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BEGIN:VEVENT
SUMMARY:Alexander Ivanov (Ruhr-Universität Bochum)
DTSTART:20240923T200000Z
DTEND:20240923T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/1
DESCRIPTION:Title: p-a
dic Deligne--Lusztig spaces\nby Alexander Ivanov (Ruhr-Universität Bo
chum) as part of Boston University Number Theory Seminar\n\nLecture held i
n CDS Room 365 in Boston University.\n\nAbstract\nI explain how to carry o
ver some definitions and results from classical Deligne--Luzstig theory (f
or reductive groups over finite fields) to a setup over p-adic fields. Mor
e precisely\, I discuss p-adic Deligne--Lusztig spaces\, defined as certai
n arc-sheaves on perfect algebras over the residue field\, as well as some
of their geometric properties. In some cases\, one can determine the coho
mology of these spaces\, and use it to construct smooth representations of
p-adic reductive groups geometrically.\n
LOCATION:https://researchseminars.org/talk/NTBU/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerson Caro (Boston University)
DTSTART:20240909T200000Z
DTEND:20240909T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/2
DESCRIPTION:Title: Dio
phantine properties for the special values of Dedekind zeta functions\
nby Jerson Caro (Boston University) as part of Boston University Number Th
eory Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nAbst
ract\nAccording to Nothcott's theorem\, any set of algebraic numbers of bo
unded height and bounded degree is finite. Analogous finiteness properties
are also satisfied by many other heights\, such as the Faltings height. G
iven the many conjectural links between heights and special values of L-fu
nctions (with the BSD conjecture as the most remarkable example)\, it is n
atural to ask whether special values of L-functions satisfy a similar Nort
hcott property. In this talk\, we will outline joint work in progress with
Fabien Pazuki and Riccardo Pengo that shows the Northcott property does n
ot hold for the Dedekind zeta function at 1/2.\n
LOCATION:https://researchseminars.org/talk/NTBU/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Bertoloni-Meli (Boston University)
DTSTART:20240916T200000Z
DTEND:20240916T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/3
DESCRIPTION:Title: The
categorical conjecture and cuspidal sheaves\nby Alexander Bertoloni-M
eli (Boston University) as part of Boston University Number Theory Seminar
\n\nLecture held in CDS Room 365 in Boston University.\n\nAbstract\nI will
discuss the categorical conjecture of Fargues and Scholze and describe wo
rk in progress with Teruhisa Koshikawa to explicate structures on the Galo
is side. In particular\, I will describe a category of cuspidal sheaves on
the stack of L-parameters and show how it explicates some classical pheno
mena.\n
LOCATION:https://researchseminars.org/talk/NTBU/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameera Vemulapalli (Harvard University)
DTSTART:20240930T200000Z
DTEND:20240930T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/4
DESCRIPTION:Title: Ste
initz classes of number fields and Tschirnhausen bundles of covers of the
projective line\nby Sameera Vemulapalli (Harvard University) as part o
f Boston University Number Theory Seminar\n\nLecture held in CDS Room 365
in Boston University.\n\nAbstract\nGiven a number field extension $L/K$ of
fixed degree\, one may consider $\\mathcal{O}_L$ as an $\\mathcal{O}_K$-m
odule. Which modules arise this way? Analogously\, in the geometric settin
g\, a cover of the complex projective line by a smooth curve yields a vect
or bundle on the projective line by pushforward of the structure sheaf\; w
hich bundles arise this way? In this talk\, I'll describe recent work with
Vakil in which we use tools in arithmetic statistics (in particular\, bin
ary forms) to completely answer the first question and make progress towar
ds the second.\n
LOCATION:https://researchseminars.org/talk/NTBU/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colby Brown (UC Davis)
DTSTART:20241007T200000Z
DTEND:20241007T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/5
DESCRIPTION:Title: An
almost linear time algorithm testing whether the Markoff graph modulo $p$
is connected\nby Colby Brown (UC Davis) as part of Boston University N
umber Theory Seminar\n\nLecture held in CDS Room 365 in Boston University.
\n\nAbstract\nThe Markoff graph modulo p is known to be connected for all
but finitely many primes p (see Eddy\, Fuchs\, Litman\, Martin\, Tripeny\,
and Vanyo [arXiv:2308.07579])\, and it is conjectured that these graphs a
re connected for all primes. In this talk\, we outline an algorithmic real
ization of the process introduced by Bourgain\, Gamburd\, and Sarnak [arXi
v:1607.01530] to test whether the Markoff graph modulo p is connected for
arbitrary primes. Our algorithm runs in o(p1+ϵ) time for every ϵ>0. Our
algorithm confirms that the Markoff graph modulo p is connected for all pr
imes less than one million.\n
LOCATION:https://researchseminars.org/talk/NTBU/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Benedetto (Amherst College)
DTSTART:20241021T200000Z
DTEND:20241021T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/6
DESCRIPTION:Title: Arb
oreal Galois groups with colliding critical points\nby Rob Benedetto (
Amherst College) as part of Boston University Number Theory Seminar\n\nLec
ture held in CDS Room 548 in Boston University (*NOT the usual room for th
e semester*).\n\nAbstract\nLet $f\\in K(z)$ be a rational function of degr
ee $d\\geq 2$ defined over a field $K$ (usually $\\mathbb{Q}$)\, and let $
x_0\\in K$. The backward orbit of $x_0$\, which is the union of the iterat
ed preimages $f^{-n}(x_0)$\, has the natural structure of a $d$-ary rooted
tree. Thus\, the Galois groups of the fields generated by roots of the eq
uations $f^n(z)=x_0$ are known as arboreal Galois groups. In 2013\, Pink o
bserved that when $d=2$ and the two critical points $c_1\,c_2$ of $f$ coll
ide\, meaning that $f^m(c_1)=f^m(c_2)$ for some $m\\geq 1$\, then the arbo
real Galois groups are strictly smaller than the full automorphism group o
f the tree. We study these arboreal Galois groups when $K$ is a number fie
ld and $f$ is either a quadratic rational function (as in Pink's setting o
ver function fields) or a cubic polynomial with colliding critical points.
We describe the maximum possible Galois groups in these cases\, and we pr
esent sufficient conditions for these maximum groups to be attained.\n\nJo
int BU Number Theory and Dynamics seminar. Note the non-standard room.\n
LOCATION:https://researchseminars.org/talk/NTBU/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Broe (Boston University)
DTSTART:20241028T200000Z
DTEND:20241028T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/7
DESCRIPTION:Title: The
Tate conjecture for a power of a CM elliptic curve\nby Matt Broe (Bos
ton University) as part of Boston University Number Theory Seminar\n\nLect
ure held in CDS Room 365 in Boston University.\n\nAbstract\nThe endomorphi
sms of an abelian variety $A$ over a field $k$ induce a natural decomposit
ion of the Chow motive of $A$. For $E$ an elliptic curve over $k$ with com
plex multiplication\, we explicitly describe the decomposition of the moti
ve of $E^g$. When $k$ is finitely generated\, we use the decomposition to
prove the full Tate conjecture for $E^g$. When $k$ is a global function fi
eld\, we formulate a version of the Beilinson-Bloch conjecture for varieti
es over $k$ and prove it in some special cases\, including for powers of a
n isotrivial elliptic curve with all its endomorphisms defined over $k$.\n
LOCATION:https://researchseminars.org/talk/NTBU/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cecilia Salgado (University of Groningen and IAS)
DTSTART:20241104T210000Z
DTEND:20241104T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/8
DESCRIPTION:Title: Mor
dell-Weil rank jumps on families of elliptic curves\nby Cecilia Salgad
o (University of Groningen and IAS) as part of Boston University Number Th
eory Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nAbst
ract\nWe will present some recent developments around the variation of the
Mordell-Weil rank in 1-dimensional families of elliptic curves\, by study
ing them in the guise of elliptic surfaces. We will revisit Néron-Shioda'
s construction of an infinite family of elliptic curves with rank at least
11 and discuss ways of generalizing it.\n
LOCATION:https://researchseminars.org/talk/NTBU/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheela Devadas
DTSTART:20241111T210000Z
DTEND:20241111T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/9
DESCRIPTION:Title: Hig
her-weight Jacobians for complex varieties of maximal Picard number\nb
y Sheela Devadas as part of Boston University Number Theory Seminar\n\nLec
ture held in CDS Room 365 in Boston University.\n\nAbstract\nThis talk is
about my work with Max Lieblich where we define and study Jacobians of Hod
ge structures with weight greater than 1. Jacobians of weight 2 or "2-Jaco
bians" naturally come up in the context of the Brauer group and the Tate c
onjecture\, and were previously studied in a special case by Beauville in
his work on surfaces of maximal Picard number. I will explain how we compu
te higher-weight Jacobians (as complex tori) for certain special classes o
f complex varieties\, namely abelian varieties of maximal Picard rank or s
ingular K3 surfaces. Surprisingly\, these $m$-Jacobians are algebraic for
all values of $m$.\n
LOCATION:https://researchseminars.org/talk/NTBU/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linli Shi (University of Connecticut)
DTSTART:20241118T210000Z
DTEND:20241118T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/10
DESCRIPTION:Title: On
higher regulators of Picard modular surfaces\nby Linli Shi (Universit
y of Connecticut) as part of Boston University Number Theory Seminar\n\nLe
cture held in CDS Room 365 in Boston University.\n\nAbstract\nThe Birch an
d Swinnerton-Dyer conjecture relates the leading coefficient of the L-func
tion of an elliptic curve at its central critical point to global arithmet
ic invariants of the elliptic curve. Beilinson’s conjectures generalize
the BSD conjecture to formulas for values of motivic L-functions at non-cr
itical points. In this talk\, I will relate motivic cohomology classes\, w
ith non-trivial coefficients\, of Picard modular surfaces to a non-critica
l value of the motivic L-function of certain automorphic representations o
f the group GU(2\,1).\n
LOCATION:https://researchseminars.org/talk/NTBU/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linus Hamann (Harvard University)
DTSTART:20241125T210000Z
DTEND:20241125T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/11
DESCRIPTION:Title: Sh
imura Varieties and Eigensheaves\nby Linus Hamann (Harvard University)
as part of Boston University Number Theory Seminar\n\nLecture held in CDS
Room 365 in Boston University.\n\nAbstract\nThe cohomology of Shimura var
ieties is a fundamental object of study in algebraic number theory by virt
ue of the fact that it is the only known geometric realization of the glob
al Langlands correspondence over number fields. Usually\, the cohomology i
s computed through very delicate techniques involving the trace formula. H
owever\, this perspective has several limitations\, especially with regard
s to questions concerning torsion. In this talk\, we will discuss a new p
aradigm for computing the cohomology of Shimura varieties by decomposing c
ertain sheaves coming from Igusa varieties into Hecke eigensheaves on the
moduli stack of G-bundles on the Fargues-Fontaine curve. Using this point
of view\, we will describe several conjectures on the torsion cohomology o
f Shimura varieties after localizing at suitably “generic” L-parameter
s\, as well as some known results in the case that the parameter factors t
hrough a maximal torus. Motivated by this\, we will sketch part of an emer
ging picture for describing the cohomology beyond this generic locus by co
nsidering certain “generalized eigensheaves” whose eigenvalues are spr
ead out in multiple cohomological degrees based on the size of a certain A
rthur SL_{2} in a way that is reminiscent of Arthur’s cohomological conj
ectures on the intersection cohomology of Shimura Varieties. This is based
on joint work with Lee\, joint work in progress with Caraiani and Zhang\,
and conversations with Bertoloni-Meli and Koshikawa.\n
LOCATION:https://researchseminars.org/talk/NTBU/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20241202T210000Z
DTEND:20241202T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/12
DESCRIPTION:by TBA as part of Boston University Number Theory Seminar\n\nL
ecture held in CDS Room 365 in Boston University.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NTBU/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Daniels (Skidmore College)
DTSTART:20241209T210000Z
DTEND:20241209T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/13
DESCRIPTION:Title: Ig
usa Stacks and the Cohomology of Shimura Varieties\nby Patrick Daniels
(Skidmore College) as part of Boston University Number Theory Seminar\n\n
Lecture held in CDS Room 365 in Boston University.\n\nAbstract\nScholze ha
s conjectured that there should exist an “Igusa stack” which interpola
tes between the various Igusa varieties associated with a given Shimura va
riety. In this talk\, we will motivate the Igusa stack conjecture and repo
rt on recent progress on the conjecture in the Hodge-type case. If time pe
rmits\, we will discuss some of the (many) consequences of the conjecture
for the study of the cohomology of Shimura varieties. Everything we will d
iscuss is from joint work with Pol van Hoften\, Dongryul Kim\, and Mingjia
Zhang.\n
LOCATION:https://researchseminars.org/talk/NTBU/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnaud Eteve (MPIM)
DTSTART:20250324T200000Z
DTEND:20250324T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/15
DESCRIPTION:Title: Sp
ectral action on isocrystals\nby Arnaud Eteve (MPIM) as part of Boston
University Number Theory Seminar\n\nLecture held in CDS Room 365 in Bosto
n University.\n\nAbstract\nThis is joint work in progress with Dennis Gait
sgory\, Alain Genestier and Vincent Lafforgue. Let $G$ be a reductive grou
p over a local function field $F$. In their seminal work\, Fargues and Sch
olze proposed a geometrization of the local Langlands correspondance for t
he pair $(G\,F)$ by constructing a 'spectral action' on the category of $\
\ell$-adic sheaves on $\\mathrm{Bun}_G$\, the stack of $G$-torsors on the
Fargues-Fontaine curve. The goal of this talk is to explain the constructi
on of a different spectral action on the category of sheaves on the stack
of $G$-isocrystals which should offer another geometrization of the local
Langlands correspondance. Our construction has the benefit of being natura
lly compatible with the announced work of Hemo and Zhu and should also be
equipped with a strong form of local-global compatibility.\n
LOCATION:https://researchseminars.org/talk/NTBU/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerson Caro (Boston University)
DTSTART:20250127T210000Z
DTEND:20250127T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/16
DESCRIPTION:Title: Ra
tional points: Curves and beyond\nby Jerson Caro (Boston University) a
s part of Boston University Number Theory Seminar\n\nLecture held in CDS R
oom 365 in Boston University.\n\nAbstract\nIn 1985\, Coleman\, building on
Chabauty's work from 1941\, established an upper bound for the number of
rational points of curves satisfying certain conditions. In this talk\, I
will present the first generalization of this method to higher dimensions\
, specifically to the case of surfaces. This is joint work with Hector Pas
ten. Furthermore\, I will discuss recent work with Jennifer Balakrishnan\,
in which we provide explicit examples of surfaces that demonstrate the ef
fectiveness of the method developed by H. Pasten and me. Specifically\, we
show that there are surfaces for which the obtained bound is sharp.\n\nFi
nally\, I will present joint work with Natalia García-Fritz\, where we pr
ove that a certain family of surfaces has a uniformly bounded number of ra
tional points. In other words\, the same upper bound applies to all surfac
es in the family.\n
LOCATION:https://researchseminars.org/talk/NTBU/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nina Zubrilina (MIT)
DTSTART:20250203T210000Z
DTEND:20250203T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/17
DESCRIPTION:Title: Ro
ot Number Correlation Bias of Fourier Coefficients of Modular Forms\nb
y Nina Zubrilina (MIT) as part of Boston University Number Theory Seminar\
n\nLecture held in CDS Room 365 in Boston University.\n\nAbstract\nIn a re
cent study\, He\, Lee\, Oliver\, and Pozdnyakov observed a striking oscill
ating pattern in the average value of the P-th Frobenius trace of elliptic
curves of prescribed rank and conductor in an interval range. Sutherland
discovered that this bias extends to Dirichlet coefficients of a much broa
der class of arithmetic L-functions when split by rootnumber.\n In my talk
\, I will discuss this root numbercorrelation in families of holomorphic a
nd Maass forms.\n
LOCATION:https://researchseminars.org/talk/NTBU/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20250210T210000Z
DTEND:20250210T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/18
DESCRIPTION:by TBA as part of Boston University Number Theory Seminar\n\nL
ecture held in CDS Room 365 in Boston University.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NTBU/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Candace Bethea (Brown University)
DTSTART:20250224T210000Z
DTEND:20250224T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/19
DESCRIPTION:Title: Co
unting rational curves equivariantly\nby Candace Bethea (Brown Univers
ity) as part of Boston University Number Theory Seminar\n\nLecture held in
CDS Room 365 in Boston University.\n\nAbstract\nThis talk will be a frien
dly introduction to using topological invariants in enumerative geometry a
nd how one might use equivariant homotopy theory to answer enumerative que
stions under the presence of a finite group action. Recent work with Kirst
en Wickelgren (Duke) defines a global and local degree in stable equivaria
nt homotopy theory that can be used to compute the equivariant Euler chara
cteristic and Euler number. I will discuss an application to counting orbi
ts of rational plane cubics through an invariant set of 8 points in genera
l position under a finite group action on $\\mathbb{C}\\mathbb{P}^2$\, val
ued in the representation ring and Burnside ring. This recovers a signed c
ount of real rational cubics when $\\mathbb{Z}/2$ acts on $\\mathbb{C}\\ma
thbb{P}^2$ by complex conjugation.\n
LOCATION:https://researchseminars.org/talk/NTBU/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rahul Dalal (University of Vienna)
DTSTART:20250303T210000Z
DTEND:20250303T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/20
DESCRIPTION:Title: Au
tomorphic Representations and Quantum Logic Gates\nby Rahul Dalal (Uni
versity of Vienna) as part of Boston University Number Theory Seminar\n\nL
ecture held in CDS Room 365 in Boston University.\n\nAbstract\nAny constru
ction of a quantum computer requires finding a good set of universal quant
um logic gates: abstractly\, a finite set of matrices in U(2^n) such that
short products of them can efficiently approximate arbitrary unitary trans
formations. The 2-qubit case n=2 is of particular practical interest. I wi
ll present the first construction of an optimal\, so-called "golden" set o
f 2-qubit gates. \n\nThe modern theory of automorphic representations on u
nitary groups---in particular\, the endoscopic classification and higher-r
ank versions of the Ramanujan bound---will play a crucial role in proving
the necessary analytic estimates.\n
LOCATION:https://researchseminars.org/talk/NTBU/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eran Assaf (MIT)
DTSTART:20250331T200000Z
DTEND:20250331T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/22
DESCRIPTION:Title: Or
thogonal modular forms from definite quaternary lattices\nby Eran Assa
f (MIT) as part of Boston University Number Theory Seminar\n\nLecture held
in CDS Room 365 in Boston University.\n\nAbstract\nIn this talk I will ma
ke precise the fact that definite quaternary orthogonal modular forms are
Hilbert modular forms. By taking the algebraic approach and using the Clif
ford functor\, we can avoid analytic difficulties in the theta lifts\, and
give a precise description of level and character on both sides of the tr
ansfer map. Building on advancements in our understanding of orders in qua
ternion algebras\, we are able to apply this result to a large class of la
ttices\, allowing for singularities of high codimension. \nThis is joint w
ork with Dan Fretwell\, Adam Logan\, Colin Ingalls\, Spencer Secord and Jo
hn Voight.\n
LOCATION:https://researchseminars.org/talk/NTBU/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Lin (Harvard University)
DTSTART:20250407T200000Z
DTEND:20250407T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/23
DESCRIPTION:Title: Sh
afarevich's conjecture for families of hypersurfaces over function fields<
/a>\nby Alice Lin (Harvard University) as part of Boston University Number
Theory Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nA
bstract\nShafarevich's conjecture suggests that over a fixed base scheme $
B$\, whether it is the $S$-integers of a number field or a quasiprojective
variety\, there should be only finitely many nonisotrivial families of pr
ojective varieties of a given type over $B$. For example\, in proving the
Mordell Conjecture\, Faltings proved that there are only finitely many fam
ilies of principally polarized abelian schemes of a given dimension over t
he $S$-integers of a number field. We prove a Shafarevich conjecture for H
odge-generic families of hypersurfaces for sufficiently large degree and d
imension over a complex quasiprojective base. The argument follows a "boun
dedness and rigidity" structure to show that the space of such families is
finite. For boundedness\, the key input is a new result of Bakker\, Brune
barbe\, and Tsimerman about the ampleness of the Griffiths line bundle for
quasifinite period mappings. For rigidity\, we use a Hodge-theoretic form
ulation due to Peters.\n\nThis is joint work with Philip Engel and Salim T
ayou.\n
LOCATION:https://researchseminars.org/talk/NTBU/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Dolgushev (Temple University)
DTSTART:20250414T200000Z
DTEND:20250414T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/24
DESCRIPTION:Title: Ex
ploration of Grothendieck-Teichmueller (GT) shadows\nby Vasily Dolgush
ev (Temple University) as part of Boston University Number Theory Seminar\
n\nLecture held in CDS Room 365 in Boston University.\n\nAbstract\nIn 1990
\, V. Drinfeld introduced the Grothendieck-Teichmueller group GT.\nThis my
sterious group receives a homomorphism from the absolute Galois group $G_Q
$\nof rational numbers\, and this homomorphism is injective due to Belyi's
theorem. \nGrothendieck-Teichmueller (GT) shadows may be thought of as ap
proximations \nof elements of the group GT. They are morphisms of a groupo
id whose objects are \ncertain finite index normal subgroups of the Artin
braid group. Exploration of the \ngroupoid of GT-shadows is motivated by v
ery hard open problems that include \nY. Ihara's question about the surjec
tivity of the homomorphism from $G_Q$ to GT.\nIn my talk\, I will introduc
e the groupoid of GT-shadows and describe \nits relation to the group GT.
I will also present promising results \nand formulate selected open proble
ms. My talk is loosely based on joint papers \nwith I. Bortnovskyi\, J.J.
Guynee\, B. Holikov and V. Pashkovskyi.\n
LOCATION:https://researchseminars.org/talk/NTBU/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Peng (MIT)
DTSTART:20250428T200000Z
DTEND:20250428T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/25
DESCRIPTION:Title: Fa
rgues-Scholze vs. classical parameters\, and applications\nby Hao Peng
(MIT) as part of Boston University Number Theory Seminar\n\nLecture held
in CDS Room 365 in Boston University.\n\nAbstract\nFor general reductive g
roups over a $p$-adic local field\, Fargues and Scholze constructed a (sem
i-simplified) local Langlands with many good properties. On the other hand
\, classical local Langlands correspondences are known for classical group
s via endoscopy theory and theta lifting. We review the construction of Fa
rgues-Scholze and related geometric objects\, and prove these two correspo
ndences are compatible for all unramified special orthogonal and unitary g
roups. As an application\, we prove torsion vanishing results for orthogon
al Shimura varieties\, generalizing results of Caraiani-Scholze\, Koshikaw
a\, Santos and Hamann-Lee\, etc.\n
LOCATION:https://researchseminars.org/talk/NTBU/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marius Leonhardt (Boston University)
DTSTART:20250908T200000Z
DTEND:20250908T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/26
DESCRIPTION:Title: Th
e affine Chabauty method\nby Marius Leonhardt (Boston University) as p
art of Boston University Number Theory Seminar\n\nLecture held in CDS Room
548 in Boston University.\n\nAbstract\nGiven a hyperbolic curve $Y$ defin
ed over the integers and a finite set of primes $S$\, the set of $S$-integ
ral points $Y(\\mathbb{Z}_S)$ is finite by theorems of Siegel\, Mahler\, a
nd Faltings. Determining this set in practice is a difficult problem for w
hich no general method is known. In this talk I report on joint work in pr
ogress with Martin Lüdtke in which we develop a Chabauty--Coleman method
for finding $S$-integral points on affine curves. We achieve this by bound
ing the image of $Y(\\mathbb{Z}_S)$ in the Mordell--Weil group of the gene
ralised Jacobian using arithmetic intersection theory on a regular model.\
n
LOCATION:https://researchseminars.org/talk/NTBU/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachi Hashimoto (Brown University)
DTSTART:20250915T200000Z
DTEND:20250915T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/27
DESCRIPTION:Title: Ra
tional points on $X_0(N)^∗$ when $N$ is non-squarefree\nby Sachi Has
himoto (Brown University) as part of Boston University Number Theory Semin
ar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstract\nThe
rational points of the modular curve $X_0(N)$ classify pairs $(E\,C_N)$ of
elliptic curves over $\\mathbb{Q}$ together with a rational cyclic subgro
up of order $N$. The curve $X_0(N)^∗$ is the quotient of $X_0(N)$ by the
full group of Atkin-Lehner involutions. Elkies showed that the rational p
oints on this curve classify elliptic curves over the algebraic closure of
$\\mathbb{Q}$ that are isogenous to their Galois conjugates\, and conject
ured that when $N$ is large enough\, the points are all CM or cuspidal. In
joint work with Timo Keller and Samuel Le Fourn\, we study the rational p
oints on the family $X_0(N)^∗$ for $N$ non-squarefree. In particular we
will report on some integrality results for the j-invariants of points on
$X_0(N)^∗$.\n
LOCATION:https://researchseminars.org/talk/NTBU/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jit Wu Yap (MIT)
DTSTART:20250922T200000Z
DTEND:20250922T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/28
DESCRIPTION:Title: On
Uniform Boundedness of Torsion Points for Abelian Varieties over Function
Fields\nby Jit Wu Yap (MIT) as part of Boston University Number Theor
y Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstrac
t\nLet $K$ be the function field of a smooth projective curve $B$ over the
complex numbers and let $g$ be a positive integer. The uniform boundednes
s conjecture predicts that there exists a constant $N$\, depending only on
$g$ and $K$\, such that for any $g$-dimensional abelian variety $A$ over
$K$\, any $K$-rational torsion point of $A$ must have order at most $N$. I
n this talk\, we will discuss some recent progress under the assumption th
at $A$ has semistable reduction over $K$. This is joint work with Nicole L
ooper.\n
LOCATION:https://researchseminars.org/talk/NTBU/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Rendell (King's College London)
DTSTART:20250929T200000Z
DTEND:20250929T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/29
DESCRIPTION:Title: Qu
adratic Chabauty for Atkin-Lehner quotients of modular curves via weakly h
olomorphic modular forms\nby Isabel Rendell (King's College London) as
part of Boston University Number Theory Seminar\n\nLecture held in CDS Ro
om 548 in Boston University.\n\nAbstract\nQuadratic Chabauty is a method t
o explicitly compute the rational points on certain modular curves of genu
s at least 2. The current algorithm\, due to Balakrishnan-Dogra-Müller-Tu
itman-Vonk\, requires as an input an explicit plane model of the curve. Th
e coefficients of such models grow rapidly with the genus of the curve and
so are inefficient to compute with when the genus is at least 7. Therefor
e\, we would like to replace this input with certain modular forms associa
ted to the curve\, hence creating a 'model-free' algorithm. In this talk I
will provide an overview of an algorithm to compute the first stage of qu
adratic Chabauty on Atkin-Lehner quotients of modular curves using weakly
holomorphic modular forms.\n
LOCATION:https://researchseminars.org/talk/NTBU/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jerson Caro (Boston University)
DTSTART:20251006T200000Z
DTEND:20251006T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/30
DESCRIPTION:Title: On
the Visibility category of elements in the Shafarevich-Tate group\nby
Jerson Caro (Boston University) as part of Boston University Number Theor
y Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstrac
t\nGiven an elliptic curve over Q and a nontrivial element sigma of its Sh
afarevich--Tate group Sha(E)\, we introduce the *Visualization category* o
f abelian varieties that ``visualize'' sigma\, in the sense of Cremona--Ma
zur\, and we study minimal objects in this category\, furnishing examples
of their nonuniqueness. In particular\, we show that there can be several
minimal visualizing abelian varieties of different dimensions\, answering
a question of Mazur. This is joint work with Barinder Banwait and Shiva Ch
idambaram.\n
LOCATION:https://researchseminars.org/talk/NTBU/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kate Finnerty (Boston University)
DTSTART:20251020T200000Z
DTEND:20251020T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/31
DESCRIPTION:Title: On
the possible adelic indices of certain families of elliptic curves\nb
y Kate Finnerty (Boston University) as part of Boston University Number Th
eory Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbst
ract\nA well-known theorem of Serre bounds the largest prime $\\ell$ for w
hich the mod $\\ell$ Galois representation of a non-CM elliptic curve $E/\
\mathbb{Q}$ is nonsurjective. Serre asked whether a universal bound on the
largest nonsurjective prime might exist. Significant partial progress has
been made toward this question. Lemos proved that it has an affirmative a
nswer for all $E$ admitting a rational cyclic isogeny. Zywina offered a mo
re ambitious conjecture about the possible adelic indices that can occur a
s $E$ varies. We will discuss an ongoing project (joint with Tyler Genao\,
Jacob Mayle\, and Rakvi) that extends Lemos's result to prove Zywina's co
njecture for certain families of elliptic curves.\n
LOCATION:https://researchseminars.org/talk/NTBU/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casimir Kothari (University of Chicago)
DTSTART:20251027T200000Z
DTEND:20251027T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/32
DESCRIPTION:Title: Di
eudonné theory for $n$-smooth group schemes\nby Casimir Kothari (Univ
ersity of Chicago) as part of Boston University Number Theory Seminar\n\nL
ecture held in CDS Room 548 in Boston University.\n\nAbstract\nDieudonné
theory is the study of families of group schemes via linear-algebraic data
. In this talk\, I will begin by recalling some motivation for Dieudonn
é theory\, with examples. Then I will explain some new classification a
nd smoothness results for certain close relatives of $p$-divisible groups
known as $n$-smooth groups\, which affirmatively answer conjectures of Dri
nfeld. This is joint work with Joshua Mundinger.\n
LOCATION:https://researchseminars.org/talk/NTBU/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Achter (Colorado State University)
DTSTART:20251103T210000Z
DTEND:20251103T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/33
DESCRIPTION:Title: Re
gular homomorphisms\, with a twist\nby Jeff Achter (Colorado State Uni
versity) as part of Boston University Number Theory Seminar\n\nLecture hel
d in CDS Room 548 in Boston University.\n\nAbstract\nLet $X$ be a smooth p
rojective variety over a field. If the field is $\\mathbb C$\, Griffiths
associates to $X$ an algebraic intermediate Jacobian $J$\, which is a comp
lex abelian variety which captures some information about pointed families
of algebraic cycles on $X$. More generally\, a regular homomorphism to a
n abelian variety accomplishes something similar for pointed families of a
lgebraic\ncycles on a variety over any perfect field.\n\nFor families of c
ycles which don't admit a point over the field of\ndefinition\, we obtain
instead a map to a torsor under that abelian\nvariety. I'll explain these
results and what they tell us about the\nrationality of certain threefold
s. (Joint work with Sebastian\nCasalaina-Martin and Charles Vial.)\n
LOCATION:https://researchseminars.org/talk/NTBU/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jialiang Zou (MIT)
DTSTART:20251110T210000Z
DTEND:20251110T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/34
DESCRIPTION:Title: Th
eta correspondence and Springer correspondence\nby Jialiang Zou (MIT)
as part of Boston University Number Theory Seminar\n\nLecture held in CDS
Room 365 in Boston University.\n\nAbstract\nLet V and W be an orthogonal a
nd a symplectic space\, respectively. The action of G=O(V)\\times Sp(W) on
V\\otimes W provides an example of G-hyperspherical varieties introduced
by D. Ben-Zvi\, Y. Sakellaridis\, and A. Venkatesh (BZSV for short). It is
the classical limit of theta correspondence from the perspective of quant
ization.. I will explain a geometric construction motivated by theta corre
spondence over finite fields\, which describes how principal series repres
entations behave under theta correspondence using Springer correspondence.
\n\nBZSV proposed a relative Langlands duality linking certain G-hypersph
erical varieties M with their dual G^\\vee-hyperspherical varieties M^\\ve
e. A remarkable instance of this duality is that the hyperspherical variet
y underlying theta correspondence is dual to the hyperspherical variety u
nderlying the branching problem in the Gan-Gross-Prasad conjecture. I will
discuss how these results fit into the broader framework of this relative
Langlands duality. This is an ongoing joint work with Jiajun Ma\, Congli
ng Qiu\, and Zhiwei Yun.\n
LOCATION:https://researchseminars.org/talk/NTBU/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ananth Shankar (Northwestern University)
DTSTART:20251117T210000Z
DTEND:20251117T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/35
DESCRIPTION:Title: $p
$-adic hyperbolicity for Shimura varieties and period images\nby Anant
h Shankar (Northwestern University) as part of Boston University Number Th
eory Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbst
ract\nBorel proved that every holomorphic map from a product of punctured
unit discs to a complex Shimura variety extends to a map from a product of
discs to its Bailey-Borel compactification. In joint work with Oswal\, Zh
u\, and Patel\, we proved a p-adic version of this theorem over discretely
valued fields for Shimura varieties of abelian type. I will speak about w
ork with Bakker\, Oswal\, and Yao\, where we prove the analogous $p$-adic
extension theorem for compact non-abelian Shimura varieties and geometric
period images for large primes $p$.\n
LOCATION:https://researchseminars.org/talk/NTBU/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Shi (MIT)
DTSTART:20251124T210000Z
DTEND:20251124T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/36
DESCRIPTION:Title: Li
fting $L$-polynomials of genus 2 curves\nby Jane Shi (MIT) as part of
Boston University Number Theory Seminar\n\nLecture held in CDS Room 548 in
Boston University.\n\nAbstract\nLet $C$ be a genus $2$ curve over $\\math
bb{Q}$. For each odd prime $p$\nof good reduction\, we denote the numerato
r \nof the zeta function of $C$ at $p$ by $L_p(T)$.\n\nHarvey and Sutherla
nd's \nimplementation of Harvey's average polynomial-time algorithm comput
es \n$L_p(T) \\bmod \\ p$ for all good primes $p\\leq B$ in $O(B\\log^{3+o
(1)}B)$ time\, which is \n$O(\\log^{4+o(1)} p)$ time on average per prime.
\nAlternatively\, their algorithm can do this for a single good prime \n$p
$ in $O(p^{1/2}\\log^{1+o(1)}p)$ time. While Harvey's algorithm \ncan also
be used to compute the full zeta function\, no practical implementation \
nof this step currently exists.\n\n\nIn this talk\, I will present an $O(\
\log^{2+o(1)}p)$ Las Vegas algorithm that \ntakes the $\\bmod \\ p$ output
of Harvey and Sutherland's implementation and \ncomputes the full zeta fu
nction. I will also show benchmark results \ndemonstrating substantial spe
edups compared to the fastest\nalgorithms currently available for computin
g the full zeta function of a genus $2$ curve.\n
LOCATION:https://researchseminars.org/talk/NTBU/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fangu Chen (UC Berkeley)
DTSTART:20251201T210000Z
DTEND:20251201T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/37
DESCRIPTION:Title: A
generalization of Elkies’ theorem on infinitely many supersingular prime
s\nby Fangu Chen (UC Berkeley) as part of Boston University Number The
ory Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstr
act\nIn 1987\, Elkies proved that every elliptic curve defined over $\\mat
hbb{Q}$ has infinitely many supersingular primes. In this talk\, I will pr
esent an extension of this result to certain abelian fourfolds in Mumford
’s families and more generally\, to some Kuga-Satake abelian varieties c
onstructed from K3-type Hodge structures with real multiplication. I will
review Elkies’ proof and explain how his strategy of intersecting with C
M cycles can be adapted to our setting. I will also discuss some of the te
chniques in our proof to study the local properties of the CM cycles.\n
LOCATION:https://researchseminars.org/talk/NTBU/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Obus (Baruch College)
DTSTART:20251208T210000Z
DTEND:20251208T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/38
DESCRIPTION:Title: Re
gular models of superelliptic curves via Mac Lane valuations\nby Andre
w Obus (Baruch College) as part of Boston University Number Theory Seminar
\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstract\nLet $X
\\rightarrow \\mathbb{P}^1$ be a $\\mathbb{Z}/n$-branched cover over a co
mplete discretely valued field $K$\, where $n$ does not divide the residue
characteristic of $K$. We explicitly construct the minimal regular norma
l crossings model of $X$ over the valuation ring of $K$. By “explicitly
”\, we mean that we construct a normal model of $\\mathbb{P}^1$ whose no
rmalization in $K(X)$ is the desired regular model. The normal model of $
\\mathbb{P}^1$ is fully encoded as a basket of finitely many discrete valu
ations on the rational function field $K(\\mathbb{P}^1)$\, each of which i
s given using Mac Lane’s 1936 notation involving finitely many polynomia
ls and rational numbers. This is joint work with Padmavathi Srinivasan.\n
LOCATION:https://researchseminars.org/talk/NTBU/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Besser (Ben Gurion University)
DTSTART:20260202T210000Z
DTEND:20260202T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/40
DESCRIPTION:Title: On
the Katz-Litt Theorem\nby Amnon Besser (Ben Gurion University) as par
t of Boston University Number Theory Seminar\n\nLecture held in CDS Room 5
48 in Boston University.\n\nAbstract\nThe Katz-Litt theorem gives an expli
cit recipe to describe Vologodsky integration on curves with semi-stable r
eduction in terms of Coleman integration on on the rigid analytic domains
reducing to the smooth components of the reduction. In work with Mueller a
nd Srinivasan we gave an alternative recipe\, more closely related to our
past work with Zerbes\, which was proved to follow from the Katz-Litt theo
rem by Katz. In this talk I will describe this alternative recipe and prov
e it directly. This new proof is significantly simpler than the original p
roof.\n
LOCATION:https://researchseminars.org/talk/NTBU/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine de Saint Germain (University of Hong Kong)
DTSTART:20260209T210000Z
DTEND:20260209T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/41
DESCRIPTION:Title: Mo
rdell-Schinzel surfaces and cluster algebras\nby Antoine de Saint Germ
ain (University of Hong Kong) as part of Boston University Number Theory S
eminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstract\n
The set of positive integer points of the celebrated Markov surface admits
the structure of a 3-regular tree. \n\nMy objective in this talk is to un
veil a similar phenomenon for Mordell-Schinzel surfaces\; namely that the
set of positive integer points of each such surface admits the structure o
f a 2-regular graph. The vertices of each graph naturally correspond to cl
usters in a suitable (generalised) cluster algebra. \n\nI will then explai
n how the structure theory of cluster algebras translates into a resolutio
n of the positive Mordell-Schinzel problem. \n\nThis is partly based on on
going joint work with Robin Zhang (MIT).\n
LOCATION:https://researchseminars.org/talk/NTBU/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Volkovich (Boston College)
DTSTART:20260223T210000Z
DTEND:20260223T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/42
DESCRIPTION:Title: A
Computational Perspective on Carmichael Numbers\nby Ilya Volkovich (Bo
ston College) as part of Boston University Number Theory Seminar\n\nLectur
e held in CDS Room 548 in Boston University.\n\nAbstract\nWe consider the
problem of deterministically factoring integers provided with oracle acces
s to important number-theoretic functions such as Euler's Totient function
- $\\Phi(\\cdot)$ and Carmichael's Lambda function - $\\Lambda(\\cdot)$.\
nWe focus on Carmichael numbers - also known as Fermat pseudoprimes. In pa
rticular\, we obtain the following results: \n\n1. Let $N$ be a `simple' C
armichael number with three prime factors (also known as simple $C_3$-numb
ers). Then\, given oracle access to $\\lambda(\\cdot)$\, we can completely
factor $N$ in deterministic polynomial time.\n\n2. There exists a determi
nistic polynomial-time algorithm that given oracle access to $\\Phi(\\cdot
)$\, completely factors simple $C_3$-numbers\, satisfying some `size' boun
ds. Although in this case our methods do not provide a theoretical guarant
ee for all such numbers due to the required size bounds\, we show experime
ntally that our algorithm can factor more than 99\\% of all simple $C_3$-n
umbers up to $10^{13}$.\n\n\nOur techniques extend the work of Morain\, Re
nault\, and Smith (Applicable\nAlgebra in Engineering\, Communication\, an
d Computation\, 2023)\, at the core of which sits the Coppersmith's method
that provides an efficient way to find bounded roots of a bivariate polyn
omial over the integers. We combine these techniques with a new upper boun
d on $\\gcd(N-1\, \\Phi(N))$ for $C_3$-numbers\, which could be of an inde
pendent interest.\n
LOCATION:https://researchseminars.org/talk/NTBU/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacksyn Bakeberg (Boston University)
DTSTART:20260302T210000Z
DTEND:20260302T220000Z
DTSTAMP:20260422T212746Z
UID:NTBU/43
DESCRIPTION:Title: Ex
cursion functions on $p$-adic $\\mathrm{SL}_2$\nby Jacksyn Bakeberg (B
oston University) as part of Boston University Number Theory Seminar\n\nLe
cture held in CDS Room 548 in Boston University.\n\nAbstract\nThe Bernstei
n center of a $p$-adic group is a commutative ring of certain distribution
s on the group\, and it interacts closely with the group’s representatio
n theory. Fargues and Scholze provide an abstract construction of a class
of elements of the Bernstein center called excursion operators\, which enc
ode a candidate for the (semisimplified) local Langlands correspondence. I
n this talk\, I will present an approach to understanding excursion operat
ors concretely as distributions on the group\, with a special emphasis on
the case of $G = \\mathrm{SL}_2$ where everything can be made quite explic
it.\n
LOCATION:https://researchseminars.org/talk/NTBU/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (University of Utah)
DTSTART:20260316T200000Z
DTEND:20260316T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/44
DESCRIPTION:Title: Ne
w supercuspidal representations from the Weil representation in characteri
stic two\nby David Schwein (University of Utah) as part of Boston Univ
ersity Number Theory Seminar\n\nLecture held in CDS Room 548 in Boston Uni
versity.\n\nAbstract\nSupercuspidal representations are the mysterious "el
ementary particles" from which all other representations of a reductive p-
adic group are built. Residue characteristic two presents additional diffi
culties in the construction of these representations\, and even for classi
cal groups\, our knowledge is incomplete. In this talk\, based on joint wo
rk with Jessica Fintzen\, I'll explain how to overcome one of these diffic
ulties: the exceptional behavior of the Heisenberg group and Weil represen
tation in characteristic two. Time permitting\, I'll also explain how to o
vercome a second difficulty: disconnected Lie-algebra centralizers.\n
LOCATION:https://researchseminars.org/talk/NTBU/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiva Chidambaram (University of Wisconsin\, Madison)
DTSTART:20260323T200000Z
DTEND:20260323T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/45
DESCRIPTION:Title: Ab
elian threefolds with imaginary multiplication\, and elliptic curves attac
hed to them\nby Shiva Chidambaram (University of Wisconsin\, Madison)
as part of Boston University Number Theory Seminar\n\nLecture held in CDS
Room 548 in Boston University.\n\nAbstract\nIt is an interesting problem t
o construct algebraic curves whose Jacobians have extra endomorphisms. Whe
n genus is 3\, there are two natural families of Jacobians with imaginary
multiplication by $\\mathbb{Z}[i]$ and $\\mathbb{Z}[\\zeta_3]$\, coming fr
om curves with a $\\mu_4$ or $\\mu_6$ action. We will report on new hypere
lliptic families with imaginary multiplication by $\\mathbb{Z}[\\sqrt{-d}]
$ for $d=2\,3\,4$\, and some instances of extending to any odd genus g. Ga
lois representations allow one to naturally attach a CM elliptic curve to
any abelian threefold with imaginary multiplication of signature (2\,1). F
or the new families\, we will explicitly compute the attached CM elliptic
curve. An analogue of this association was used by Laga-Shnidman to get re
sults on vanishing of Ceresa cycles for Picard curves. Based on ongoing wo
rk with Francesc Fite and Pip Goodman.\n
LOCATION:https://researchseminars.org/talk/NTBU/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Youcis (University of Toronto)
DTSTART:20260330T200000Z
DTEND:20260330T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/46
DESCRIPTION:Title: A
new approach to canonical integral models of Shimura varieties\nby Ale
x Youcis (University of Toronto) as part of Boston University Number Theor
y Seminar\n\nLecture held in CDS Room 548 in Boston University.\n\nAbstrac
t\nSince Langlands's earliest paper on his now famous program\, canonical
integral models of Shimura varieties have occupied a central role in moder
n number theory. In this talk I will discuss how recent advances in integr
al $p$-adic Hodge theory allows one to make great progress in understandin
g these models: both in constructing new examples of such models\, and gre
atly explicating the structure of already-existing models. No prior knowle
dge of advanced $p$-adic Hodge theory or Shimura varieties will be assumed
\, but familiarity with elliptic curves/abelian varieties and $p$-divisibl
e groups will be very helpful.\n\nThis talk is based on joint works: one w
ith Keerthi Madapusi\, and the other with Naoki Imai and Hiroki Kato.\n
LOCATION:https://researchseminars.org/talk/NTBU/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Swaminathan (Harvard University)
DTSTART:20260406T200000Z
DTEND:20260406T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/47
DESCRIPTION:Title: Tw
ist hypercubes and the distribution of $2$-Selmer ranks of elliptic curves
\nby Ashvin Swaminathan (Harvard University) as part of Boston Univers
ity Number Theory Seminar\n\nLecture held in CDS Room 548 in Boston Univer
sity.\n\nAbstract\nThe Poonen–Rains heuristics conjecture an explicit di
stribution for the $2$-Selmer ranks of elliptic curves over $\\mathbb{Q}$.
Their conjecture predicts in particular that every nonnegative integer sh
ould occur as the $2$-Selmer rank of a positive proportion of curves. This
qualitative prediction has remained entirely open: prior to this work\, n
ot a single value of $r$ was known to occur with positive proportion. We p
rove this prediction for every $r$.\n\nOur method organizes quadratic twis
ts of elliptic curves into hypercubes whose $2$-Selmer ranks are tightly c
onstrained by Poitou–Tate duality. We classify all valid rank patterns b
y simple graphs and use this classification to obtain the first two-sided
bounds on rank densities in congruence families. In a complementary direct
ion\, we show that the $2$-Selmer rank evolves as a birth–death chain ac
ross the hypercube\, and prove that this chain converges to the Poonen–R
ains distribution. Analogous results hold for Jacobians of hyperelliptic c
urves of any genus.\n\nThis is joint work with Manjul Bhargava\, Wei Ho\,
Ari Shnidman\, and Alexander Smith.\n
LOCATION:https://researchseminars.org/talk/NTBU/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Zureick-Brown (Amherst College)
DTSTART:20260413T200000Z
DTEND:20260413T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/48
DESCRIPTION:Title: An
gle ranks of Abelian varieties\nby David Zureick-Brown (Amherst Colleg
e) as part of Boston University Number Theory Seminar\n\nLecture held in C
DS Room 548 in Boston University.\n\nAbstract\nI will discuss an elementar
y notion -- the rank of the multiplicative group generated by roots of a p
olynomial. For Weil polynomials one calls this the angle rank. I'll prese
nt new results about angle ranks and give some applications to the Tate co
njecture for Abelian varieties over finite fields and to arithmetic statis
tics.\n
LOCATION:https://researchseminars.org/talk/NTBU/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Vogt (Brown University)
DTSTART:20260427T200000Z
DTEND:20260427T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/49
DESCRIPTION:Title: Un
likely ramification of algebraic points on curves\nby Isabel Vogt (Bro
wn University) as part of Boston University Number Theory Seminar\n\nLectu
re held in CDS Room 365 in Boston University.\n\nAbstract\nA slogan of ari
thmetic geometry is that ''geometry controls arithmetic'': as the geometri
c complexity increases\, the arithmetic also becomes more complicated. In
this talk\, I will discuss results in this direction that show that there
are many number fields that cannot appear as the residue field of points
on a fixed curve of genus at least 2. This is joint work with Bianca Vira
y.\n
LOCATION:https://researchseminars.org/talk/NTBU/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Holiday: Indigenous People's Day
DTSTART:20251013T200000Z
DTEND:20251013T210000Z
DTSTAMP:20260422T212746Z
UID:NTBU/50
DESCRIPTION:by Holiday: Indigenous People's Day as part of Boston Universi
ty Number Theory Seminar\n\nLecture held in CDS Room 548 in Boston Univers
ity.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/NTBU/50/
END:VEVENT
END:VCALENDAR