUE=DATE-TIME:20220201T130000Z
DTEND;VALUE=DATE-TIME:20220201T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/11
DESCRIPTION:Title: Totally singular algebraic groups\nby Cristian David Gonzalez Aviles
(Universidad de La Serena) as part of FGC-HRI-IPM Number Theory Webinars\n
\n\nAbstract\nI will define the groups of the title and discuss some examp
les.\nWhen they are of positive dimension\, these groups exist only\nover
an imperfect field. We will see examples in dimension 1 related to the\npu
rely inseparable forms of the additive group\nstudied by Russell in 1970.
We will also see some examples of arbitrarily\nhigh dimensions. I hope to
convince the audience that this class of\nalgebraic groups is both interes
ting and quite large!\n\nMeeting ID: 908 611 6889\,\n\nPasscode: The order
of the symmetric group over nine letters (Please type the 6-digit number)
.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200315T130000Z
DTEND;VALUE=DATE-TIME:20200315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/12
DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu
mber Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200315T130000Z
DTEND;VALUE=DATE-TIME:20200315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/13
DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu
mber Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200315T130000Z
DTEND;VALUE=DATE-TIME:20200315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/14
DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu
mber Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200315T130000Z
DTEND;VALUE=DATE-TIME:20200315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/15
DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu
mber Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20200315T130000Z
DTEND;VALUE=DATE-TIME:20200315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/16
DESCRIPTION:by Semih Ozlem (Yeditepe University) as part of FGC-HRI-IPM Nu
mber Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART;VALUE=DATE-TIME:20220315T130000Z
DTEND;VALUE=DATE-TIME:20220315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/17
DESCRIPTION:Title: On the motivic Galois group of a number field\nby Semih Ozlem (Yedite
pe University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract
\nAim of this talk is to briefly introduce the motivic Galois group and st
ate a potential answer to Langlands' conjecture regarding the relation of
Langlands' group and motivic Galois group.\n\nMeeting ID: 908 611 6889\;\n
Passcode: the order of the symmetric group on 9 letters (please type the 6
-digit number)\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farzad Aryan (Göttingen University)
DTSTART;VALUE=DATE-TIME:20220405T120000Z
DTEND;VALUE=DATE-TIME:20220405T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/18
DESCRIPTION:Title: On the Riemann Zeta Function\nby Farzad Aryan (Göttingen University)
as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will discu
ss the Riemann zeta function and the significance of its zeros to prime nu
mbers. Also\, I will look at the distribution of zeta zeros and mention so
me of my related works on the subject.\n\nJoin Zoom Meeting\nhttps://us06w
eb.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting I
D: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chirantan Chowdhury (University of Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20220419T120000Z
DTEND;VALUE=DATE-TIME:20220419T130000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/19
DESCRIPTION:Title: Motivic Homotopy Theory of Algebraic Stacks\nby Chirantan Chowdhury (
University of Duisburg-Essen) as part of FGC-HRI-IPM Number Theory Webinar
s\n\nAbstract: TBA\n\nZoom link:\nhttps://us06web.zoom.us/j/87212146791?pw
d=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPasscode:
362880\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamza Yesilyurt (Bilkent University)
DTSTART;VALUE=DATE-TIME:20220517T120000Z
DTEND;VALUE=DATE-TIME:20220517T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/20
DESCRIPTION:Title: A Modular Equation of Degree 61\nby Hamza Yesilyurt (Bilkent Universi
ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nA modular
equation of degree $n$ is an equation that relates classical theta functi
ons with arguments $q$ and $q^n$. The theory of modular equations started
with the works of Landen\, Jacobi and Legendre. The theory gained populari
ty again with enormous contributions made by Ramanujan. In this talk we wi
ll give a brief introduction to the theory of modular equations and then o
btain a new modular equation of degree $61$ by using a generalization of
a theta function identity due to David M. Bressoud. This is a joint work
with Ahmet Güloğlu.\n\nJoin Zoom Meeting:\nhttps://us06web.zoom.us/j/872
12146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791
\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Somnath Jha (IIT Kanpur)
DTSTART;VALUE=DATE-TIME:20220531T120000Z
DTEND;VALUE=DATE-TIME:20220531T130000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/21
DESCRIPTION:Title: Fine Selmer group of elliptic curves over global fields\nby Somnath J
ha (IIT Kanpur) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac
t\nThe (p-infinity) fine Selmer group (also called the 0-Selmer group) of
an elliptic curve is a subgroup of the usual p-infinity Selmer group of an
elliptic curve and is related to the first and the second Iwasawa cohomol
ogy groups. Coates-Sujatha observed that the structure of the fine Selmer
group over the cyclotomic Z_p extension of a number field K is intricately
related to Iwasawa's \\mu-invariant vanishing conjecture on the growth of
p-part of the ideal class group of K in the cyclotomic tower. In this tal
k\, we will discuss the structure and properties of the fine Selmer group
over certain p-adic Lie extensions of global fields. This talk is based on
joint work with Sohan Ghosh and Sudhanshu Shekhar.\n\nZoom link:\nhttps:
//us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMe
eting ID: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (Institute for Research in Fundamental Sciences
(IPM))
DTSTART;VALUE=DATE-TIME:20220614T120000Z
DTEND;VALUE=DATE-TIME:20220614T130000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/22
DESCRIPTION:Title: On BRZ exact sequence for finite Galois extensions of number fields\n
by Abbas Maarefparvar (Institute for Research in Fundamental Sciences (IPM
)) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this ta
lk\, I will shortly explain how to use some cohomological results of Brume
r-Rosen and Zantema to obtain a four-term exact sequence\, called ``BRZ’
’ standing for these authors\, which reveals some information about str
ongly ambiguous ideal classes (coinciding with relative Polya group) of a
finite Galois extension of number fields. As an application of the BRZ\, I
will reprove some well known results in the literature. Then\, as a minor
modification on relative Polya group for a finite extension of number fie
lds\, I will introduce the notion of ``relative Ostrowski quotient'' and
give some new approaches of the BRZ exact sequence. The main part of my t
alk is concerning a joint work with Ali Rajaei and Ehsan Shahoseini.\n\nZo
om link:\nhttps://us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbk
lEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammad Sadek
DTSTART;VALUE=DATE-TIME:20221024T130000Z
DTEND;VALUE=DATE-TIME:20221024T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/23
DESCRIPTION:Title: How often do polynomials hit squares?\nby Mohammad Sadek as part of F
GC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGiven a polynomial with r
ational coefficients\, one may investigate the possible values that may be
attained by these polynomials over the set of rational numbers. For centu
ries\, number theorists have been giving due attention to square rational
values assumed by rational polynomials. It turns out that seeking an answe
r to this question connects number theory and geometry. Answering this que
stion for a polynomial in one variable will lead us to study the arithmeti
c of certain algebraic curves. We will spend some time explaining the geom
etry beneath the question when the degree of the polynomial is at least 3.
For polynomials in more than one variable\, the geometric structure is re
mote. In the latter case\, we will present some of the old and recent deve
lopments in the theory shedding some light on some classical Diophantine q
uestions.\n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID:
856 1386 0958\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haydar Goral
DTSTART;VALUE=DATE-TIME:20221107T130000Z
DTEND;VALUE=DATE-TIME:20221107T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/24
DESCRIPTION:Title: Lehmer’s conjecture via model theory\nby Haydar Goral as part of FG
C-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we first in
troduce the height function and the Mahler measure on the field of algebra
ic numbers. We state and give a survey on Lehmer’s conjecture for the Ma
hler measure\, which is still an open problem. Then\, we consider the fiel
d of algebraic numbers with elements of small Mahler measures in terms of
model theory\, and we link this theory with Lehmer’s conjecture. Our ap
proach is based on Van der Waerden's theorem from additive combinatorics.\
n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID: 856 1386
0958\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Akbary
DTSTART;VALUE=DATE-TIME:20221121T130000Z
DTEND;VALUE=DATE-TIME:20221121T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/25
DESCRIPTION:Title: Value-distribution of automorphic L-functions\nby Amir Akbary as part
of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nAfter a brief introd
uction on the value-distribution of arithmetic functions and L-functions\,
we give an overview of our joint work with Alia Hamieh (University of Nor
thern British Colombia) on the value-distribution of logarithmic derivativ
e of certain automorphic L-functions. Among other things\, we describe an
upper bound for the discrepancy of the distribution of the values (at a po
int on the edge of the critical strip) of the twists of a fixed automorphi
c L-function with quadratic Dirichlet characters. Our result can be consid
ered as an automorphic analogue of a result of Lamzouri\, Lester\, and Rad
ziwill for the logarithm of the Riemann zeta function. Our estimate is con
ditional on certain expected bounds on the local parameters of L-functions
which is known to be true for GL(1) and GL(2).\n\nZoom Meeting ID: 856 13
86 0958\nPasscode: 513 992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enis Kaya
DTSTART;VALUE=DATE-TIME:20221219T130000Z
DTEND;VALUE=DATE-TIME:20221219T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/26
DESCRIPTION:Title: Computing Schneider p-adic heights on hyperelliptic Mumford curves\nb
y Enis Kaya as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nT
here are several definitions of p-adic height pairings on curves in the li
terature\, and algorithms for computing them play a crucial role in\, for
example\, carrying out the quadratic Chabauty method\, which is a p-adic m
ethod that attempts to determine rational points on curves of genus at lea
st two.\n\n \n\nThe $p$-adic height pairing constructed by Peter Schneider
in $1982$ is particularly important because the corresponding $p$-adic re
gulator fits into $p$-adic versions of Birch and Swinnerton-Dyer conjectur
e. In this talk\, we present an algorithm to compute the Schneider $p$-adi
c height pairing on hyperelliptic Mumford curves. We illustrate this algor
ithm with a numerical example computed in the computer algebra system Sage
Math.\n\n \n\nThis talk is based on a joint work in progress with Marc Mas
deu\, J. Steffen Müller and Marius van der Put.\n\nZoom Meeting ID: 856 1
386 0958\nPasscode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan (Koc University)
DTSTART;VALUE=DATE-TIME:20221205T130000Z
DTEND;VALUE=DATE-TIME:20221205T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/27
DESCRIPTION:Title: CANCELLED - On inverse theorems and conjectures in ergodic theory and add
itive combinatorics\nby Asgar Jamneshan (Koc University) as part of FG
C-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will provide a non-techn
ical overview of some interactions between ergodic theory and additive com
binatorics. The focus will be on inverse theorems and conjectures for the
Gowers uniformity norms for finite abelian groups in additive combinatoric
s and their counterparts for the Host-Kra-Gowers uniformity seminorms for
abelian measure-preserving systems in ergodic theory.\n\nUnfortunately our
speaker cannot make it today due to an emergency. We will reschedule his
talk for another time. Sorry for the inconvenience.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-Tsung Chen
DTSTART;VALUE=DATE-TIME:20230116T130000Z
DTEND;VALUE=DATE-TIME:20230116T140000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/29
DESCRIPTION:Title: On the partial derivatives of Drinfeld modular forms of arbitrary rank\nby Yen-Tsung Chen as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAb
stract\nIn the 1980's\, the study of Drinfeld modular forms for the rank 2
setting was initiated by Goss. Recently\, by the contributions of Basson\
, Breuer\, Häberli\, Gekeler\, Pink et. al.\, the theory of Drinfeld modu
lar forms has been successfully generalized to the arbitrary rank setting.
In this talk\, we introduce an analogue of the Serre derivation acting on
the product of spaces of Drinfeld modular forms of rank r>1\, which also
generalizes the differential operator introduced by Gekeler in the rank tw
o case. This is joint work with Oğuz Gezmiş.\n\nZoom Meeting ID: 856 138
6 0958\nPasscode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Inam
DTSTART;VALUE=DATE-TIME:20230315T140000Z
DTEND;VALUE=DATE-TIME:20230315T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/30
DESCRIPTION:Title: Fast Computation of Half-Integral Weight Modular Forms\nby Ilker Inam
as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nModular form
s continue to attract attention for decades with many different applicatio
n areas. To study statistical properties of modular forms\, including for
instance Sato-Tate like problems\, it is essential to be able to compute a
large number of Fourier coefficients. In this talk\, we will show that th
is can be achieved in level 4 for a large range of half-integral weights b
y making use of one of three explicit bases\, the elements of which can be
calculated via fast power series operations.\nThis is joint work with Gab
or Wiese (Luxembourg).\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\
n
LOCATION:https://researchseminars.org/talk/FGC-IPM/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alia Hamieh
DTSTART;VALUE=DATE-TIME:20230405T140000Z
DTEND;VALUE=DATE-TIME:20230405T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/32
DESCRIPTION:Title: Moments of $L$-functions and Mean Values of Long Dirichlet Polynomials\nby Alia Hamieh as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
act\nEstablishing asymptotic formulae for moments of $L$-functions is a ce
ntral theme in analytic number theory. This topic is related to various no
n-vanishing conjectures and the generalized Lindelöf Hypothesis. A major
breakthrough in analytic number theory occurred in 1998 when Keating and S
naith established a conjectural formula for moments of the Riemann zeta fu
nction using ideas from random matrix theory. The methods of Keating and S
naith led to similar conjectures for moments of many families of $L$-funct
ions. These conjectures have become a driving force in this field which ha
s witnessed substantial progress in the last two decades. \nIn this talk\,
I will review the history of this subject and survey some recent results.
I will also discuss recent joint work with Nathan Ng on the mean values o
f long Dirichlet polynomials which could be used to model moments of the z
eta function.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan
DTSTART;VALUE=DATE-TIME:20230419T140000Z
DTEND;VALUE=DATE-TIME:20230419T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/33
DESCRIPTION:Title: On inverse theorems and conjectures in ergodic theory and additive combin
atorics\nby Asgar Jamneshan as part of FGC-HRI-IPM Number Theory Webin
ars\n\n\nAbstract\nI will provide a non-technical overview of some interac
tions between ergodic theory and additive combinatorics. The focus will be
on inverse theorems and conjectures for the Gowers uniformity norms for f
inite abelian groups in additive combinatorics and their counterparts for
the Host-Kra-Gowers uniformity seminorms for abelian measure-preserving sy
stems in ergodic theory.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 51399
2\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Gupta
DTSTART;VALUE=DATE-TIME:20230503T140000Z
DTEND;VALUE=DATE-TIME:20230503T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/34
DESCRIPTION:Title: Tame class field theory\nby Rahul Gupta as part of FGC-HRI-IPM Number
Theory Webinars\n\n\nAbstract\nAs a part of global class field theory\, w
e construct a reciprocity map that describes the unramified (resp. tame)
étale fundamental group as a pro-completion of a suitable idele class gro
up (resp. tame idele class group) for smooth curves over finite fields. Th
ese results were extended to higher-dimensional smooth varieties over fini
te fields by Kato-Saito (unramified case\, in 1986) and\nSchmidt-Spiess (t
ame case\, in 2000). We begin the talk by recalling these results.\n\nThe
main focus of the talk is to work with smooth varieties over local fields.
The class field theory over local fields is not as nice as that over fini
te fields. We discuss results in the unramified class field theory over lo
cal fields achieved in the period 1981--2015 by various mathematicians (Bl
och\, Saito\, Jennsen\, Forre\, etc.). We then move to the main topic of t
he talk which is the tame class field theory over local fields and prove t
hat the results in the tame case are similar to that in the case of unrami
fied class field theory.\n\nThis talk will be based on a joint work with A
. Krishna and J. Rathore.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 5139
92\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiana Bertolin
DTSTART;VALUE=DATE-TIME:20230517T140000Z
DTEND;VALUE=DATE-TIME:20230517T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/35
DESCRIPTION:Title: Periods of 1-motives and their polynomials relations\nby Cristiana Be
rtolin as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe in
tegration of differential forms furnishes an isomorphism between the De Rh
am and the Hodge realizations of a 1-motive M. The coefficients of the mat
rix representing this isomorphism are the so-called "periods" of M.\n In t
he semi-elliptic case (i.e. the underlying extension of the 1-motive is an
extension of an elliptic curve by the multiplicative group)\, we compute
explicitly these periods. \n \nIf the 1-motive M is defined over an algebr
aically closed field\, Grothendieck's conjecture asserts that the transcen
dence degree of the field generated by the periods is equal to the dimensi
on of the motivic Galois group of M. If we denote by I the ideal generated
by the polynomial relations between the periods\, we have that "the numbe
rs of periods of M minus the rank of the ideal I is equal to the dimension
of the motivic Galois group of M"\, that is a decrease in the dimension o
f the motivic Galois group is equivalent to an increase of the rank of the
ideal I. We list the geometrical phenomena which imply the decrease in th
e dimension of the motivic Galois group and in each case we compute the po
lynomials which generate the corresponding ideal I.\n\nZoom Meeting ID: 85
6 1386 0958 Passcode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano
DTSTART;VALUE=DATE-TIME:20230531T140000Z
DTEND;VALUE=DATE-TIME:20230531T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/36
DESCRIPTION:Title: Abelian arboreal representations\nby Carlo Pagano as part of FGC-HRI-
IPM Number Theory Webinars\n\n\nAbstract\nI will present joint work with A
ndrea Ferraguti which makes progress on a Conjecture of Andrews and Petsch
e that classifies abelian dynamical Galois groups over number fields\, in
the unicritical case. I will explain how to reduce the conjecture to the p
ost-critically finite case and the key tools to handle all unicritical PCF
with periodic critical orbit over any number field and all PCF over quadr
atic number fields. Along the way I will present an earlier rigidity resul
t of ours on the maximal closed subgroup of the automorphism group of a bi
nary rooted tree\, which offered us with the main input to translate the c
ommutativity of the Galois image into diophantine equations. I will also o
verview progress on the tightly related problem of lower bounding arboreal
degrees.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Lukina (Leiden University)
DTSTART;VALUE=DATE-TIME:20230614T140000Z
DTEND;VALUE=DATE-TIME:20230614T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/37
DESCRIPTION:Title: Weyl groups in Cantor dynamics\nby Olga Lukina (Leiden University) as
part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nArboreal repres
entations of absolute Galois groups of number fields are given by profinit
e groups of automorphisms of regular rooted trees\, with the geometry of t
he tree determined by a polynomial which defines such a representation. Th
us arboreal representations give rise to dynamical systems on a Cantor set
\, and allow to apply the methods of topological dynamics to study problem
s in number theory. In this talk we consider the conjecture of Boston and
Jones\, which states that the images of Frobenius elements under arboreal
representations have a certain cycle structure. To study this conjecture\,
we borrow from the Lie group theory the concepts of maximal tori and Weyl
groups\, and introduce maximal tori and Weyl groups in the profinite sett
ing. We then use this new technique to give a partial answer to the conjec
ture by Boston and Jones in the case when an arboreal representations is d
efined by a post-critically finite quadratic polynomial over a number fiel
d. Based on a joint work with Maria Isabel Cortez.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berkay Kebeci (Koc University)
DTSTART;VALUE=DATE-TIME:20231025T140000Z
DTEND;VALUE=DATE-TIME:20231025T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/38
DESCRIPTION:Title: Mixed Tate Motives and Aomoto Polylogarithms\nby Berkay Kebeci (Koc U
niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGr
othendieck proposed the category of motives as a Tannakian category\, offe
ring a universal framework for Weil cohomology theories. In this talk\, we
will consider motives in the sense of Nori. One expects the Hopf algebra
R of mixed Tate motives to be isomorphic to the bi-algebra A of Aomoto pol
ylogarithms. Our aim is to reconstruct A using Nori motives. This allows u
s to write a morphism from A to R.\n\nEmail ozlemejderff at gmail.com for
the passcode.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Sertöz (Leiden University)
DTSTART;VALUE=DATE-TIME:20231206T140000Z
DTEND;VALUE=DATE-TIME:20231206T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/39
DESCRIPTION:Title: (Cancelled!!!)Computing linear relations between univariate integrals
\nby Emre Sertöz (Leiden University) as part of FGC-HRI-IPM Number Theory
Webinars\n\nLecture held in https://kocun.zoom.us/j/99715471656.\n\nAbstr
act\nThe study of integrals of univariate algebraic functions (1-periods)
provided the impetus to develop much of algebraic geometry and transcenden
tal number theory. This old saga is now at a point of resolution. In 2022\
, Huber and Wüstholz gave a "qualitative description" of all linear relat
ions with algebraic coefficients between 1-periods. New techniques for det
ermining symmetries of complex tori allow us to develop algorithms to expl
icate these qualitative relations and decide the transcendence of 1-period
s. This is a work-in-progress with Joël Ouaknine (MPI SWS) and James Worr
ell (Oxford).\n\nThe talk is cancelled.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Türkü Özlüm Çelik (Koc University)
DTSTART;VALUE=DATE-TIME:20231011T140000Z
DTEND;VALUE=DATE-TIME:20231011T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/40
DESCRIPTION:Title: Algebraic Curves from Polygons\nby Türkü Özlüm Çelik (Koc Univer
sity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nWe stud
y constructing an algebraic curve from a Riemann surface given via a trans
lation surface\, which is a collection of finitely many polygons in the pl
ane with sides identified by translation. We use the theory of discrete Ri
emann surfaces to give an algorithm for approximating the Jacobian variety
of a translation surface whose polygon can be decomposed into squares. We
first implement the algorithm in the case of L-shaped polygons where the
algebraic curve is already known. The algorithm is also implemented in any
genus for specific examples of Jenkins-Strebel representatives\, a dense
family of translation surfaces that\, until now\, lived on the analytic si
de of the transcendental divide between Riemann surfaces and algebraic cur
ves. Using Riemann theta functions\, we give numerical experiments and res
ulting conjectures up to genus 5.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (Utrecht University)
DTSTART;VALUE=DATE-TIME:20231122T140000Z
DTEND;VALUE=DATE-TIME:20231122T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/41
DESCRIPTION:Title: Counting points on stacks and elliptic curves with a rational N-isogeny<
/a>\nby Soumya Sankar (Utrecht University) as part of FGC-HRI-IPM Number T
heory Webinars\n\n\nAbstract\nThe classical problem of counting elliptic c
urves with a rational N-isogeny can be phrased in terms of counting ration
al points on certain moduli stacks of elliptic curves. Counting points on
stacks\, while posing various challenges\, has also opened up several new
avenues of exploration in the last few years. In this talk\, I will give a
n introduction to modular curves from the stacky perspective\, discuss som
e notions of height on them\, and use some of these notions to answer the
counting question mentioned above. Time permitting\, I will talk about thi
s in the context of the stacky version of the Batyrev-Manin conjecture. Th
e talk assumes no prior knowledge of stacks and is based on joint work wit
h Brandon Boggess.\n\npassword is eight four eight zero eight four\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farzad Aryan
DTSTART;VALUE=DATE-TIME:20231108T140000Z
DTEND;VALUE=DATE-TIME:20231108T150000Z
DTSTAMP;VALUE=DATE-TIME:20231211T001058Z
UID:FGC-IPM/42
DESCRIPTION:Title: Cancellations in Character Sums and the Vinogradov Conjecture\nby Far
zad Aryan as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn
this talk\, we will explore conjectures related to cancellations in charac
ter sums.\nAdditionally\, we will examine the potential impact on the dist
ribution of zeros of Dirichlet L-functions if these conjectures prove to b
e false.\n\nplease send an email to ozlemejderff at gmail.com for the pass
code.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/42/
END:VEVENT
END:VCALENDAR