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BEGIN:VEVENT
SUMMARY:Ashay Burungale
DTSTART;VALUE=DATE-TIME:20231017T190000Z
DTEND;VALUE=DATE-TIME:20231017T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/3
DESCRIPTION:Title: Z
eta elements for elliptic curves and some applications\nby Ashay Burun
gale as part of BC-MIT number theory seminar\n\nLecture held in Maloney 56
0 at Boston College.\n\nAbstract\nThe talk plans to outline the existence
of two-variable zeta element over an imaginary quadratic field for an elli
ptic curve defined over Q. Its arithmetic consequences include proof of Ko
bayashi's main conjecture for semistable curves and special cases of the B
irch--Swinnerton-Dyer conjecture. (Joint with C. Skinner\, Y. Tian and X.
Wan.)\n
LOCATION:https://researchseminars.org/talk/BC-MIT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Chan (University of Michigan)
DTSTART;VALUE=DATE-TIME:20231017T203000Z
DTEND;VALUE=DATE-TIME:20231017T213000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/4
DESCRIPTION:Title: S
upercuspidal representations and very regular elements\nby Charlotte C
han (University of Michigan) as part of BC-MIT number theory seminar\n\nLe
cture held in Maloney 560 at Boston College.\n\nAbstract\nIn the 1990s\, H
enniart proved that certain supercuspidal\nrepresentations of p-adic GLn a
re characterized by their character\nvalues on very regular elements\, a s
pecial class of regular semisimple\nelements on which character formulae a
re remarkably simple. Henniart's\nresult has seen many interesting applica
tions---for example\, in\ndetermining algebraic descriptions of geometrica
lly arising\nrepresentations. In this talk\, we'll discuss a generalizatio
n of\nHenniart's theorem to general G. As a byproduct of our methods\, we\
nobtain an easy\, non-cohomological condition distinguishing unipotent\nsu
percuspidal representations\, yielding a p-adic analogue of Lusztig's\ncri
terion for finite fields. This is joint work with M. Oi.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (University of Michigan)
DTSTART;VALUE=DATE-TIME:20231114T200000Z
DTEND;VALUE=DATE-TIME:20231114T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/5
DESCRIPTION:Title: D
ivisibility of character values of the symmetric group\nby Sarah Pelus
e (University of Michigan) as part of BC-MIT number theory seminar\n\nLect
ure held in MIT room 4-163.\n\nAbstract\nIn 2017\, Miller computed the cha
racter tables of $S_n$ for all $n$ up to $38$ and looked at various statis
tical properties of the entries. Characters of symmetric groups take only
integer values\, and\, based on his computations\, Miller conjectured that
almost all entries of the character table of $S_n$ are divisible by any f
ixed prime power as $n$ tends to infinity. In this talk\, I will discuss j
oint work with K. Soundararajan that resolves this conjecture\, and mentio
n some related open problems.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samit Dasgupta (Duke University)
DTSTART;VALUE=DATE-TIME:20231114T213000Z
DTEND;VALUE=DATE-TIME:20231114T223000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/6
DESCRIPTION:Title: O
n the Brumer-Stark Conjecture and Refinements\nby Samit Dasgupta (Duke
University) as part of BC-MIT number theory seminar\n\nLecture held in MI
T room 2-449.\n\nAbstract\nIn this talk I will describe my recent work wit
h Mahesh Kakde on the Brumer-Stark Conjecture and certain refinements. I w
ill give a broad overview that motivates the conjecture and gives connecti
ons to explicit class field theory. I will conclude with a description of
recent work (joint w/ Kakde\, Jesse Silliman\, and Jiuya Wang) in which we
complete the proof of the conjecture. Moreover\, we deduce a certain spec
ial case of the Equivariant Tamagawa Number Conjecture\, which has importa
nt corollaries. The key aspect of the most recent results\, which allows u
s to handle the prime $p=2$\, is the proof of a version of Ribet's Lemma i
n the case of characters that are congruent modulo $p$.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander D. Smith (UCLA)
DTSTART;VALUE=DATE-TIME:20240409T190000Z
DTEND;VALUE=DATE-TIME:20240409T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/7
DESCRIPTION:Title: S
imple abelian varieties over finite fields with extreme point counts\n
by Alexander D. Smith (UCLA) as part of BC-MIT number theory seminar\n\nLe
cture held in Maloney 560 at Boston College.\n\nAbstract\nGiven a compactl
y supported probability measure on the reals\, we will give a necessary an
d sufficient condition for there to be a sequence of totally real algebrai
c integers whose distribution of conjugates approaches the measure. We use
this result to prove that there are infinitely many totally positive alge
braic integers X satisfying tr(X)/deg(X) < 1.899\; previously\, there were
only known to be infinitely many such integers satisfying tr(X)/deg(X) <
2. We also will explain how our method can be used in the search for simpl
e abelian varieties with extreme point counts.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Bennett (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20240409T203000Z
DTEND;VALUE=DATE-TIME:20240409T213000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/8
DESCRIPTION:Title: A
rithmetic progressions in sumsets of geometric progressions\nby Michae
l Bennett (University of British Columbia) as part of BC-MIT number theory
seminar\n\nLecture held in Maloney 560 at Boston College.\n\nAbstract\nIf
A and B are two geometric progressions\, we characterize all 3-term arith
metic progressions in the sumset A+B. Somewhat surprisingly\, while mostly
elementary\, this appears to require quite deep machinery from Diophantin
e Approximation.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20240319T190000Z
DTEND;VALUE=DATE-TIME:20240319T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/9
DESCRIPTION:Title: R
elative Langlands duality\, past and future.\nby Yiannis Sakellaridis
(Johns Hopkins University) as part of BC-MIT number theory seminar\n\nLect
ure held in MIT room 2-449.\n\nAbstract\nSince Riemann's 1859 report on th
e zeta function\, it is known that certain automorphic $L$-functions can b
e represented as ("period") integrals\, which often proves analytic proper
ties such as the functional equation. The method was advanced by Jacquet\,
Piatetski-Shapiro\, Rallis\, and many others since the 1970s\, giving ris
e to the "relative" Langlands program. It turns out that the relationship
between periods and $L$-functions reflects a duality between certain Hamil
tonian varieties for a reductive group and its Langlands dual group. I wil
l set up this duality in a limited setting (joint work with David Ben-Zvi
and Akshay Venkatesh)\, and speculate on how it might be expanded in the f
uture.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ben-Zvi (University of Texas at Austin)
DTSTART;VALUE=DATE-TIME:20240319T203000Z
DTEND;VALUE=DATE-TIME:20240319T213000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/10
DESCRIPTION:Title:
Geometric Arthur Parameters\nby David Ben-Zvi (University of Texas at
Austin) as part of BC-MIT number theory seminar\n\nLecture held in MIT roo
m 2-449.\n\nAbstract\nArthur proposed a description of automorphic forms i
n terms of tempered automorphic forms for centralizers of SL2 homomorphism
s. I will explain a point of view on the Arthur parameterization in the se
tting of function fields coming from relative Langlands duality\, emphasiz
ing the role of $shearing$ (the symmetry of the derived category of graded
vector spaces which simultaneously shifts weights and cohomological degre
es). Shearing helps account for a deficit of Tannakian formalism in the de
rived context - there are more eigenvalues for tensor actions than one mig
ht expect. The talk reports on joint work with Yiannis Sakellaridis and Ak
shay Venkatesh.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (Berkeley)
DTSTART;VALUE=DATE-TIME:20240514T190000Z
DTEND;VALUE=DATE-TIME:20240514T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/11
DESCRIPTION:Title:
The arithmetic of power series and applications to irrationality\nby Y
unqing Tang (Berkeley) as part of BC-MIT number theory seminar\n\nLecture
held in Maloney 560 at Boston College.\n\nAbstract\nIn this talk\, we will
discuss various irrationality and linear independence problems including
certain products of two (classical or p-adic) log values. The proofs use a
n arithmetic holonomicity theorem\, the special case of which was used in
the proof of the unbounded denominators conjecture\; our arithmetic holono
micity theorem is inspired from Andre’s work on Grothendieck-Katz p-curv
ature conjecture on arithmetic differential equations. A geometric version
of our arithmetic holonomicity theorems have also been studied in recent
work of Bost and Charles.\n\nThis is joint work in progress with Frank Cal
egari and Vesselin Dimitrov.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20240514T203000Z
DTEND;VALUE=DATE-TIME:20240514T213000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044627Z
UID:BC-MIT/12
DESCRIPTION:Title:
Vanishing criteria for Ceresa cycles\nby Ari Shnidman (Hebrew Universi
ty of Jerusalem) as part of BC-MIT number theory seminar\n\nLecture held i
n Maloney 560 at Boston College.\n\nAbstract\nThe Ceresa cycle of a curve
is perhaps the simplest example of a\nhomologically trivial algebraic cycl
e which need not be algebraically\ntrivial. Its vanishing in the Chow (res
p. Griffiths) group has various\nimplications\, but the locus of vanishing
Ceresa cycles in $M_g$ is quite\nmysterious\, beyond the fact that it con
tains the hyperelliptic locus. I'll\npresent new vanishing criteria for th
e Ceresa cycle of curves with\nautomorphisms\, one of them conditional on
the Hodge conjecture. In certain\nlow genus cases the relevant Hodge conje
cture is known\, and using this we\ndescribe the locus of Picard curves wi
th vanishing Ceresa cycle. This is\njoint work with Jef Laga.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/12/
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