BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ramin Takloo-Bighash (Department of Math\, Stat\, and Computer Sci
ence\, UIC Chicago\, IL)
DTSTART:20210928T150000Z
DTEND:20210928T170000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/1
DESCRIPTION:Title: The distribution of rational points on some spherical varieties.\nby Ramin Takloo-Bighash (Department of Math\, Stat\, and Computer Scien
ce\, UIC Chicago\, IL) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n
Abstract\nIn this talk I will discuss a work in progress in which\, togeth
er with Sho Tanimoto and Yuri Tschinkel\, we study the distribution of rat
ional points on some anisotropic spherical varieties of rank 1 over an arb
itrary number field. Our work is the non-split analogue of the results of
Valentin Blomer\, Jörg Brüdern\, Ulrich Derenthal\, and Giuliano Gagliar
di where they consider split spherical varieties of rank 1 over the ration
al numbers\, 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
analysis is done\, the result on the distribution of rational points follo
ws from a standard Tauberian theorem. We hope to address split spherical v
arieties of rank 1 over an arbitrary number field using similar methods in
a future work.\n\nMeeting ID: 908 611 6889\nPasscode: ''the order of the
symmetric group on 9 elements (type the 6-digit number)''\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kisin (Harvard University)
DTSTART:20211012T140000Z
DTEND:20211012T160000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/2
DESCRIPTION:Title: Essential dimension via prismatic cohomology\nby Mark Kisin (Ha
rvard University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
act\nLet $f:Y \\rightarrow X$ be a finite covering map of complex algebrai
c varieties. The essential dimension of $f$ is the smallest integer $e$ su
ch that\, birationally\, $f$ arises as the pullback of a covering $Y'\\rig
htarrow X'$ of dimension $e$\, via a map $X \\rightarrow X'$. This invaria
nt goes back to classical questions about reducing the number of parameter
s in a solution to a general $n$-th degree polynomial\, and appeared in wo
rk of Kronecker and Klein on solutions of the quintic. \n\nI will report o
n joint work with Benson Farb and Jesse Wolfson\, where we introduce a new
technique\, using prismatic cohomology\, to obtain lower bounds on the es
sential dimension of certain coverings. For example\, we show that for an
abelian variety $A$ of dimension $g$ the multiplication by $p$ map $A \\r
ightarrow A$ has essential dimension $g$ for almost all primes $p$.\n\nMee
ting ID: 908 611 6889 \,\nPasscode: order of the symmetric group on 9 lett
ers (type the 6-digit number)\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reza Taleb (Shahid Beheshti University)
DTSTART:20211026T140000Z
DTEND:20211026T160000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/3
DESCRIPTION:Title: The Coates-Sinnott Conjecture\nby Reza Taleb (Shahid Beheshti U
niversity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nTh
e Coates-Sinnott Conjecture was formulated in 1974 as a K-theory analogue
of Stickelberger's Theorem. For a finite abelian extension $E/F$ of number
fields and any integer $n\\geq 2$\, this conjecture constructs an element
in terms 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 r
ing of integers $O_E$ over the group ring $\\mathbb{Z}[Gal(E/F)]$. In this
talk after describing the precise formulation of the conjecture we presen
t the recent results. Part of this is a joint work with Manfred Kolster.\
n\nMeeting ID: 908 611 6889 \,\nPasscode: Order of the symmetric group on
9 letters (Type the 6-digit number)\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shabnam Akhatri (University of Oregon)
DTSTART:20211109T140000Z
DTEND:20211109T160000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/4
DESCRIPTION:Title: Monogenic cubic rings and Thue equations\nby Shabnam Akhatri (U
niversity of Oregon) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAb
stract\nLet K be a cubic number field. We give an absolute upper bound for
the number of monogenic orders which have small index (compared to the di
scriminant of K) in the ring of integers of K. This is done by counting t
he number of integral solutions of some cubic Thue equations. This reducti
on to the resolution of Thue equations will also allow us to count the num
ber of monogenic orders with a fixed index in the ring of integers of K.\n
\nMeeting ID: 908 611 6889\, \nPasscode: The order of the symmetric group
on 9 elements (Type the 6-digit number)\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Mohammadi (IPM)
DTSTART:20211123T113000Z
DTEND:20211123T133000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/5
DESCRIPTION:Title: Bounds on point-conic incidences over finite fields and application
s\nby Ali Mohammadi (IPM) as part of FGC-HRI-IPM Number Theory Webinar
s\n\n\nAbstract\nI will begin with a brief overview of some well-known res
ults in incidence geometry and go on to discuss a recent joint work with T
hang Pham and Audie Warren\, in which we prove upper bounds on the number
of incidences between sets of points and conics over finite fields. I will
conclude the talk by considering applications to certain finite field var
iants of Erd\\H{o}s type problems on the number of distinct algebraic dist
ances formed by point sets\, including improvements to results of Koh and
Sun (2014) and Shparlinski (2006).\n\nMeeting ID: 908 611 6889\,\nPasscode
: The order of the symmetric group on 9 elements (Type the 6-digit number)
\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Dabrowski (University of Szczecin)
DTSTART:20211207T113000Z
DTEND:20211207T133000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/6
DESCRIPTION:Title: On a class of generalized Fermat equations of signature $(2\,2n\,3)
$\nby Andrzej Dabrowski (University of Szczecin) as part of FGC-HRI-IP
M Number Theory Webinars\n\n\nAbstract\nWe will discuss the generalized Fe
rmat equations\n$Ax^2 + By^{2n} = 4z^3$\, assuming (for simplicity) that\
nthe class number of the imaginary quadratic field\n$\\mathbb Q(\\sqrt{-AB
})$ is one. The methods use techniques\ncoming from Galois representations
and modular forms\; for\nsmall $n$'s one needs Chabauty type methods. Our
results\,\nconjectures (and methods) extend those given by Bruin\, Chen\n
et al. in the case $x^2 + y^{2n} = z^3$. This is a joint work\nwith K. Cha
łupka and G. Soydan.\n\nMeeting ID: 989 8485 8471\, \nPasscode: 039129\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Ghadermarzi (University of Tehran)
DTSTART:20211221T140000Z
DTEND:20211221T160000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/7
DESCRIPTION:Title: Integral points on Mordell curves of rank 1\nby Amir Ghadermarz
i (University of Tehran) as part of FGC-HRI-IPM Number Theory Webinars\n\n
\nAbstract\nA well-known theorem of Siegel states that any elliptic curve
$E/\\mathbb{Q}$ has only finitely many integral points. Lang conjectured t
hat the number of integral points on a quasi-minimal model of an elliptic
curve should be bounded solely in terms of the rank of the group of ration
al points. Silverman proved Lang's conjecture for the curves with at most
a fixed number of primes dividing the denominator of the $j$-invariant. Us
ing more explicit methods\, Silverman and Gross compute the dependence of
the bounds on the various constants. In the case of curves of rank 1\, tec
hniques of Ingram on multiples of integral points enable one to prove much
better bounds for special families of elliptic curves. In this talk\, we
investigate the integral points on Mordell curves of rank 1.\n\nMeeting ID
: 908 611 6889\, \nPasscode: the order of the symmetric group on 9 letters
(Type the 6-digit number).\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IITGandhinagar)
DTSTART:20210104T113000Z
DTEND:20210104T133000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/8
DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IITGandhinag
ar) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IIT Gandhinagar)
DTSTART:20210104T113000Z
DTEND:20210104T133000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/9
DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhina
gar) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IIT Gandhinagar)
DTSTART:20220104T113000Z
DTEND:20220104T133000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/10
DESCRIPTION:Title: Selberg’s Central Limit Theorem\nby Fatma Cicek (IIT Gandhin
agar) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nSelb
erg's central limit theorem is an influential probabilistic result in anal
ytic number theory which roughly states that the logarithm of the Riemann
zeta-function $\\zeta(s)$ on the half-line\, that is $\\Re s = \\fra
c12$\, has an approximate two-dimensional Gaussian distribution as $
\\Im s \\to \\infty$. We will carefully review the important ideas i
n the proof 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 a
pplications.\n\nMeeting ID: 922 2650 4686 \; Passcode: 645549\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristian David Gonzalez Aviles (Universidad de La Serena)
DTSTART:20220201T130000Z
DTEND:20220201T150000Z
DTSTAMP:20260404T094308Z
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 Web
inars\n\n\nAbstract\nI will define the groups of the title and discuss som
e examples.\nWhen they are of positive dimension\, these groups exist only
\nover an imperfect field. We will see examples in dimension 1 related to
the\npurely inseparable forms of the additive group\nstudied by Russell in
1970. We will also see some examples of arbitrarily\nhigh dimensions. I h
ope to convince the audience that this class of\nalgebraic groups is both
interesting and quite large!\n\nMeeting ID: 908 611 6889\,\n\nPasscode: Th
e order of the symmetric group over nine letters (Please type the 6-digit
number).\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20200315T130000Z
DTEND:20200315T150000Z
DTSTAMP:20260404T094308Z
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://stable.researchseminars.org/talk/FGC-IPM/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20200315T130000Z
DTEND:20200315T150000Z
DTSTAMP:20260404T094308Z
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://stable.researchseminars.org/talk/FGC-IPM/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20200315T130000Z
DTEND:20200315T150000Z
DTSTAMP:20260404T094308Z
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://stable.researchseminars.org/talk/FGC-IPM/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20200315T130000Z
DTEND:20200315T150000Z
DTSTAMP:20260404T094308Z
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://stable.researchseminars.org/talk/FGC-IPM/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20200315T130000Z
DTEND:20200315T150000Z
DTSTAMP:20260404T094308Z
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://stable.researchseminars.org/talk/FGC-IPM/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Ozlem (Yeditepe University)
DTSTART:20220315T130000Z
DTEND:20220315T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/17
DESCRIPTION:Title: On the motivic Galois group of a number field\nby Semih Ozlem
(Yeditepe University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nA
bstract\nAim of this talk is to briefly introduce the motivic Galois group
and state a potential answer to Langlands' conjecture regarding the relat
ion of Langlands' group and motivic Galois group.\n\nMeeting ID: 908 611 6
889\;\nPasscode: the order of the symmetric group on 9 letters (please typ
e the 6-digit number)\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farzad Aryan (Göttingen University)
DTSTART:20220405T120000Z
DTEND:20220405T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/18
DESCRIPTION:Title: On the Riemann Zeta Function\nby Farzad Aryan (Göttingen Univ
ersity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI wil
l discuss the Riemann zeta function and the significance of its zeros to p
rime numbers. Also\, I will look at the distribution of zeta zeros and men
tion some of my related works on the subject.\n\nJoin Zoom Meeting\nhttps:
//us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMe
eting ID: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chirantan Chowdhury (University of Duisburg-Essen)
DTSTART:20220419T120000Z
DTEND:20220419T130000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/19
DESCRIPTION:Title: Motivic Homotopy Theory of Algebraic Stacks\nby Chirantan Chow
dhury (University of Duisburg-Essen) as part of FGC-HRI-IPM Number Theory
Webinars\n\nAbstract: TBA\n\nZoom link:\nhttps://us06web.zoom.us/j/8721214
6791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPa
sscode: 362880\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamza Yesilyurt (Bilkent University)
DTSTART:20220517T120000Z
DTEND:20220517T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/20
DESCRIPTION:Title: A Modular Equation of Degree 61\nby Hamza Yesilyurt (Bilkent U
niversity) 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
functions with arguments $q$ and $q^n$. The theory of modular equations s
tarted with the works of Landen\, Jacobi and Legendre. The theory gained p
opularity again with enormous contributions made by Ramanujan. In this tal
k we will give a brief introduction to the theory of modular equations and
then obtain a new modular equation of degree $61$ by using a generalizat
ion of a theta function identity due to David M. Bressoud. This is a join
t work with Ahmet Güloğlu.\n\nJoin Zoom Meeting:\nhttps://us06web.zoom.u
s/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT09\n\nMeeting ID: 872 12
14 6791\nPasscode: 362880\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Somnath Jha (IIT Kanpur)
DTSTART:20220531T120000Z
DTEND:20220531T130000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/21
DESCRIPTION:Title: Fine Selmer group of elliptic curves over global fields\nby So
mnath Jha (IIT Kanpur) as part of FGC-HRI-IPM Number Theory Webinars\n\n\n
Abstract\nThe (p-infinity) fine Selmer group (also called the 0-Selmer gro
up) of an elliptic curve is a subgroup of the usual p-infinity Selmer grou
p of an elliptic curve and is related to the first and the second Iwasawa
cohomology groups. Coates-Sujatha observed that the structure of the fine
Selmer group over the cyclotomic Z_p extension of a number field K is intr
icately related to Iwasawa's \\mu-invariant vanishing conjecture on the gr
owth of p-part of the ideal class group of K in the cyclotomic tower. In t
his talk\, we will discuss the structure and properties of the fine Selmer
group over certain p-adic Lie extensions of global fields. This talk is b
ased on joint work with Sohan Ghosh and Sudhanshu Shekhar.\n\nZoom link:\
nhttps://us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0NERWNLbklEV2NqUT0
9\n\nMeeting ID: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Maarefparvar (Institute for Research in Fundamental Sciences
(IPM))
DTSTART:20220614T120000Z
DTEND:20220614T130000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/22
DESCRIPTION:Title: On BRZ exact sequence for finite Galois extensions of number field
s\nby Abbas Maarefparvar (Institute for Research in Fundamental Scienc
es (IPM)) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn
this talk\, I will shortly explain how to use some cohomological results o
f Brumer-Rosen and Zantema to obtain a four-term exact sequence\, called `
`BRZ’’ standing for these authors\, which reveals some information ab
out strongly 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 num
ber fields\, I will introduce the notion of ``relative Ostrowski quotient'
' and give some new approaches of the BRZ exact sequence. The main part
of my talk is concerning a joint work with Ali Rajaei and Ehsan Shahoseini
.\n\nZoom link:\nhttps://us06web.zoom.us/j/87212146791?pwd=d0pmbVZJanpDV0N
ERWNLbklEV2NqUT09\n\nMeeting ID: 872 1214 6791\nPasscode: 362880\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammad Sadek
DTSTART:20221024T130000Z
DTEND:20221024T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/23
DESCRIPTION:Title: How often do polynomials hit squares?\nby Mohammad Sadek as pa
rt of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGiven a polynomial
with rational coefficients\, one may investigate the possible values that
may be attained by these polynomials over the set of rational numbers. Fo
r centuries\, number theorists have been giving due attention to square ra
tional values assumed by rational polynomials. It turns out that seeking a
n answer to this question connects number theory and geometry. Answering t
his question for a polynomial in one variable will lead us to study the ar
ithmetic of certain algebraic curves. We will spend some time explaining t
he geometry beneath the question when the degree of the polynomial is at l
east 3. For polynomials in more than one variable\, the geometric structur
e is remote. In the latter case\, we will present some of the old and rece
nt developments in the theory shedding some light on some classical Diopha
ntine questions.\n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeet
ing ID: 856 1386 0958\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haydar Goral
DTSTART:20221107T130000Z
DTEND:20221107T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/24
DESCRIPTION:Title: Lehmer’s conjecture via model theory\nby Haydar Goral as par
t of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this talk\, we f
irst introduce the height function and the Mahler measure on the field of
algebraic numbers. We state and give a survey on Lehmer’s conjecture for
the Mahler measure\, which is still an open problem. Then\, we consider t
he field of algebraic numbers with elements of small Mahler measures in te
rms of model theory\, and we link this theory with Lehmer’s conjecture.
Our approach is based on Van der Waerden's theorem from additive combinat
orics.\n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID: 85
6 1386 0958\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Akbary
DTSTART:20221121T130000Z
DTEND:20221121T140000Z
DTSTAMP:20260404T094308Z
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
introduction on the value-distribution of arithmetic functions and L-func
tions\, we give an overview of our joint work with Alia Hamieh (University
of Northern British Colombia) on the value-distribution of logarithmic de
rivative of certain automorphic L-functions. Among other things\, we descr
ibe an upper bound for the discrepancy of the distribution of the values (
at a point on the edge of the critical strip) of the twists of a fixed aut
omorphic L-function with quadratic Dirichlet characters. Our result can be
considered as an automorphic analogue of a result of Lamzouri\, Lester\,
and Radziwill for the logarithm of the Riemann zeta function. Our estimate
is conditional on certain expected bounds on the local parameters of L-fu
nctions which is known to be true for GL(1) and GL(2).\n\nZoom Meeting ID:
856 1386 0958\nPasscode: 513 992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enis Kaya
DTSTART:20221219T130000Z
DTEND:20221219T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/26
DESCRIPTION:Title: Computing Schneider p-adic heights on hyperelliptic Mumford curves
\nby Enis Kaya as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbst
ract\nThere are several definitions of p-adic height pairings on curves in
the literature\, and algorithms for computing them play a crucial role in
\, for example\, carrying out the quadratic Chabauty method\, which is a p
-adic method that attempts to determine rational points on curves of genus
at least two.\n\n \n\nThe $p$-adic height pairing constructed by Peter Sc
hneider in $1982$ is particularly important because the corresponding $p$-
adic regulator fits into $p$-adic versions of Birch and Swinnerton-Dyer co
njecture. In this talk\, we present an algorithm to compute the Schneider
$p$-adic height pairing on hyperelliptic Mumford curves. We illustrate thi
s algorithm with a numerical example computed in the computer algebra syst
em SageMath.\n\n \n\nThis talk is based on a joint work in progress with M
arc Masdeu\, J. Steffen Müller and Marius van der Put.\n\nZoom Meeting ID
: 856 1386 0958\nPasscode: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan (Koc University)
DTSTART:20221205T130000Z
DTEND:20221205T140000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/27
DESCRIPTION:Title: CANCELLED - On inverse theorems and conjectures in ergodic theory
and additive combinatorics\nby Asgar Jamneshan (Koc University) as par
t of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will provide a no
n-technical overview of some interactions between ergodic theory and addit
ive combinatorics. The focus will be on inverse theorems and conjectures f
or the Gowers uniformity norms for finite abelian groups in additive combi
natorics and their counterparts for the Host-Kra-Gowers uniformity seminor
ms for abelian measure-preserving systems in ergodic theory.\n\nUnfortunat
ely our speaker cannot make it today due to an emergency. We will reschedu
le his talk for another time. Sorry for the inconvenience.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen-Tsung Chen
DTSTART:20230116T130000Z
DTEND:20230116T140000Z
DTSTAMP:20260404T094308Z
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\nAbstract\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 Drinfe
ld modular forms has been successfully generalized to the arbitrary rank s
etting. In this talk\, we introduce an analogue of the Serre derivation ac
ting on the product of spaces of Drinfeld modular forms of rank r>1\, whic
h also generalizes the differential operator introduced by Gekeler in the
rank two case. This is joint work with Oğuz Gezmiş.\n\nZoom Meeting ID:
856 1386 0958\nPasscode: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilker Inam
DTSTART:20230315T140000Z
DTEND:20230315T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/30
DESCRIPTION:Title: Fast Computation of Half-Integral Weight Modular Forms\nby Ilk
er Inam as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nModul
ar forms continue to attract attention for decades with many different app
lication areas. To study statistical properties of modular forms\, includi
ng for instance Sato-Tate like problems\, it is essential to be able to co
mpute a large number of Fourier coefficients. In this talk\, we will show
that this can be achieved in level 4 for a large range of half-integral we
ights by making use of one of three explicit bases\, the elements of which
can be calculated via fast power series operations.\nThis is joint work w
ith Gabor Wiese (Luxembourg).\n\nZoom Meeting ID: 856 1386 0958 Passcode:
513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alia Hamieh
DTSTART:20230405T140000Z
DTEND:20230405T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/32
DESCRIPTION:Title: Moments of $L$-functions and Mean Values of Long Dirichlet Polynom
ials\nby Alia Hamieh as part of FGC-HRI-IPM Number Theory Webinars\n\n
\nAbstract\nEstablishing asymptotic formulae for moments of $L$-functions
is a central theme in analytic number theory. This topic is related to var
ious non-vanishing conjectures and the generalized Lindelöf Hypothesis. A
major breakthrough in analytic number theory occurred in 1998 when Keatin
g and Snaith established a conjectural formula for moments of the Riemann
zeta function using ideas from random matrix theory. The methods of Keatin
g and Snaith led to similar conjectures for moments of many families of $L
$-functions. These conjectures have become a driving force in this field w
hich has witnessed substantial progress in the last two decades. \nIn this
talk\, I will review the history of this subject and survey some recent r
esults. I will also discuss recent joint work with Nathan Ng on the mean v
alues of long Dirichlet polynomials which could be used to model moments o
f the zeta function.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asgar Jamneshan
DTSTART:20230419T140000Z
DTEND:20230419T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/33
DESCRIPTION:Title: On inverse theorems and conjectures in ergodic theory and additive
combinatorics\nby Asgar Jamneshan as part of FGC-HRI-IPM Number Theor
y Webinars\n\n\nAbstract\nI will provide a non-technical overview of some
interactions between ergodic theory and additive combinatorics. The focus
will be on inverse theorems and conjectures for the Gowers uniformity norm
s for finite abelian groups in additive combinatorics and their counterpar
ts for the Host-Kra-Gowers uniformity seminorms for abelian measure-preser
ving systems in ergodic theory.\n\nZoom Meeting ID: 856 1386 0958 Passcode
: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Gupta
DTSTART:20230503T140000Z
DTEND:20230503T150000Z
DTSTAMP:20260404T094308Z
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 the
ory\, we construct a reciprocity map that describes the unramified (resp.
tame) étale fundamental group as a pro-completion of a suitable idele cla
ss group (resp. tame idele class group) for smooth curves over finite fiel
ds. These results were extended to higher-dimensional smooth varieties ove
r finite fields by Kato-Saito (unramified case\, in 1986) and\nSchmidt-Spi
ess (tame 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 f
ields. The class field theory over local fields is not as nice as that ove
r finite fields. We discuss results in the unramified class field theory o
ver local fields achieved in the period 1981--2015 by various mathematicia
ns (Bloch\, Saito\, Jennsen\, Forre\, etc.). We then move to the main topi
c of the talk which is the tame class field theory over local fields and p
rove that the results in the tame case are similar to that in the case of
unramified 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
: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiana Bertolin
DTSTART:20230517T140000Z
DTEND:20230517T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/35
DESCRIPTION:Title: Periods of 1-motives and their polynomials relations\nby Crist
iana Bertolin as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\
nThe integration of differential forms furnishes an isomorphism between th
e De Rham and the Hodge realizations of a 1-motive M. The coefficients of
the matrix representing this isomorphism are the so-called "periods" of M.
\n In the semi-elliptic case (i.e. the underlying extension of the 1-motiv
e is an extension of an elliptic curve by the multiplicative group)\, we c
ompute explicitly these periods. \n \nIf the 1-motive M is defined over an
algebraically closed field\, Grothendieck's conjecture asserts that the t
ranscendence degree of the field generated by the periods is equal to the
dimension of the motivic Galois group of M. If we denote by I the ideal ge
nerated by the polynomial relations between the periods\, we have that "th
e numbers of periods of M minus the rank of the ideal I is equal to the di
mension of the motivic Galois group of M"\, that is a decrease in the dime
nsion of the motivic Galois group is equivalent to an increase of the rank
of the ideal I. We list the geometrical phenomena which imply the decreas
e in the dimension of the motivic Galois group and in each case we compute
the polynomials which generate the corresponding ideal I.\n\nZoom Meeting
ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Pagano
DTSTART:20230531T140000Z
DTEND:20230531T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/36
DESCRIPTION:Title: Abelian arboreal representations\nby Carlo Pagano as part of F
GC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nI will present joint work
with Andrea Ferraguti which makes progress on a Conjecture of Andrews and
Petsche that classifies abelian dynamical Galois groups over number field
s\, in the unicritical case. I will explain how to reduce the conjecture t
o the post-critically finite case and the key tools to handle all unicriti
cal PCF with periodic critical orbit over any number field and all PCF ove
r quadratic number fields. Along the way I will present an earlier rigidit
y result of ours on the maximal closed subgroup of the automorphism group
of a binary rooted tree\, which offered us with the main input to translat
e the commutativity of the Galois image into diophantine equations. I will
also overview progress on the tightly related problem of lower bounding a
rboreal degrees.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Lukina (Leiden University)
DTSTART:20230614T140000Z
DTEND:20230614T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/37
DESCRIPTION:Title: Weyl groups in Cantor dynamics\nby Olga Lukina (Leiden Univers
ity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nArboreal
representations of absolute Galois groups of number fields are given by p
rofinite groups of automorphisms of regular rooted trees\, with the geomet
ry of the tree determined by a polynomial which defines such a representat
ion. Thus arboreal representations give rise to dynamical systems on a Can
tor set\, and allow to apply the methods of topological dynamics to study
problems in number theory. In this talk we consider the conjecture of Bost
on and Jones\, which states that the images of Frobenius elements under ar
boreal representations have a certain cycle structure. To study this conje
cture\, we borrow from the Lie group theory the concepts of maximal tori a
nd Weyl groups\, and introduce maximal tori and Weyl groups in the profini
te setting. We then use this new technique to give a partial answer to the
conjecture by Boston and Jones in the case when an arboreal representatio
ns is defined by a post-critically finite quadratic polynomial over a numb
er field. Based on a joint work with Maria Isabel Cortez.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berkay Kebeci (Koc University)
DTSTART:20231025T140000Z
DTEND:20231025T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/38
DESCRIPTION:Title: Mixed Tate Motives and Aomoto Polylogarithms\nby Berkay Kebeci
(Koc University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
act\nGrothendieck proposed the category of motives as a Tannakian category
\, offering a universal framework for Weil cohomology theories. In this ta
lk\, we will consider motives in the sense of Nori. One expects the Hopf a
lgebra R of mixed Tate motives to be isomorphic to the bi-algebra A of Aom
oto polylogarithms. Our aim is to reconstruct A using Nori motives. This a
llows us to write a morphism from A to R.\n\nEmail ozlemejderff at gmail.c
om for the passcode.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Sertöz (Leiden University)
DTSTART:20231206T140000Z
DTEND:20231206T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/39
DESCRIPTION:Title: (Cancelled!!!)Computing linear relations between univariate integr
als\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
\nAbstract\nThe study of integrals of univariate algebraic functions (1-pe
riods) provided the impetus to develop much of algebraic geometry and tran
scendental number theory. This old saga is now at a point of resolution. I
n 2022\, Huber and Wüstholz gave a "qualitative description" of all linea
r relations with algebraic coefficients between 1-periods. New techniques
for determining symmetries of complex tori allow us to develop algorithms
to explicate these qualitative relations and decide the transcendence of 1
-periods. This is a work-in-progress with Joël Ouaknine (MPI SWS) and Jam
es Worrell (Oxford).\n\nThe talk is cancelled.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Türkü Özlüm Çelik (Koc University)
DTSTART:20231011T140000Z
DTEND:20231011T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/40
DESCRIPTION:Title: Algebraic Curves from Polygons\nby Türkü Özlüm Çelik (Koc
University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\n
We study constructing an algebraic curve from a Riemann surface given via
a translation surface\, which is a collection of finitely many polygons in
the plane with sides identified by translation. We use the theory of disc
rete Riemann surfaces to give an algorithm for approximating the Jacobian
variety of a translation surface whose polygon can be decomposed into squa
res. We first implement the algorithm in the case of L-shaped polygons whe
re 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 anal
ytic side of the transcendental divide between Riemann surfaces and algebr
aic curves. Using Riemann theta functions\, we give numerical experiments
and resulting conjectures up to genus 5.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (Utrecht University)
DTSTART:20231122T140000Z
DTEND:20231122T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/41
DESCRIPTION:Title: Counting points on stacks and elliptic curves with a rational N-i
sogeny\nby Soumya Sankar (Utrecht University) as part of FGC-HRI-IPM N
umber Theory Webinars\n\n\nAbstract\nThe classical problem of counting ell
iptic curves with a rational N-isogeny can be phrased in terms of counting
rational points on certain moduli stacks of elliptic curves. Counting poi
nts on stacks\, while posing various challenges\, has also opened up sever
al new avenues of exploration in the last few years. In this talk\, I will
give an introduction to modular curves from the stacky perspective\, disc
uss some notions of height on them\, and use some of these notions to answ
er the counting question mentioned above. Time permitting\, I will talk ab
out this in the context of the stacky version of the Batyrev-Manin conject
ure. The talk assumes no prior knowledge of stacks and is based on joint w
ork with Brandon Boggess.\n\npassword is eight four eight zero eight four\
n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farzad Aryan
DTSTART:20231108T140000Z
DTEND:20231108T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/42
DESCRIPTION:Title: Cancellations in Character Sums and the Vinogradov Conjecture\
nby Farzad Aryan as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstra
ct\nIn this talk\, we will explore conjectures related to cancellations in
character sums.\nAdditionally\, we will examine the potential impact on t
he distribution of zeros of Dirichlet L-functions if these conjectures pro
ve to be false.\n\nplease send an email to ozlemejderff at gmail.com for t
he passcode.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamed Mousavi (King's College London)
DTSTART:20240306T140000Z
DTEND:20240306T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/43
DESCRIPTION:Title: POINTWISE ERGODIC THEOREM ALONG PRIMES\nby Hamed Mousavi (King
's College London) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbst
ract\nIn this talk\, we will be exploring the pointwise convergence of erg
odic averages along\nthe primes. Our discussion will begin by explaining t
he contributions of Birkhoff\, as\nwell as the efforts made by Bourgain an
d Wierdl in this direction\, which was concluded\nby Mirek’s proof of po
intwise ergodic convergence for primes. Additionally\, we will be\npresent
ing some of our own results on structure theorems in the endpoint case Lpl
ogq\,\nalong with a pointwise ergodic theorem in the Gaussian setting. Mov
ing forward\, we will\nbriefly mention the breakthrough result made by Kra
use-Mirek-Tao on bilinear ergodic\naverages. This will be departing point
in our current project on the pointwise ergodic\ntheorem for bilinear aver
ages along prime numbers. If time allows\, we will provide a toy\nmodel ex
ample in linear theory\, which will demonstrate a typical method used in t
his\narea of study.\n\npassword is 848084.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Myerson (University of Warwick)
DTSTART:20240207T140000Z
DTEND:20240207T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/44
DESCRIPTION:Title: A two dimensional delta method and applications to quadratic forms
\nby Simon Myerson (University of Warwick) as part of FGC-HRI-IPM Numb
er Theory Webinars\n\n\nAbstract\nWe develop a two dimensional version of
the delta symbol method and apply it to establish quantitative Hasse princ
iple for a smooth pair of quadrics defined over Q in at least 10 variables
. This is a joint work with Pankaj Vishe (Durham) and Junxian Li (Bonn).\n
\npassword: 848084\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Sertoz (Leiden University)
DTSTART:20240320T140000Z
DTEND:20240320T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/45
DESCRIPTION:Title: Computing linear relations between univariate integrals\nby Em
re Sertoz (Leiden University) as part of FGC-HRI-IPM Number Theory Webinar
s\n\n\nAbstract\nThe study of integrals of univariate algebraic functions
(1-periods) provided the impetus to develop much of algebraic geometry and
transcendental number theory. This old saga is now at a point of resoluti
on. In 2022\, Huber and Wüstholz gave a "qualitative description" of all
linear relations with algebraic coefficients between 1-periods. New techni
ques for determining symmetries of complex tori allow us to develop algori
thms to explicate these qualitative relations and decide the transcendence
of 1-periods. This is a work-in-progress with Joël Ouaknine (MPI SWS) an
d James Worrell (Oxford).\n\npassword is 848084\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Firtina Kucuk (University College\, Dublin)
DTSTART:20240403T140000Z
DTEND:20240403T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/46
DESCRIPTION:Title: Factorization of algebraic p-adic Rankin-Selberg L-functions\n
by Firtina Kucuk (University College\, Dublin) as part of FGC-HRI-IPM Numb
er Theory Webinars\n\n\nAbstract\nI will give a brief review of Artin form
alism and its p-adic variant. Artin formalism gives a factorization of L-f
unctions whenever the associated Galois representation decomposes. I will
explain why establishing the p-adic Artin formalism (or its algebraic coun
terpart via the Iwasawa Main Conjectures) is a non-trivial problem when th
ere are no critical L-values. In particular\, I will focus on the case whe
re the Galois representation arises from a self-Rankin-Selberg product of
a newform\, and present the results in this direction including the one I
obtained in my PhD thesis.\n\npassword is 848084\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haydar Goral (Izmir Institute of Technology)
DTSTART:20240221T140000Z
DTEND:20240221T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/47
DESCRIPTION:Title: Counting arithmetic progressions modulo p\nby Haydar Goral (Iz
mir Institute of Technology) as part of FGC-HRI-IPM Number Theory Webinars
\n\n\nAbstract\nIn 1975\, Szemeredi gave an affirmative answer to Erdös a
nd Turan's conjecture which states that any subset of positive integers wi
th a positive upper density contains arbitrarily long arithmetic progressi
ons. Szemeredi-type problems have also been extensively studied in subsets
of finite fields. While much work has been done on the problem of whether
subsets of finite fields contain arithmetic progressions\, in this talk w
e concentrate on how many arithmetic progressions we have in certain subse
ts of finite fields. The technique is based on certain types of Weil estim
ates. We obtain an asymptotic for the number of k-term arithmetic progress
ions in squares with a better error term. Moreover our error term is sharp
and best possible when k is small\, owing to the Sato-Tate conjecture. Th
is work is supported by the Scientific and Technological Research Council
of Turkey with the project number 122F027.\n\npassword is 848084\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmed El-Guindy (Cairo University)
DTSTART:20241024T133000Z
DTEND:20241024T143000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/48
DESCRIPTION:Title: Some l-adic properties of modular forms with quadratic nebentypus
and l-regular partition congruences\nby Ahmed El-Guindy (Cairo Univers
ity) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn this
talk\, we discuss a framework for studying l-regular partitions by definin
g a sequence of\nmodular forms of level l and quadratic character which en
code the l-adic behavior of the so-called l-regular\npartitions. We show t
hat this sequence is congruent modulo increasing powers of l to level 1 mo
dular forms of\nincreasing weights. We then prove that certain modules gen
erated by our sequence are isomorphic to certain\nsubspaces of level 1 cus
p forms of weight independent of the power of l\, leading to a uniform bou
nd on the\nranks of those modules and consequently to l-adic relations bet
ween l-regular partition values. This\ngeneralizes earlier work of Folsom\
, Kent and Ono on the partition function\, where the relevant forms had no
\nnebentypus\, and is joint work with Mostafa Ghazy.\n\npassword is 848084
\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erman Isik (The Univ. of Ottowa)
DTSTART:20241106T133000Z
DTEND:20241106T143000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/49
DESCRIPTION:Title: The growth of Tate-Shafarevich groups of p-supersingular elliptic
curves over anticyclotomic Zp- extensions at inert primes\nby Erman Is
ik (The Univ. of Ottowa) as part of FGC-HRI-IPM Number Theory Webinars\n\n
\nAbstract\nIn this talk\, we will discuss the asymptotic growth of both t
he Mordell-Weil ranks and the Tate–Shafarevich groups for an elliptic cu
rve E defined over the rational numbers\, focusing on its behaviour along
the anticyclotomic Zp-extension of an imaginary quadratic K. Here\, p is a
prime at which E has good supersingular reduction and is inert in K. We w
ill review the definitions and properties of the plus and minus Selmer gro
ups from Iwasawa theory and discuss how these groups can be used to derive
arithmetic information about the elliptic curve.\n\nhttps://kocun.zoom.us
/j/99715471656\npassword is 848084\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amina Abdurrahman (IHES)
DTSTART:20241120T133000Z
DTEND:20241120T143000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/50
DESCRIPTION:Title: A formula for symplectic L-functions and Reidemeister torsion\
nby Amina Abdurrahman (IHES) as part of FGC-HRI-IPM Number Theory Webinars
\n\n\nAbstract\nWe give a global cohomological formula for the central val
ue of the L-function of a symplectic representation on a curve up to squar
es. The proof relies crucially on a similar formula for the Reidemeister t
orsion of 3-manifolds together with a symplectic local system. We sketch b
oth analogous arithmetic and topological pictures. This is based on joint
work with A. Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Ferraguti (Università di Torino)
DTSTART:20241204T140000Z
DTEND:20241204T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/51
DESCRIPTION:Title: Frobenius and settled elements in iterated Galois extensions\n
by Andrea Ferraguti (Università di Torino) as part of FGC-HRI-IPM Number
Theory Webinars\n\n\nAbstract\nUnderstanding Frobenius elements in iterate
d Galois extensions is a major goal in arithmetic dynamics. In 2012 Boston
and Jones conjectured that any quadratic polynomial f over a finite field
that is different from x^2 is settled\, namely the weighted proportion of
f-stable factors in the factorization of the n-th iterate of f tends to 1
as n tends to infinity. This can be rephrased in terms of Frobenius eleme
nts: given a quadratic polynomial f over a number field K\, an element \\a
lpha in K and the extension K_\\infty generated by all the f^n-preimages o
f \\alpha\, the Frobenius elements of unramified primes in K_\\infty are s
ettled. In this talk\, we will explain how to construct uncountably many n
on-conjugate settled elements that cannot be the Frobenius of any ramified
or unramified prime\, for any quadratic polynomial. The key result is a d
escription of the critical orbit modulo squares for quadratic polynomials
over local fields. This is joint work with Carlo Pagano.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomos Parry (Bilkent University)
DTSTART:20241218T140000Z
DTEND:20241218T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/52
DESCRIPTION:Title: Primes in arithmetic progressions on average\nby Tomos Parry (
Bilkent University) as part of FGC-HRI-IPM Number Theory Webinars\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ahmet Guloglu (Bilkent University)
DTSTART:20250129T140000Z
DTEND:20250129T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/53
DESCRIPTION:Title: Non-vanishing of L-functions at the central point.\nby Ahmet G
uloglu (Bilkent University) as part of FGC-HRI-IPM Number Theory Webinars\
n\n\nAbstract\nI will talk about two methods used to derive non-vanishing
results for a family of L-functions\; the one-level density and the moment
s of L-functions. I will mention what these methods are and how they are u
sed to get non-vanishing.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ratko Darda (Sabanci University)
DTSTART:20250212T140000Z
DTEND:20250212T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/54
DESCRIPTION:Title: Malle conjecture for finite group schemes\nby Ratko Darda (Sab
anci University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstra
ct\nThe Inverse Galois Problem asks whether every finite group G is the Ga
lois group of a Galois extension of the field of rational numbers Q. The M
alle conjecture offers a quantitative perspective: it predicts the number
of Galois extensions of Q (or any other number field)\, with G as the Galo
is group\, of bounded "size" (such as the discriminant). In this talk\, w
e explore a generalization of the conjecture to finite étale group scheme
s. We show how the generalization helps explain inconsistencies of the Mal
le conjecture found by Klüners. Additionally\, we discuss the case of the
conjecture when G is a commutative finite étale group scheme\, which gen
eralizes the classical work of Wright on the number of abelian extensions
of bounded discriminant. The talk is based on a joint work with Takehiko Y
asuda.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keerthi Madapusi (Boston College)
DTSTART:20250226T140000Z
DTEND:20250226T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/55
DESCRIPTION:Title: A new approach to p-Hecke correspondences and Rapoport-Zink spaces
\nby Keerthi Madapusi (Boston College) as part of FGC-HRI-IPM Number T
heory Webinars\n\n\nAbstract\nWe will present a new notion of isogeny betw
een ‘p-divisible groups with additional structure’ that employs the co
homological stacks of Drinfeld and Bhatt-Lurie—-in particular the theory
of apertures developed in prior work with Gardner—-and combines it with
some invariant theoretic tools familiar to the geometric Langlands and re
presentation theory community\, namely the Vinberg monoid and the wonderfu
l compactification. This gives a uniform construction of p-Hecke correspon
deces and Rapoport-Zink spaces associated with unramified local Shimura da
ta. In particular\, we give the first general construction of RZ spaces as
sociated with exceptional groups. This work is joint with Si Ying Lee.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Bartling
DTSTART:20250507T140000Z
DTEND:20250507T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/56
DESCRIPTION:Title: Rapoport-Zink spaces and close p-adic fields.\nby Sebastian Ba
rtling as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nRapopo
rt-Zink spaces are moduli spaces of p-divisible groups\n(with extra struct
ure). These are p-adic analogues of integral models of\nShimura varieties.
Their function field versions were introduced by\nHartl-Viehmann. I want
to explain a construction approximating\nHartl-Viehmann spaces via Rapopor
t-Zink spaces using the philosophy of\nclose p-adic fields. If time permit
s I want to sketch how one may use\nthis construction to deduce the Arithm
etic Fundamental Lemma in the\nfunction field case. This is joint work\, p
artly in progress\, with\nAndreas Mihatsch.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirti Joshi (University of Arizona)
DTSTART:20251009T160000Z
DTEND:20251009T170000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/57
DESCRIPTION:Title: Deformations of arithmetic of number fields and the abc-conjecture
\nby Kirti Joshi (University of Arizona) as part of FGC-HRI-IPM Number
Theory Webinars\n\n\nAbstract\nIn this lecture I will provide an accessib
le overview of my\nrecent work on deformation of arithmetic of number fiel
ds (as\nsuggested by Shinichi Mochizuki) and its relationship to the\nabc-
conjecture following Mochizuki's strategy for its proof.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ferruh Özbudak (Sabanci University)
DTSTART:20251022T140000Z
DTEND:20251022T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/58
DESCRIPTION:Title: Some Results on Covering Radius of Codes\nby Ferruh Özbudak (
Sabanci University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbs
tract\nThe covering radius is an important parameter in coding theory. In
this talk\,\nwe present several results concerning the covering radius of
various classes of codes\,\nobtained using techniques involving algebraic
curves over finite fields. Connections to algebra\, number theory\,\nand g
eometry will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anette Huber-Klawitter (University of Freiburg)
DTSTART:20251105T140000Z
DTEND:20251105T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/59
DESCRIPTION:Title: Motives and transcendence\nby Anette Huber-Klawitter (Universi
ty of Freiburg) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstrac
t\nPeriods are complex numbers defined by integrating algebraic differenti
al forms over paths (on algebraic varieties) with algebraic end points. Th
e set contains many interesting numbers like \nlog(2) or π that have been
studied intensely in transcendence theorem. By the linear version of the
Period Conjecture (a theorem of Wüstholz and myself in this case)\, all r
elations between them are described in terms of 1-motives. In this exposit
ory talk\, we will explain this result and give a couple of examples.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ertan Elma (Mathematics Research Center-Azerbaijan State Oil and I
ndustry University)
DTSTART:20251119T150000Z
DTEND:20251119T160000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/60
DESCRIPTION:Title: Number of prime factors with a given multiplicity\nby Ertan El
ma (Mathematics Research Center-Azerbaijan State Oil and Industry Universi
ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nFor natur
al numbers $k\, n \\ge 1$\, let $\\omega_k(n)$ be the number of prime fact
ors of $n$ with multiplicity $k$. The functions $\\omega_k(n)$ with $k \\g
e 1$ are refined versions of the well-known function $\\omega(n)$ counting
the number of distinct prime factors of $n$ without any conditions on the
multiplicities. In this talk\, we will cover several elementary\, analyti
c and probabilistic results about the functions $\\omega_k(n)$ with $k \\g
e 1$ and their function field analogues in polynomial rings with coefficie
nts from a finite field. In particular\, we will see that the function $\\
omega_1(n)$ and its function field analogue satisfy the Erd\\H{o}s--Kac Th
eorem. The results we will see in this talk are based on joint works with
Yu-Ru Liu\, with Sourabhashis Das\, Wentang Kuo and Yu-Ru Liu\, and with G
reg Martin.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Borger
DTSTART:20251203T090000Z
DTEND:20251203T095000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/61
DESCRIPTION:Title: Scheme Theory over Semirings\nby James Borger as part of FGC-H
RI-IPM Number Theory Webinars\n\n\nAbstract\nUsual scheme theory can be vi
ewed as the syntactic theory of\npolynomial equations with coefficients in
a ring\, most importantly the\nring of integers. But none of its most fun
damental ingredients\, such\nas\nfaithfully flat descent\, require subtrac
tion. So we can set up a\nscheme theory over semirings (``rings but possib
ly without additive\ninverses’’\, such as the non-negative integers or
reals)\, thus\nbringing positivity in to the foundations of scheme theory
. It is then\nreasonable to view non-negativity as integrality at the infi
nite\nplace\, the Boolean semiring as the residue field there\, and the no
n-negative\nreals as the completion.\n\n In this talk\, I'll discuss some
recent developments in module theory\n over semirings. While the classical
definitions of ``vector bundle''\n are\nnot all equivalent over semirings
\, the classical definitions of ``line\nbundle'' are all equivalent\, whic
h allows us to define Picard groups\nand\nPicard stacks. The narrow class
group of a number field can be\nrecovered\nas the reflexive class group of
the semiring of its totally\n nonnegative\nintegers\, i.e. the arithmetic
compactification of the spectrum of the\nring of integers. This gives a s
cheme-theoretic definition of the\nnarrow\nclass group\, as was done for t
he ordinary class group a long time ago.\n\nThis is based mostly on arXiv:
2405.18645\, which is joint work with\n Jaiung Jun\, and also on forthcomi
ng paper with Johan de Jong and Ivan\nZelich.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lejla Smajlovic
DTSTART:20251217T140000Z
DTEND:20251217T150000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/62
DESCRIPTION:Title: On some nonholomorphic automorphic forms\, their inner products an
d generating functions\nby Lejla Smajlovic as part of FGC-HRI-IPM Numb
er Theory Webinars\n\n\nAbstract\nIn this talk we focus on the following t
hree automorphic forms on a Fuchsian group of the first kind with at least
one cusp: the Eisenstein series and the Niebur-Poincaré series associate
d to the cusp at infinity\, and the resolvent kernel/Green's function. We
discuss how those functions can be viewed as building blocks for describin
g log-norms of some meromorphic functions in terms of their divisors and d
erive a generalization of the Rorlich-Jensen type formula\, which is based
on an evaluation of the Petersson inner product of the Niebur-Poincaré s
eries with the suitably regularized Green's function. Then\, we turn our a
ttention to the generating functions of the Niebur-Poincaré series and it
s derivative at s=1. Both functions depend upon two variables in the upper
half-plane. We prove that\, for any Fuchsian group of the first kind\, th
e generating function of the Niebur-Poincaré series in each variable is a
polar harmonic Maass form of a certain weight\, describe its polar part a
nd discuss how it can be viewed as a building block for describing weight
two meromorphic modular forms in terms of their divisors. Moreover\, we pr
ove that the generating function of the derivative of the Niebur-Poincaré
series at s=1 can be expressed\, up to a certain function appearing in th
e Kronecker limit formula\, as a derivative of an automorphic kernel assoc
iated to a new point-pair invariant expressed in terms of the Rogers dilog
arithm.\n\nThe talk is based on the joint work with Kathrin Bringmann\, Ja
mes Cogdell and Jay Jorgenson.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kübra Benli (Bogazici University)
DTSTART:20260114T160000Z
DTEND:20260114T170000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/63
DESCRIPTION:Title: Sums of proper divisors with missing digits\nby Kübra Benli (
Bogazici University) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAb
stract\nLet $s(n)$ denote the sum of proper divisors of a positive integer
$n$. In 1992\, Erd\\H{o}s\, Granville\, Pomerance\, and Spiro conjectured
that if $\\mathcal{A}$ is a set of integers with asymptotic density zero
then the preimage set $s^{-1}(\\mathcal{A})$ also has asymptotic density z
ero. In this talk\, we will discuss the verification of this conjecture wh
en $\\mathcal{A}$ is the set of integers with missing digits (also known
as ellipsephic integers) by giving a quantitative estimate on the size of
the set $s^{-1}(\\mathcal{A})$. This talk is based on the joint work with
Giulia Cesana\, C\\'{e}cile Dartyge\, Charlotte Dombrowsky\, Paul Pollack
and Lola Thompson.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Lochak
DTSTART:20260128T160000Z
DTEND:20260128T170000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/64
DESCRIPTION:Title: A historical introduction to Grothendieck-Teichmüller theory\
nby Pierre Lochak as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
act\nStarting with the statement of Belyi's theorem\, I will explain\nhow
Grothendieck-Teichmüller theory was born\, then move\nto a (necessarily i
ncomplete) exposition of its main tenets\,\nthe already existing results a
nd the main conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg German
DTSTART:20260211T190000Z
DTEND:20260211T195000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/65
DESCRIPTION:Title: On the transference principle in Diophantine approximation\nby
Oleg German as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\n
In 1842\, Dirichlet published his famous theorem which became\nthe foundat
ion of Diophantine approximation. The phenomenon he found\ninspired Liouvi
lle to study how well algebraic numbers can be\napproximated by rationals\
, and thus\, to come up with a method of\nconstructing transcendental numb
ers explicitly. The development of these\nideas led to the concepts of irr
ationality measure and transcendence\nmeasure. Thanks to Minkowski\, it be
came clear that many problems arising\nin the theory of Diophantine approx
imation could be addressed quite\neffectively using the tools of geometry
of numbers. In particular\, the\ngeometric approach naturally offers a wid
e variety of multidimensional\nanalogues of the concept of irrationality m
easure — so called\nDiophantine exponents. In the talk\, we will discuss
various Diophantine\nexponents and the geometry that arises when studying
them. We will pay\nspecial attention to the phenomenon discovered by Khin
tchine\, which he\ncalled the transference principle.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özge Ülkem (Academia Sinica\, Taipei)
DTSTART:20260225T100000Z
DTEND:20260225T110000Z
DTSTAMP:20260404T094308Z
UID:FGC-IPM/66
DESCRIPTION:Title: Drinfeld's Elliptic Sheaves and Generalizations\nby Özge Ülk
em (Academia Sinica\, Taipei) as part of FGC-HRI-IPM Number Theory Webinar
s\n\n\nAbstract\nIn this talk\, we will explore the area of function field
\narithmetic\, with a focus on Drinfeld's elliptic sheaves and their\ngene
ralizations\, as well as analogies to the number field setting.\nDrinfeld
modules\, introduced in 1974 as analogues of elliptic curves in\nthe funct
ion field setting\, play a central role in this context. To\nestablish a L
anglands correspondence\, Drinfeld studied moduli spaces of\nelliptic shea
ves\, or equivalently\, shtukas. After a brief introduction\nto the functi
on field framework\, we will examine some well-known\ngeneralizations of e
lliptic sheaves\, concentrating on generalized\nD-elliptic sheaves and pre
senting results on their moduli spaces. In the\nfinal part of the talk\, w
e will explore the connections between\n(generalized) shtukas and (general
ized) elliptic sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/FGC-IPM/66/
END:VEVENT
END:VCALENDAR