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BEGIN:VEVENT
SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200317T203000Z
DTEND;VALUE=DATE-TIME:20200317T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/1
DESCRIPTION:Title: An arithmetic holonomicity criterion and irrationality
of the 2-adic period $\\zeta_2(5)$\nby Vesselin Dimitrov (University of To
ronto) as part of MIT number theory seminar\n\n\nAbstract\nI will present
a new arithmetic criterion for a formal power\nseries to satisfy a linear
ODE on an affine curve over a global field.\nThis result characterizes the
holonomic functions by a sharp positivity\ncondition on a suitably define
d arithmetic degree for an adelic set where\na given formal power series i
s analytic. As an application\, based on\nCalegari's method with overconve
rgent p-adic modular forms\, we derive an\nirrationality proof of the Leop
oldt-Kubota 2-adic zeta value $\\zeta_2(5)$.\nThis is a joint work in prog
ress with Frank Calegari and Yunqing Tang.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicole Looper (Brown University)
DTSTART;VALUE=DATE-TIME:20200331T203000Z
DTEND;VALUE=DATE-TIME:20200331T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/2
DESCRIPTION:Title: Equidistribution techniques in arithmetic dynamics\nby
Nicole Looper (Brown University) as part of MIT number theory seminar\n\n\
nAbstract\nThis talk is about the arithmetic of points of small canonical
height\nrelative to dynamical systems over number fields\, particularly th
ose\naspects amenable to the use of equidistribution techniques. Past mile
stones\nin the subject include the proof of the Manin-Mumford Conjecture g
iven by\nSzpiro-Ullmo-Zhang\, and Baker-DeMarco's work on the finiteness o
f common\npreperiodic points of rational functions. Recently\, quantitativ
e\nequidistribution techniques have emerged both as a way of improving upo
n\nsome of these old results\, and as an avenue to studying previously\nin
accessible problems\, such as the Uniform Boundedness Conjecture of Morton
\nand Silverman. I will describe the key ideas behind these developments\,
and\nraise related questions for future research.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriya First (University of Haifa)
DTSTART;VALUE=DATE-TIME:20200428T203000Z
DTEND;VALUE=DATE-TIME:20200428T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/3
DESCRIPTION:Title: Generation of algebras and versality of torsors\nby Uri
ya First (University of Haifa) as part of MIT number theory seminar\n\n\nA
bstract\nThe primitive element theorem states that every finite separable
field\nextension L/K is generated by a single element. An almost equally k
nown\nfolklore fact states that every central simple algebra over a field
can be\ngenerated by 2-elements.\n\nI will discuss two recent works with Z
inovy Reichstein (one is forthcoming)\nwhere we establish global analogues
of these results. In more detail\, over\na ring R (or a scheme X)\, separ
able field extensions and central simple\nalgebras globalize to finite eta
le algebras and Azumaya algebras\,\nrespectively. We show that if R is of
finite type over an infinite field K\nand has Krull dimension d\, then eve
ry finite etale R-algebra is generated\nby d+1 elements and every Azumaya
R-algebra of degree n is generated by\n2+floor(d/[n-1]) elements. The case
d=0 recovers the well-known facts\nstated above. Recent works of B. Willi
ams\, A.K. Shukla and M. Ojanguren\nshow that these bounds are tight in th
e etale case and suggest that they\nshould also be tight in the Azumaya ca
se.\n\nThe proof makes use of principal homogeneous G-bundles T-->X (G is
an\naffine algebraic group over K) which can specialize to any principal\n
homogeneous G-bundle over an affine K-variety of dimension at most d. In\n
particular\, such G-bundles exist for all G and d.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Vonk (Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20200505T203000Z
DTEND;VALUE=DATE-TIME:20200505T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/4
DESCRIPTION:Title: Singular moduli for real quadratic fields\nby Jan Vonk
(Institute for Advanced Study) as part of MIT number theory seminar\n\n\nA
bstract\nIn the early 20th century\, Hecke studied the diagonal restrictio
ns of Eisenstein series over real quadratic fields. An infamous sign error
caused him to miss an important feature\, which later lead to highly infl
uential developments in the theory of complex multiplication (CM) initiate
d by Gross and Zagier in their famous work on Heegner points on elliptic c
urves. In this talk\, we will explore what happens when we replace the ima
ginary quadratic fields in CM theory with real quadratic fields\, and prop
ose a framework for a tentative 'RM theory'\, based on the notion of rigid
meromorphic cocycles\, introduced in joint work with Henri Darmon. I will
discuss several of their arithmetic properties\, and their apparent relev
ance in the study of explicit class field theory of real quadratic fields\
, the construction of rational points on elliptic curves\, and the theory
of Borcherds lifts. This concerns various joint works\, with Henri Darmon\
, Alice Pozzi\, and Yingkun Li.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen (Cambridge/Duke/IAS)
DTSTART;VALUE=DATE-TIME:20200908T143000Z
DTEND;VALUE=DATE-TIME:20200908T153000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/6
DESCRIPTION:Title: Representations of p-adic groups and applications\nby J
essica Fintzen (Cambridge/Duke/IAS) as part of MIT number theory seminar\n
\n\nAbstract\nThe Langlands program is a far-reaching collection of conjec
tures that relate different areas of mathematics including number theory a
nd representation theory. A fundamental problem on the representation theo
ry side of the Langlands program is the construction of all (irreducible\,
smooth\, complex) representations of p-adic groups. \n\nI will provide an
overview of our understanding of the representations of p-adic groups\, w
ith an emphasis on recent progress. \n\nI will also outline how new result
s about the representation theory of p-adic groups can be used to obtain c
ongruences between arbitrary automorphic forms and automorphic forms which
are supercuspidal at p\, which is joint work with Sug Woo Shin. This simp
lifies earlier constructions of attaching Galois representations to automo
rphic representations\, i.e. the global Langlands correspondence\, for gen
eral linear groups. Moreover\, our results apply to general p-adic groups
and have therefore the potential to become widely applicable beyond the ca
se of the general linear group.\n\nNote the this talk will take place at 1
0:30 rather than 16:30 (Eastern time).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lawrence (University of Chicago)
DTSTART;VALUE=DATE-TIME:20200915T203000Z
DTEND;VALUE=DATE-TIME:20200915T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/7
DESCRIPTION:Title: The Shafarevich conjecture for hypersurfaces in abelian
varieties\nby Brian Lawrence (University of Chicago) as part of MIT numbe
r theory seminar\n\n\nAbstract\nLet K be a number field\, S a finite set o
f primes of O_K\, and g a positive integer. Shafarevich conjectured\, and
Faltings proved\, that there are only finitely many curves of genus g\, d
efined over K and having good reduction outside S. Analogous results have
been proven for other families\, replacing "curves of genus g" with "K3 s
urfaces"\, "del Pezzo surfaces" etc.\; these results are also called Shafa
revich conjectures. There are good reasons to expect the Shafarevich conj
ecture to hold for many families of varieties: the moduli space should hav
e only finitely many integral points.\n\nWill Sawin and I prove this for h
ypersurfaces in abelian varieties of dimension not equal to 3.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shou-Wu Zhang (Princeton University)
DTSTART;VALUE=DATE-TIME:20200922T203000Z
DTEND;VALUE=DATE-TIME:20200922T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/8
DESCRIPTION:Title: Decomposition theorems for arithmetic cycles\nby Shou-W
u Zhang (Princeton University) as part of MIT number theory seminar\n\n\nA
bstract\nWe will describe some decomposition theorems for cycles over
polarized varieties in both local and global settings under some conj
ectures of Lefschetz type. In local settings\, our decomposition theorem
s are essentially non-archimedean analogues of ``harmonic forms" on Kahl
er manifolds. As an application\, we will define a notion of ``admissi
ble pairings" of algebraic cycles which is a simultaneous generalization
of Beilinson--Bloch height pairing\, and the local intersection pairing
s \ndeveloped by Arakelov\, Faltings\, and Gillet--Soule on Kahler ma
nifolds. In global setting\,\nour decomposition theorems provide canonic
al splittings of some canonical filtrations\, including canonical liftin
gs of homological cycles to algebraic cycles.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Creutz (University of Canterbury)
DTSTART;VALUE=DATE-TIME:20200929T203000Z
DTEND;VALUE=DATE-TIME:20200929T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/9
DESCRIPTION:Title: Quadratic points on del Pezzo surfaces of degree 4\nby
Brendan Creutz (University of Canterbury) as part of MIT number theory sem
inar\n\n\nAbstract\nI will report on joint work (in progress) with Bianca
Viray concerning the following question. If $X/k$ is a smooth complete int
ersection of $2$ quadrics in $\\mathbb{P}^n$ over a field $k$\, does $X$ h
ave a rational point over some quadratic extension of $k$?\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salim Tayou (Harvard)
DTSTART;VALUE=DATE-TIME:20201006T203000Z
DTEND;VALUE=DATE-TIME:20201006T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/10
DESCRIPTION:Title: Exceptional jumps of Picard rank of K3 surfaces over nu
mber fields\nby Salim Tayou (Harvard) as part of MIT number theory seminar
\n\n\nAbstract\nGiven a K3 surface X over a number field K\, we prove that
the set of primes of K where the geometric Picard rank jumps is infinite\
, assuming that X has everywhere potentially good reduction. This result i
s formulated in the general framework of GSpin Shimura varieties and I wil
l explain other applications to abelian surfaces. I will also discuss appl
ications to the existence of rational curves on K3 surfaces. The results i
n this talk are joint work with Ananth Shankar\, Arul Shankar and Yunqing
Tang.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20201020T203000Z
DTEND;VALUE=DATE-TIME:20201020T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/11
DESCRIPTION:Title: Iwasawa theory of elliptic curves at Eisenstein primes
and applications\nby Francesc Castella (UC Santa Barbara) as part of MIT n
umber theory seminar\n\n\nAbstract\nIn the study of Iwasawa theory of elli
ptic curves $E/\\mathbb{Q}$\, it is often assumed that $p$ is a non-Eisens
tein prime\, meaning that $E[p]$ is irreducible as a $G_{\\mathbb{Q}}$-mod
ule. Because of this\, most of the recent results on the $p$-converse to t
he theorem of Gross–Zagier and Kolyvagin (following Skinner and Wei Zhan
g) and on the $p$-part of the Birch–Swinnerton-Dyer formula in analytic
rank 1 (following Jetchev–Skinner–Wan) were only known for non-Eisenst
ein primes $p$. In this talk\, I’ll explain some of the ingredients in a
joint work with Giada Grossi\, Jaehoon Lee\, and Christopher Skinner in w
hich we study the (anticyclotomic) Iwasawa theory of elliptic curves over
$\\mathbb{Q}$ at Eisenstein primes. As a consequence of our study\, we obt
ain an extension of the aforementioned results to the Eisenstein case. In
particular\, for $p=3$ this leads to an improvement on the best known resu
lts towards Goldfeld’s conjecture in the case of elliptic curves over $\
\mathbb{Q}$ with a rational $3$-isogeny.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Winnie Li (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20201027T203000Z
DTEND;VALUE=DATE-TIME:20201027T213000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/12
DESCRIPTION:Title: Pair arithmetical equivalence for quadratic fields\nby
Winnie Li (Pennsylvania State University) as part of MIT number theory sem
inar\n\n\nAbstract\nGiven two distinct number fields $K$ and $M$\, and two
finite order Hecke characters $\\chi$ of $K$ and $\\eta$ of $M$ respectiv
ely\, we say that the pairs $(\\chi\, K)$ and $(\\eta\, M)$ are arithmetic
ally equivalent if the associated L-functions coincide: $L(s\, \\chi\, K)
= L(s\, \\eta\, M)$. When the characters are trivial\, this reduces to the
question of fields with the same Dedekind zeta function\, investigated by
Gassmann in 1926\, who found such fields of degree 180\, and by Perlis in
1977 and others\, who showed that there are no nonisomorphic fields of de
gree less than 7.\n\nIn this talk we discuss arithmetically equivalent pai
rs where the fields are quadratic. They give rise to dihedral automorphic
forms induced from characters of different quadratic fields. We characteri
ze when a given pair is arithmetically equivalent to another pair\, explic
itly construct such pairs for infinitely many quadratic extensions with od
d class number\, and classify such characters of order 2.\n\nThis is a joi
nt work with Zeev Rudnick.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Caraiani (Imperial College London)
DTSTART;VALUE=DATE-TIME:20201103T153000Z
DTEND;VALUE=DATE-TIME:20201103T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/13
DESCRIPTION:Title: Vanishing theorems for Shimura varieties\nby Ana Caraia
ni (Imperial College London) as part of MIT number theory seminar\n\n\nAbs
tract\nThe Langlands program is a vast network of conjectures that connect
number theory to other areas of mathematics\, such as representation theo
ry and harmonic analysis. The global Langlands correspondence can often be
realised through the cohomology of Shimura varieties\, which are certain
moduli spaces equipped with many symmetries. In this talk\, I will survey
some recent vanishing results for the cohomology of Shimura varieties with
mod p coefficients and mention several applications to the Langlands prog
ram and beyond. I will discuss some results that have an l-adic flavour
\, where l is a prime different from p\, that are primarily joint work wit
h Peter Scholze. I will then mention some results that have a p-adic fl
avour\, that are primarily joint work with Dan Gulotta and Christian Johan
sson. I will highlight the different kinds of techniques that are needed i
n these different settings using the toy model of the modular curve.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cong Xue (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20201110T153000Z
DTEND;VALUE=DATE-TIME:20201110T163000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/14
DESCRIPTION:by Cong Xue (University of Cambridge) as part of MIT number th
eory seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiuya Wang (Duke University)
DTSTART;VALUE=DATE-TIME:20201117T213000Z
DTEND;VALUE=DATE-TIME:20201117T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/15
DESCRIPTION:by Jiuya Wang (Duke University) as part of MIT number theory s
eminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201201T213000Z
DTEND;VALUE=DATE-TIME:20201201T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/16
DESCRIPTION:by Yiannis Sakellaridis (Johns Hopkins University) as part of
MIT number theory seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lola Thompson (Utrecht University)
DTSTART;VALUE=DATE-TIME:20201208T213000Z
DTEND;VALUE=DATE-TIME:20201208T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/17
DESCRIPTION:by Lola Thompson (Utrecht University) as part of MIT number th
eory seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART;VALUE=DATE-TIME:20201215T213000Z
DTEND;VALUE=DATE-TIME:20201215T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/18
DESCRIPTION:by Lillian Pierce (Duke University) as part of MIT number theo
ry seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lue Pan (University of Chicago)
DTSTART;VALUE=DATE-TIME:20201124T213000Z
DTEND;VALUE=DATE-TIME:20201124T223000Z
DTSTAMP;VALUE=DATE-TIME:20201031T045623Z
UID:MITNT/19
DESCRIPTION:by Lue Pan (University of Chicago) as part of MIT number theor
y seminar\n\nAbstract: TBA\n
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