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BEGIN:VEVENT
SUMMARY:Jacob Tsimerman (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200408T190000Z
DTEND;VALUE=DATE-TIME:20200408T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/1
DESCRIPTION:Title: Bounding torsion in class groups and families of local
systems\nby Jacob Tsimerman (University of Toronto) as part of Harvard num
ber theory seminar\n\n\nAbstract\n(joint w/ Arul Shankar) We discuss a new
method to bound 5-torsion in class groups of quadratic fields using the r
efined BSD conjecture for elliptic curves. The most natural “trivial”
bound on the n-torsion is to bound it by the size of the entire class grou
p\, for which one has a global class number formula. We explain how to mak
e sense of the n-torsion of a class group intrinsically as a selmer group
of a Galois module. We may then similarly bound its size by the Tate-Shafa
revich group of an appropriate elliptic curve\, which we can bound using t
he BSD conjecture. This fits into a general paradigm where one bounds selm
er groups of finite Galois modules by embedding into global objects\, and
using class number formulas. If time permits\, we explain how the function
field picture yields unconditional results and suggests further generaliz
ations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kriz (MIT)
DTSTART;VALUE=DATE-TIME:20200415T190000Z
DTEND;VALUE=DATE-TIME:20200415T201500Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/2
DESCRIPTION:Title: Converse theorems for supersingular CM elliptic curves\
nby Daniel Kriz (MIT) as part of Harvard number theory seminar\n\nAbstract
: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Weinstein (BU)
DTSTART;VALUE=DATE-TIME:20200422T190000Z
DTEND;VALUE=DATE-TIME:20200422T201500Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/3
DESCRIPTION:Title: Modularity for self-products of elliptic curves over fu
nction fields\nby Jared Weinstein (BU) as part of Harvard number theory se
minar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Newton (Kings College London)
DTSTART;VALUE=DATE-TIME:20200506T190000Z
DTEND;VALUE=DATE-TIME:20200506T201500Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/4
DESCRIPTION:Title: Symmetric power functoriality for modular forms\nby Jam
es Newton (Kings College London) as part of Harvard number theory seminar\
n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur-Cesar Le Bras (CNRS/Paris-13)
DTSTART;VALUE=DATE-TIME:20200513T190000Z
DTEND;VALUE=DATE-TIME:20200513T201500Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/5
DESCRIPTION:Title: Prismatic Dieudonne theory\nby Arthur-Cesar Le Bras (CN
RS/Paris-13) as part of Harvard number theory seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Preston Wake (Michigan State)
DTSTART;VALUE=DATE-TIME:20200520T190000Z
DTEND;VALUE=DATE-TIME:20200520T201500Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/6
DESCRIPTION:Title: Tame derivatives and the Eisenstein ideal\nby Preston W
ake (Michigan State) as part of Harvard number theory seminar\n\nAbstract:
TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (Stanford University)
DTSTART;VALUE=DATE-TIME:20201104T200000Z
DTEND;VALUE=DATE-TIME:20201104T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/7
DESCRIPTION:Title: A geometric approach to the Cohen-Lenstra heuristics\nb
y Aaron Landesman (Stanford University) as part of Harvard number theory s
eminar\n\nInteractive livestream: https://harvard.zoom.us/j/96767001802\nP
assword hint: The order of the permutation group on 9 elements\n\nAbstract
\nFor any positive integer $n$\,\nwe explain why the total number of order
$n$ elements\nin class groups of quadratic fields of discriminant\nhaving
absolute value at most $X$ is $O_n(X^{5/4})$.\n
URL:https://harvard.zoom.us/j/96767001802
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Koziol (University of Michigan)
DTSTART;VALUE=DATE-TIME:20201028T190000Z
DTEND;VALUE=DATE-TIME:20201028T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/8
DESCRIPTION:Title: Supersingular representations of $p$-adic reductive gro
ups\nby Karol Koziol (University of Michigan) as part of Harvard number th
eory seminar\n\n\nAbstract\nThe local Langlands conjectures predict that (
packets of) irreducible complex representations of $p$-adic reductive grou
ps (such as $\\mathrm{GL}_n(\\mathbb{Q}_p)$\, $\\mathrm{GSp}_{2n}(\\mathbb
{Q}_p)$\, etc.) should be parametrized by certain representations of the W
eil-Deligne group. A special role in this hypothetical correspondence is
held by the supercuspidal representations\, which generically are expecte
d to correspond to irreducible objects on the Galois side\, and which serv
e as building blocks for all irreducible representations. Motivated by r
ecent advances in the mod-$p$ local Langlands program (i.e.\, with mod-$p$
coefficients instead of complex coefficients)\, I will give an overview o
f what is known about supersingular representations of $p$-adic reductive
groups\, which are the "mod-$p$ coefficients" analogs of supercuspidal rep
resentations. This is joint work with Florian Herzig and Marie-France Vi
gneras.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arul Shankar (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201202T200000Z
DTEND;VALUE=DATE-TIME:20201202T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/9
DESCRIPTION:by Arul Shankar (University of Toronto) as part of Harvard num
ber theory seminar\n\nInteractive livestream: https://harvard.zoom.us/j/96
767001802\nPassword hint: The order of the permutation group on 9 elements
\nAbstract: TBA\n
URL:https://harvard.zoom.us/j/96767001802
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Marc Couveignes (University of Bordeaux)
DTSTART;VALUE=DATE-TIME:20201209T200000Z
DTEND;VALUE=DATE-TIME:20201209T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/10
DESCRIPTION:by Jean-Marc Couveignes (University of Bordeaux) as part of Ha
rvard number theory seminar\n\nInteractive livestream: https://harvard.zoo
m.us/j/96767001802\nPassword hint: The order of the permutation group on 9
elements\nAbstract: TBA\n
URL:https://harvard.zoom.us/j/96767001802
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Cass (Harvard University)
DTSTART;VALUE=DATE-TIME:20200909T190000Z
DTEND;VALUE=DATE-TIME:20200909T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/11
DESCRIPTION:Title: A mod p geometric Satake isomorphism\nby Robert Cass (H
arvard University) as part of Harvard number theory seminar\n\n\nAbstract\
nWe apply methods from geometric representation theory toward the mod p\nL
anglands program.\nMore specifically\, we explain a mod p version of the g
eometric Satake\nisomorphism\, which gives a sheaf-theoretic description o
f the spherical mod\np Hecke algebra. In our setup the mod p Satake catego
ry is not controlled\nby the dual group but rather a certain affine monoid
scheme. Along the way\nwe will discuss some new results about the F-singu
larities of affine\nSchubert varieties. Time permitting\, we will explain
how to geometrically\nconstruct central elements in the Iwahori mod p Heck
e algebra by adapting a\nmethod due to Gaitsgory.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zijian Yao (CNRS/Harvard)
DTSTART;VALUE=DATE-TIME:20201111T200000Z
DTEND;VALUE=DATE-TIME:20201111T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/12
DESCRIPTION:by Zijian Yao (CNRS/Harvard) as part of Harvard number theory
seminar\n\nInteractive livestream: https://harvard.zoom.us/j/96767001802\n
Password hint: The order of the permutation group on 9 elements\nAbstract:
TBA\n
URL:https://harvard.zoom.us/j/96767001802
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Mantovan (Caltech)
DTSTART;VALUE=DATE-TIME:20201021T190000Z
DTEND;VALUE=DATE-TIME:20201021T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/13
DESCRIPTION:Title: p-adic differential operators on automorphic forms\, an
d mod p Galois representations\nby Elena Mantovan (Caltech) as part of Har
vard number theory seminar\n\n\nAbstract\nIn this talk\, we will discuss a
geometric construction of p-adic analogues of Maass--Shimura differential
operators on automorphic forms on Shimura varieties of PEL type A or C (t
hat is\, unitary or symplectic)\, at p an unramified prime. Maass--Shimura
operators are smooth weight raising differential operators used in the st
udy of special values of L-functions\, and in the arithmetic setting for t
he construction of p-adic L-functions. In this talk\, we will focus in pa
rticular on the case of unitary groups of arbitrary signature\, when new p
henomena arise for p non split. We will also discuss an application to t
he study of modular mod p Galois representations. This talk is based on jo
int work with Ellen Eischen (in the unitary case for p non split)\, and wi
th Eischen\, Flanders\, Ghitza\, and Mc Andrew (in the other cases).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Si Ying Lee (Harvard University)
DTSTART;VALUE=DATE-TIME:20201118T200000Z
DTEND;VALUE=DATE-TIME:20201118T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/14
DESCRIPTION:by Si Ying Lee (Harvard University) as part of Harvard number
theory seminar\n\nInteractive livestream: https://harvard.zoom.us/j/967670
01802\nPassword hint: The order of the permutation group on 9 elements\nAb
stract: TBA\n
URL:https://harvard.zoom.us/j/96767001802
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Loeffler (University of Warwick)
DTSTART;VALUE=DATE-TIME:20201014T190000Z
DTEND;VALUE=DATE-TIME:20201014T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/15
DESCRIPTION:Title: The Bloch--Kato conjecture for GSp(4)\nby David Loeffle
r (University of Warwick) as part of Harvard number theory seminar\n\n\nAb
stract\nThe Bloch--Kato conjecture predicts that the dimension of the Selm
er group of a global Galois representation is equal to the order of vanish
ing of its L-function. In this talk\, I will focus on the 4-dimensional Ga
lois representations arising from cohomological automorphic representation
s of GSp(4) (i.e. from genus two Siegel modular forms). I will show that i
f the L-function is non-vanishing at some critical value\, then the corres
ponding Selmer group is zero\, under a long list of technical hypotheses.
The proof of this theorem relies on an Euler system\, a p-adic L-function\
, and a reciprocity law connecting those together. I will also survey work
in progress aiming to extend this result to some other classes of automor
phic representations.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiuya Wang (Duke University)
DTSTART;VALUE=DATE-TIME:20200930T190000Z
DTEND;VALUE=DATE-TIME:20200930T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/16
DESCRIPTION:Title: Pointwise Bound for $\\ell$-torsion of Class Groups\nby
Jiuya Wang (Duke University) as part of Harvard number theory seminar\n\n
\nAbstract\n$\\ell$-torsion conjecture states that $\\ell$-torsion of the
class group $|\\text{Cl}_K[\\ell]|$ for every number field $K$ is bounded
by $\\text{Disc}(K)^{\\epsilon}$. It follows from a classical result of Br
auer-Siegel\, or even earlier result of Minkowski that the class number $|
\\text{Cl}_K|$ of a number field $K$ are always bounded by $\\text{Disc}(K
)^{1/2+\\epsilon}$\, therefore we obtain a trivial bound $\\text{Disc}(K)^
{1/2+\\epsilon}$ on $|\\text{Cl}_K[\\ell]|$. We will talk about results on
this conjecture\, and recent works on breaking the trivial bound for $\\e
ll$-torsion of class groups in some cases based on a work of Ellenberg-Ven
katesh.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen (Cambridge/Duke/IAS)
DTSTART;VALUE=DATE-TIME:20200916T190000Z
DTEND;VALUE=DATE-TIME:20200916T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/17
DESCRIPTION:Title: Representations of p-adic groups and applications\nby J
essica Fintzen (Cambridge/Duke/IAS) as part of Harvard number theory semin
ar\n\n\nAbstract\nThe Langlands program is a far-reaching collection of co
njectures that relate different areas of mathematics including number theo
ry and representation theory. A fundamental problem on the representation
theory side of the Langlands program is the construction of all (irreducib
le\, smooth\, complex) representations of p-adic groups.\n\nI will provide
an overview of our understanding of the representations of p-adic groups\
, with an emphasis on recent progress.\n\nI will also outline how new resu
lts about the representation theory of p-adic groups can be used to obtain
congruences between arbitrary automorphic forms and automorphic forms whi
ch are supercuspidal at p\, which is joint work with Sug Woo Shin. This si
mplifies earlier constructions of attaching Galois representations to auto
morphic representations\, i.e. the global Langlands correspondence\, for g
eneral linear groups. Moreover\, our results apply to general p-adic group
s and have therefore the potential to become widely applicable beyond the
case of the general linear group.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (University of Turku)
DTSTART;VALUE=DATE-TIME:20200923T140000Z
DTEND;VALUE=DATE-TIME:20200923T150000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/18
DESCRIPTION:Title: Multiplicative functions in short intervals revisited\n
by Kaisa Matomäki (University of Turku) as part of Harvard number theory
seminar\n\n\nAbstract\nA few years ago Maksym Radziwill and I showed that
the average of a multiplicative function in almost all very short interval
s $[x\, x+h]$ is close to its average on a long interval $[x\, 2x]$. This
result has since been utilized in many applications.\nI will talk about re
cent work\, where Radziwill and I revisit the problem and generalise our r
esult to functions which vanish often as well as prove a power-saving uppe
r bound for the number of exceptional intervals (i.e. we show that there a
re $O(X/h^\\kappa)$ exceptional $x \\in [X\, 2X]$).\nWe apply this result
for instance to studying gaps between norm forms of an arbitrary number fi
eld.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziyang Gao (CNRS/IMJ-PRG)
DTSTART;VALUE=DATE-TIME:20201007T190000Z
DTEND;VALUE=DATE-TIME:20201007T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045710Z
UID:HarvardNT/19
DESCRIPTION:Title: Bounding the number of rational points on curves\nby Zi
yang Gao (CNRS/IMJ-PRG) as part of Harvard number theory seminar\n\n\nAbst
ract\nMazur conjectured\, after Faltings’s proof of the Mordell conjectu
re\, that the number of rational points on a curve of genus g at least 2 d
efined over a number field of degree d is bounded in terms of g\, d and th
e Mordell-Weil rank. In particular the height of the curve is not involved
. In this talk I will explain how to prove this conjecture and some genera
lizations. I will focus on how functional transcendence and unlikely inter
sections are applied in the proof. If time permits\, I will talk about how
the dependence on d can be furthermore removed if we moreover assume the
relative Bogomolov conjecture. This is joint work with Vesselin Dimitrov a
nd Philipp Habegger.\n
END:VEVENT
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