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BEGIN:VEVENT
SUMMARY:Jigu Kim (Postech)
DTSTART:20250320T070000Z
DTEND:20250320T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/1
DESCRIPTION:Title: Genus character L-functions and their applications\nby Jigu Kim
(Postech) as part of Postech-PMI Number Theory Seminar\n\nLecture held in
Room 404.\n\nAbstract\nWe introduce the general genus character for two d
istinct (not necessarily relatively prime) discriminants of quadratic fiel
ds. We provide an explicit formula for the genus character L-function of a
quadratic order\, along with two different proofs. As applications\, we g
eneralize the Hirzebruch-Zagier formula for the class numbers of imaginary
quadratic fields and investigate congruences between Hirzebruch sums and
class numbers modulo powers of two. This is joint work with Yoshinori Mizu
no.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Disegni (Université d'Aix-Marseille)
DTSTART:20250327T080000Z
DTEND:20250327T090000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/2
DESCRIPTION:Title: Gan-Gross-Prasad cycles and derivatives of p-adic L-functions\n
by Daniel Disegni (Université d'Aix-Marseille) as part of Postech-PMI Num
ber Theory Seminar\n\n\nAbstract\nCertain Rankin-Selberg motives of rank n
(n+1) are endowed with algebraic cycles arising from maps of unitary Shimu
ra varieties. Gan-Gross-Prasad conjectured that these cycles are analogous
to Heegner points\, in the sense that their nontriviality should be detec
ted by derivatives of L-functions.\n\nI will discuss another nontriviality
criterion\, based on p-adic L-functions. Under some local conditions\, th
is variant can be established in a refined quantitative form\, via the con
struction and comparison of two p-adic relative-trace formulas. (Joint wor
k with Wei Zhang.)\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wanlin Li (Washington University in St. Louis)
DTSTART:20250403T000000Z
DTEND:20250403T010000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/3
DESCRIPTION:Title: Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles\nby Wan
lin Li (Washington University in St. Louis) as part of Postech-PMI Number
Theory Seminar\n\n\nAbstract\nThe Ceresa cycle and the Gross—Kudla—Sch
oen modified diagonal cycle are algebraic 1-cycles associated to a smooth
algebraic curve. They are algebraically trivial for a hyperelliptic curve
and non-trivial for a very general complex curve of genus >2. Given an alg
ebraic curve\, it is an interesting question to study whether the Ceresa a
nd GKS cycles associated to it are rationally or algebraically trivial. In
this talk\, I will discuss some methods and tools to study this problem.\
n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Koziol (Baruch College\, City University of New York)
DTSTART:20250515T000000Z
DTEND:20250515T010000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/4
DESCRIPTION:Title: Derived Satake morphisms in characteristic p\nby Karol Koziol (
Baruch College\, City University of New York) as part of Postech-PMI Numbe
r Theory Seminar\n\n\nAbstract\nThe classical Satake transform gives an is
omorphism between the complex spherical Hecke algebra of a p-adic reductiv
e group G\, and the Weyl-invariants of the complex spherical Hecke algebra
of a maximal torus of G. This provides a way for understanding the K-inva
riant vectors in smooth irreducible complex representations of G (where K
is a maximal compact subgroup of G)\, and allows one to construct instance
s of unramified Langlands correspondences. In this talk\, I'll present joi
nt work with Cédric Pépin in which we attempt to understand the analogou
s situation with mod p coefficients\, and working at the level of the deri
ved category of smooth G-representations.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myungjun Yu (Yonsei University)
DTSTART:20250605T070000Z
DTEND:20250605T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/5
DESCRIPTION:Title: The distribution of the cokernel of a random p-adic matrix\nby
Myungjun Yu (Yonsei University) as part of Postech-PMI Number Theory Semin
ar\n\nLecture held in Room 404.\n\nAbstract\nThe cokernel of a random p-ad
ic matrix can be used to study the distribution of objects that arise natu
rally in number theory. For example\, Cohen and Lenstra suggested a conjec
tural distribution of the p-parts of the ideal class groups of imaginary q
uadratic fields. Friedman and Washington proved that the distribution of t
he cokernel of a random p-adic matrix is the same as the Cohen–Lenstra d
istribution. Recently\, Wood generalized the result of Friedman–Washingt
on by considering a far more general class of measure on p-adic matrices.
In this talk\, we explain a further generalization of Wood’s work. This
is joint work with Dong Yeap Kang and Jungin Lee.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Gyu Choi (KAIST)
DTSTART:20250501T070000Z
DTEND:20250501T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/6
DESCRIPTION:Title: On degeneration of D-shtukas over ramified legs\nby Yong-Gyu Ch
oi (KAIST) as part of Postech-PMI Number Theory Seminar\n\nLecture held in
Room 404.\n\nAbstract\nThe canonical integral models of Shimura varieties
associated with reductive groups that are anisotropic modulo center are e
xpected to be proper. However\, an analogous property is known to be false
for the moduli stack of shtukas over global function fields. More precise
ly\, given a proper smooth curve X over a finite field and a parahoric gro
up scheme G over X corresponding to a maximal order of a central division
algebra D over the function field of X\, Eike Lau obtained a numerical cri
terion for the properness of the moduli stack of bounded G-shtukas with le
gs in the split locus of D. As a consequence\, there exists an instance wh
ere the moduli stack of bounded G-shtukas is not proper over the split loc
us of D.\n\nBased on the work of Arasteh Rad—Hartl and Bieker\, the modu
li stack of bounded G-shtukas is allowed to have legs in the ramification
locus of D. We extend Lau's result to the case where the legs are allowed
to lie in the ramification locus\, showing in particular that the moduli s
tack of G-shtukas can be proper when the legs are restricted to the split
locus of D\, but not proper when the legs run over the whole curve. This i
s joint work with Wansu Kim and Junyeong Park.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Luo (University of Wisconsin–Madison)
DTSTART:20250904T000000Z
DTEND:20250904T010000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/7
DESCRIPTION:Title: A new proof of the arithmetic Siegel-Weil formula\nby Yu Luo (U
niversity of Wisconsin–Madison) as part of Postech-PMI Number Theory Sem
inar\n\n\nAbstract\nThe arithmetic Siegel-Weil formula establishes a profo
und connection between intersection numbers in Shimura varieties and the F
ourier coefficients of central derivatives of Eisenstein series. This resu
lt was proven by C. Li and W. Zhang in 2021 using local methods. In this t
alk\, I will present a new proof of the formula that uses the local-global
compatibility and the modularity of generating series of special divisors
.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Chen (Princeton University)
DTSTART:20250925T000000Z
DTEND:20250925T010000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/8
DESCRIPTION:Title: Near-center derivatives and arithmetic 1-cycles\nby Ryan Chen (
Princeton University) as part of Postech-PMI Number Theory Seminar\n\n\nAb
stract\nTheta series for lattices count lattice vectors of fixed norm. Suc
h theta series give some of the first examples of automorphic forms.\n\nIt
is possible to form "theta series" in other geometric contexts\, e.g. for
counting problems involving abelian varieties.\nIt is expected that these
theta series again have additional automorphic symmetry.\n\nI will explai
n some “near-central” instances of an arithmetic Siegel--Weil formula
from Kudla’s program. These "geometrize" the classical Siegel--Weil form
ulas\, on lattice and lattice vector counting via Eisenstein series.\n\nAt
these near-central points of functional symmetry\, we observe that both t
he "leading" special value (complex volumes) and the "subleading" first de
rivative (arithmetic volume) simultaneously have geometric meaning.\n\nThe
key input is a new "limit phenomenon" relating positive characteristic in
tersection numbers and heights in mixed characteristic\, as well as its au
tomorphic counterpart.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyuk Jun Kweon (Seoul National University)
DTSTART:20251120T070000Z
DTEND:20251120T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/9
DESCRIPTION:Title: On the p-adic Group Cohomology of Finite Group Schemes\nby Hyuk
Jun Kweon (Seoul National University) as part of Postech-PMI Number Theor
y Seminar\n\nLecture held in Room 404.\n\nAbstract\nWe introduce a cohomol
ogy theory for finite group schemes with commutative formal groups as coef
ficients. Using Fontaine's Witt covectors\, this theory provides a p-adic
cohomology theory for finite group schemes and is motivated by the failure
of étale cohomology to detect inseparable extensions. We define a G-modu
le structure on commutative formal group schemes and prove that their cate
gory forms a Grothendieck category\, so it has enough injectives. We show
that\, with Witt covectors as coefficients\, the derived functors of the i
nvariants functor coincide with the cohomology computed via the bar resolu
tion. As an application\, we identify the first cohomology of a finite com
mutative p-group scheme G with its Dieudonné module.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heejong Lee (KIAS)
DTSTART:20251113T070000Z
DTEND:20251113T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/10
DESCRIPTION:Title: Families of mod p local Galois representations\nby Heejong Lee
(KIAS) as part of Postech-PMI Number Theory Seminar\n\nLecture held in Ro
om 404.\n\nAbstract\nProblems in Number Theory are often reduced to local
problems. Here\, local means focusing on one prime number p (e.g. solving
polynomials modulo p)\, as opposed to all prime numbers. The p-adic number
s were introduced in 1897 as a new foundation to study local problems in N
umber Theory. \n\nIn this talk\, I will introduce local Galois groups and
their representations. They play a key role in understanding congruence ph
enomenon in the Langlands program\, which already appeared in the work of
Wiles on Fermat's Last Theorem. I will explain how to study these objects
geometrically. In turn\, this suggests a intriguing connection to the repr
esentation theory of finite groups of Lie type. I will explain why this is
a shadow of a bigger picture—the mod p local Langlands program—and di
scuss my results in this direction.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Marseglia (Université Côte d'Azur)
DTSTART:20251030T070000Z
DTEND:20251030T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/11
DESCRIPTION:Title: Singular ideals in orders\nby Stefano Marseglia (Université C
ôte d'Azur) as part of Postech-PMI Number Theory Seminar\n\n\nAbstract\nI
n this talk\, we introduce the notion of multiplicator ladder of an order
in a product of number fields. Examples of orders admitting such a structu
re are quadratic orders\, or\, more generally\, Bass orders. If an order h
as a multiplicator ladder then the lattice of inclusions of its overorders
is rigidly structured. We prove this result\, use it to recover a recent
Theorem of Cho-Hong-Lee\, and if time permits\, we discuss an application
to the theory of abelian varieties over finite fields and their isogeny gr
aphs.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Muller (NCTS\, National Taiwan University)
DTSTART:20260312T070000Z
DTEND:20260312T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/12
DESCRIPTION:Title: Bruhat-Tits stratification for the GU(1\,n-1) Shimura variety with
parahoric reduction over an inert prime\nby Joseph Muller (NCTS\, Nat
ional Taiwan University) as part of Postech-PMI Number Theory Seminar\n\n\
nAbstract\nThe basic locus of certain Shimura varieties is known to be str
atified by (classical) Deligne-Lusztig varieties. Such a stratification is
usually called the Bruhat-Tits stratification\, because the incidence rel
ation is expected to be determined by the Bruhat-Tits building of some rel
ated p-adic group. By the work of Görtz-He-Nie on affine Deligne-Lusztig
varieties\, we know precisely which Shimura varieties must admit a Bruhat-
Tits stratification. However\, determining the actual incidence relations
usually requires a case-by-case analysis.\nIn this talk\, we consider PEL
unitary Shimura varieties of signature (1\,n-1) over an inert prime. For t
hese varieties\, so far the Bruhat-Tits stratification had only been descr
ibed for hyperspecial level (Vollaard-Wedhorn) and maximal parahoric level
(Cho). Building upon these works\, we describe the stratification for arb
itrary parahoric levels. If time permits\, we will discuss how the Bruhat-
Tits stratification compares with the EKOR strata on the basic locus.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazuki Morimoto (Kobe University)
DTSTART:20260319T070000Z
DTEND:20260319T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/13
DESCRIPTION:Title: On an Ichino-Ikeda type formula for Whittaker periods and theta li
fts\nby Kazuki Morimoto (Kobe University) as part of Postech-PMI Numbe
r Theory Seminar\n\n\nAbstract\nAn Ichino-Ikeda type formula provides an e
xplicit identity between special values of $L$-functions and periods of au
tomorphic forms. For example\, in joint works with Furusawa\, we proved Ic
hino-Ikeda type formulas for Bessel periods for any irreducible cuspidal t
empered automorphic representations of $(\\mathrm{SO}(5)\, \\mathrm{SO}(2)
)$\, using theta lifts for several dual pairs. In this talk\, I will discu
ss about an extension of this approach to automorphic representations that
are not necessarily tempered but generic. As a specific example of this a
pproach\, I will give a proof of an Ichino-Ikeda type formula of Whittaker
periods for any irreducible cuspidal automorphic representations of $\\ma
thrm{GSp}(4)$.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Seymour-Howell (Chonnam National University)
DTSTART:20260423T070000Z
DTEND:20260423T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/14
DESCRIPTION:Title: Numerical computations of Maass cusp forms via the trace formula\nby Andrei Seymour-Howell (Chonnam National University) as part of Post
ech-PMI Number Theory Seminar\n\nLecture held in Room 404.\n\nAbstract\nIn
the 1950s Selberg derived his well celebrated trace formula to prove the
existence and infinitude of Maass cusp forms. Explicit examples of such fo
rms though have been rare\, only occurring from examples that Maass origin
ally constructed and those arising from Galois representations. From this\
, we mainly rely on numerical approximations to study specific cusp forms.
In this talk I will give an overview and history of numerical computation
s of Maass cusp forms and furthermore\, I will discuss personal progress i
n this area in using the trace formula for numerical computations.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongryul Kim (Stanford University)
DTSTART:20260409T070000Z
DTEND:20260409T080000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/15
DESCRIPTION:Title: Igusa stacks and the cohomology of Shimura varieties\nby Dongr
yul Kim (Stanford University) as part of Postech-PMI Number Theory Seminar
\n\n\nAbstract\nIgusa stacks are $p$-adic geometric objects\, recently int
roduced by\nMingjia Zhang\, that roughly parametrize ways to $p$-adically\
nuniformize (global) Shimura varieties by local Shimura varieties. In\njoi
nt work with Patrick Daniels\, Pol van Hoften\, and Mingjia Zhang\, we\nco
nstruct Igusa stacks for all abelian type Shimura data and apply\nthem to
the study of $\\ell$-adic cohomology of Shimura varieties. I\nwill discuss
the geometric ingredients that go into the construction\nas well as how i
t naturally fits into Fargues--Scholze's framework of\ncategorical local L
anglands.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haseo Ki (Yonsei University)
DTSTART:20260417T060000Z
DTEND:20260417T070000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/16
DESCRIPTION:Title: On the Bogomolny-Schmit Conjecture for Maass Forms\nby Haseo K
i (Yonsei University) as part of Postech-PMI Number Theory Seminar\n\nLect
ure held in Room 104.\n\nAbstract\nI will introduce the Bogomolny-Schmit C
onjecture for Maass Forms.\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunqing Tang (UC Berkeley)
DTSTART:20260514T000000Z
DTEND:20260514T010000Z
DTSTAMP:20260422T212749Z
UID:Postech-PMI-NT/17
DESCRIPTION:by Yunqing Tang (UC Berkeley) as part of Postech-PMI Number Th
eory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Postech-PMI-NT/17/
END:VEVENT
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