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BEGIN:VEVENT
SUMMARY:Stefan Patrikis (Ohio State Univ.)
DTSTART:20200922T170000Z
DTEND:20200922T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/1
DESCRIPTION:Title: Lifting Galois representations\nby Stefan Patrikis (Ohio State U
niv.) as part of University of Arizona Algebra and Number Theory Seminar\n
\n\nAbstract\nI will survey joint work with Najmuddin Fakhruddin and Chand
rashekhar Khare in which we prove in many cases existence of geometric p-a
dic lifts of "odd" mod p Galois representations\, valued in general reduct
ive groups. Then I will discuss applications to modularity of reducible mo
d p Galois representations.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wanlin Li (MIT)
DTSTART:20200929T210000Z
DTEND:20200929T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/2
DESCRIPTION:Title: The Ceresa class: tropical\, topological\, and algebraic\nby Wan
lin Li (MIT) as part of University of Arizona Algebra and Number Theory Se
minar\n\n\nAbstract\nThe Ceresa cycle is an algebraic cycle attached to a
smooth algebraic curve\, which is trivial in the Chow ring when the curve
is hyperelliptic. Its image under a cycle class map provides a class in é
tale cohomology called the Ceresa class. There are few examples where the
Ceresa class is known for non-hyperelliptic curves. We explain how to defi
ne a Ceresa class for a tropical algebraic curve\, and also for a Riemann
surface endowed with a multiset of commuting Dehn twists (where it is rela
ted to the Morita cocycle on the mapping class group). Finally\, we explai
n how these are related to the Ceresa class of a smooth algebraic curve ov
er C((t))\, and show that in this setting the Ceresa class is torsion.\
n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Fintzen (Univ. of Cambridge)
DTSTART:20201006T170000Z
DTEND:20201006T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/3
DESCRIPTION:Title: Representations of p-adic groups and applications\nby Jessica Fi
ntzen (Univ. of Cambridge) as part of University of Arizona Algebra and Nu
mber Theory Seminar\n\n\nAbstract\nThe Langlands program is a far-reaching
collection of conjectures that relate different areas of mathematics incl
uding number theory and representation theory. A fundamental problem on th
e representation theory side of the Langlands program is the construction
of all (irreducible\, smooth\, complex) representations of p-adic groups.
I will provide an overview of our understanding of the representations of
p-adic groups\, with an emphasis on recent progress.\n\nI will also outlin
e how new results about the representation theory of p-adic groups can be
used to obtain congruences between arbitrary automorphic forms and automor
phic forms which are supercuspidal at p\, which is joint work with Sug Woo
Shin. This simplifies earlier constructions of attaching Galois represent
ations to automorphic representations\, i.e. the global Langlands correspo
ndence\, for general linear groups. Moreover\, our results apply to genera
l p-adic groups and have therefore the potential to become widely applicab
le beyond the case of the general linear group.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesc Castella (UCSB)
DTSTART:20201027T210000Z
DTEND:20201027T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/4
DESCRIPTION:Title: Iwasawa theory of elliptic curves at Eisenstein primes and applicati
ons\nby Francesc Castella (UCSB) as part of University of Arizona Alge
bra and Number Theory Seminar\n\n\nAbstract\nIn the study of Iwasawa theor
y of elliptic curves $E/\\mathbb{Q}$\, it is often assumed that $p$ is a n
on-Eisenstein prime\, meaning that $E[p]$ is irreducible as a $G_{\\mathbb
{Q}}$-module. Because of this\, most of the recent results on the $p$-conv
erse to the theorem of Gross–Zagier and Kolyvagin (following Skinner and
Wei Zhang) and on the $p$-part of the Birch–Swinnerton-Dyer formula in
analytic rank 1 (following Jetchev–Skinner–Wan) were only known for no
n-Eisenstein primes $p$. In this talk\, I’ll explain some of the ingredi
ents in a joint work with Giada Grossi\, Jaehoon Lee\, and Christopher Ski
nner in which we study the (anticyclotomic) Iwasawa theory of elliptic cur
ves over $\\mathbb{Q}$ at Eisenstein primes. As a consequence of our study
\, we obtain an extension of the aforementioned results to the Eisenstein
case. In particular\, for $p=3$ this leads to an improvement on the best k
nown results towards Goldfeld’s conjecture in the case of elliptic curve
s over $\\mathbb{Q}$ with a rational $3$-isogeny.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Gemuenden (ETH Zurich)
DTSTART:20201103T170000Z
DTEND:20201103T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/5
DESCRIPTION:Title: Non-Abelian Orbifold Theory\nby Thomas Gemuenden (ETH Zurich) as
part of University of Arizona Algebra and Number Theory Seminar\n\n\nAbst
ract\nIn this talk\, we will discuss the theory of holomorphic extensions
of non-abelian orbifold vertex operator algebras. We will give a brief ove
rview of the concepts and motivations of vertex operator algebras and thei
r modules. Then we will construct the module category of non-abelian orbif
old vertex operator algebras and classify their holomorphic extensions. If
time permits we will prove that there exist holomorphic vertex operator a
lgebras at central charge 72 that cannot be constructed as a holomorphic e
xtension of a cyclic orbifold of a lattice vertex operator algebra.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Emory (Univ. of Toronto)
DTSTART:20201110T210000Z
DTEND:20201110T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/6
DESCRIPTION:Title: A multiplicity one theorem for general spin groups\nby Melissa E
mory (Univ. of Toronto) as part of University of Arizona Algebra and Numbe
r Theory Seminar\n\n\nAbstract\nA classical problem in representation theo
ry is how a\nrepresentation of a group decomposes when restricted to a sub
group. In the\n1990s\, Gross-Prasad formulated a conjecture regarding the\
nrestriction of representations\, also known as branching laws\, of specia
l\northogonal groups. Gan\, Gross and Prasad extended this conjecture\, n
ow\nknown as the local Gan-Gross-Prasad (GGP) conjecture\, to the remainin
g\nclassical groups. There are many ingredients needed to prove a local GG
P\nconjecture. In this talk\, we will focus on the first ingredient: a\nm
ultiplicity at most one theorem.\nAizenbud\, Gourevitch\, Rallis and Schif
fmann proved a multiplicity at\nmost one theorem for restrictions of irred
ucible representations of\ncertain p-adic classical groups and Waldspurger
proved the same theorem\nfor the special orthogonal groups. We will discu
ss work that establishes a\nmultiplicity at most one theorem for restricti
ons of irreducible\nrepresentations for a non-classical group\, the genera
l spin group. This is\njoint work with Shuichiro Takeda.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Dotto (Univ. of Chicago)
DTSTART:20201117T210000Z
DTEND:20201117T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/7
DESCRIPTION:Title: Mod p Bernstein centres of p-adic groups\nby Andrea Dotto (Univ.
of Chicago) as part of University of Arizona Algebra and Number Theory Se
minar\n\n\nAbstract\nThe centre of the category of smooth mod p representa
tions of a p-adic reductive group does not distinguish the blocks of finit
e length representations\, in contrast with Bernstein's theory in characte
ristic zero. Motivated by this observaton and the known connections betwee
n the Bernstein centre and the local Langlands correspondence in families\
, we consider the case of GL_2(Q_p) and we prove that its category of repr
esentations extends to a stack on the Zariski site of a simple geometric o
bject: a chain X of projective lines\, whose points are in bijection with
Paskunas's blocks. Taking the centre over each open subset we obtain a she
af of rings on X\, and we expect the resulting space to be closely related
to the Emerton--Gee stack for 2-dimensional representations of the absolu
te Galois group of Q_p. Joint work in progress with Matthew Emerton and To
by Gee.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Pollack (UCSD)
DTSTART:20201124T210000Z
DTEND:20201124T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/8
DESCRIPTION:Title: Singular modular forms on quaternionic E_8\nby Aaron Pollack (UC
SD) as part of University of Arizona Algebra and Number Theory Seminar\n\n
\nAbstract\nThe exceptional group $E_{7\,3}$ has a symmetric space with He
rmitian tube structure. On it\, Henry Kim wrote down low weight holomorphi
c modular forms that are "singular" in the sense that their Fourier expans
ion has many terms equal to zero. The symmetric space associated to the ex
ceptional group $E_{8\,4}$ does not have a Hermitian structure\, but it ha
s what might be the next best thing: a quaternionic structure and associat
ed "modular forms". I will explain the construction of singular modular fo
rms on $E_{8\,4}$\, and the proof that these special modular forms have ra
tional Fourier expansions\, in a precise sense. This builds off of work of
Wee Teck Gan and uses key input from Gordan Savin.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuan Liu (Univ. of Michigan)
DTSTART:20201201T210000Z
DTEND:20201201T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/9
DESCRIPTION:Title: Presentations of Galois groups of maximal extensions with restricted
ramifications\nby Yuan Liu (Univ. of Michigan) as part of University
of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nIn this talk\,
we are going to discuss how to use Galois cohomology to study the present
ation of Galois groups of maximal extensions with restricted ramifications
. In previous work with Melanie Matchett Wood and David Zureick-Brown\, we
conjecture that an explicitly-defined random profinite group model can pr
edict the distribution of the Galois groups of maximal unramified extensio
n of global fields that range over $\\Gamma$-extensions of $\\mathbb{Q}$ o
r $\\mathbb{F}_q(t)$. In the function field case\, our conjecture is suppo
rted by the moment computation\, but very little is known in the number fi
eld case. Interestingly\, our conjecture suggests that the random group sh
ould simulate the maximal unramified Galois groups\, and hence suggests so
me particular requirements on the structure of these Galois groups. In thi
s talk\, we will prove that the maximal unramified Galois groups are alway
s achievable by our random group model\, which verifies those interesting
requirements.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Wootton (Univ. of Arizona)
DTSTART:20201208T210000Z
DTEND:20201208T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/10
DESCRIPTION:Title: Non-Abelian simple groups act with almost all signatures\nby Aa
ron Wootton (Univ. of Arizona) as part of University of Arizona Algebra an
d Number Theory Seminar\n\n\nAbstract\nThe topological data of a finite gr
oup $G$ acting conformally on a compact Riemann surface is often encoded
using a tuple of non-negative integers $(h\;m_1\,\\ldots \,m_s)$ called it
s signature\, where the $m_i$ are orders of non-trivial elements in the gr
oup. There are two easily verifiable arithmetic conditions on a tuple whic
h are necessary for it to be a signature of some group action. We derive n
ecessary and sufficient conditions on a group for the situation where all
but finitely many tuples that satisfy these arithmetic conditions actually
occur as the signature for an action of $G$ on some Riemann surface. As a
consequence\, we show that all non-abelian finite simple groups exhibit t
his property.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Bartlett (Univ. of Münster)
DTSTART:20210209T170000Z
DTEND:20210209T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/11
DESCRIPTION:Title: Some Breuil-Mezard identities in moduli spaces of Breuil-Kisin modu
les\nby Robin Bartlett (Univ. of Münster) as part of University of Ar
izona Algebra and Number Theory Seminar\n\n\nAbstract\nThe Breuil--Mezard
conjecture predicts certain identities between cycles in moduli spaces of
mod p Galois representations in terms of the Fp-representation theory of G
Ln(Fq).\n\nIn this talk I will discuss work in progress which considers th
e situtation arising from (the reduction modulo p of) two dimensional crys
talline Galois representation with suitably small* Hodge--Tate weights. We
will discuss how the predected identities can also seen in ``resolutions`
` of these spaces of Galois representations described in terms of semilina
r algebra.\n\n*small will be precisely the bound which ensures that the Fp
-representation theory of GL2(Fq) appearing behaves precisely as it would
with char 0 coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Wang Erickson (Univ. of Pittsburgh)
DTSTART:20210223T210000Z
DTEND:20210223T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/12
DESCRIPTION:Title: Small non-Gorenstein residually Eisenstein Hecke algebras\nby C
arl Wang Erickson (Univ. of Pittsburgh) as part of University of Arizona A
lgebra and Number Theory Seminar\n\n\nAbstract\nIn Mazur's work proving th
e torsion theorem for rational elliptic curves\, he studied congruences be
tween cusp forms and Eisenstein series in weight two and prime level. One
of his innovations was to measure such congruences using a residually Eise
nstein Hecke algebra. He asked for generalizations of his theory to square
free levels. The speaker made progress toward such generalizations in join
t work with Preston Wake\; however\, a crucial condition in their work was
that the Hecke algebra be Gorenstein\, which is often but by no means alw
ays true. We present joint work with Catherine Hsu and Preston Wake in whi
ch we study the smallest possible non-Gorenstein case and leverage this sm
allness to draw an explicit link between its size and an invariant from al
gebraic number theory.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Columbia Univ.)
DTSTART:20210126T210000Z
DTEND:20210126T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/13
DESCRIPTION:Title: Beilinson-Bloch conjecture for unitary Shimura varieties\nby Ch
ao Li (Columbia Univ.) as part of University of Arizona Algebra and Number
Theory Seminar\n\n\nAbstract\nFor certain automorphic representations $\\
pi$ on unitary groups\, we show that if $L(s\, \\pi)$ vanishes to order on
e at the center $s=1/2$\, then the associated $\\pi$-localized Chow group
of a unitary Shimura variety is nontrivial. This proves part of the Beilin
son-Bloch conjecture for unitary Shimura varieties\, which generalizes the
BSD conjecture. Assuming the modularity of Kudla's generating series of s
pecial cycles\, we further prove a precise height formula for $L'(1/2\, \\
pi)$. This proves the conjectural arithmetic inner product formula\, which
generalizes the Gross-Zagier formula to Shimura varieties of higher dimen
sion. We will motivate these conjectures and discuss some aspects of the p
roof. This is joint work with Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Suk Moon (Univ. of Arizona)
DTSTART:20210216T210000Z
DTEND:20210216T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/14
DESCRIPTION:Title: Relative Fontaine-Messing theory over power series rings\nby Yo
ng-Suk Moon (Univ. of Arizona) as part of University of Arizona Algebra an
d Number Theory Seminar\n\n\nAbstract\nLet k be a perfect field of char p
> 2. For a smooth proper scheme over W(k)\, Fontaine-Messing theory gives
a nice way to compare its torsion crystalline cohomology H^i_cris and tors
ion etale cohomology H^i_et when i < p-1. We will explain how one can gene
ralize Fontaine-Messing theory in the relative setting over power series r
ings\, and discuss some applications. This is joint work with Tong Liu and
Deepam Patel.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Mihatsch (Univ. of Bonn)
DTSTART:20210323T170000Z
DTEND:20210323T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/15
DESCRIPTION:Title: AFL over F\nby Andreas Mihatsch (Univ. of Bonn) as part of Univ
ersity of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nI will
report on the recent proof of the AFL over a general p-adic local field (p
> n). The previous proof of the AFL (due to W. Zhang) was restricted to Q
_p since it relied on the modularity of Kudla divisor generating series on
integral models of unitary Shimura varieties\, which is only known over Q
. The new proof merely requires modularity for the generic fiber generatin
g series\, allowing us to work with an arbitrary totally real field. This
is joint work with W. Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Congling Qiu (Yale Univ.)
DTSTART:20210406T210000Z
DTEND:20210406T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/16
DESCRIPTION:Title: Modularity and Heights of CM cycles on Kuga-Sato varieties\nby
Congling Qiu (Yale Univ.) as part of University of Arizona Algebra and Num
ber Theory Seminar\n\n\nAbstract\nWe study CM cycles on Kuga-Sato varietie
s over X(N). Our first result is the modularity of the unramified Hecke
module generated by CM cycles. This result enable us to decompose the spa
ce of CM cycles according to the unramified Hecke action. Our second resu
lt is the full modularity of all CM cycles in the components of representa
tions with vanishing central (base change) L-values. Finally\, we prove a
higher weight analog of the general Gross-Zagier formula of Yuan\, S. Zhan
g and W. Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Quinones (Gallaudet Univ.)
DTSTART:20210413T210000Z
DTEND:20210413T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/17
DESCRIPTION:Title: Slow-Growing Weak Jacobi Forms\nby Jason Quinones (Gallaudet Un
iv.) as part of University of Arizona Algebra and Number Theory Seminar\n\
n\nAbstract\nWeak Jacobi forms of weight 0 can be exponentially lifted to
meromorphic Siegel paramodular forms. It was recently observed that the Fo
urier coefficients of such lifts are then either fast growing or slow grow
ing. Those weak Jacobi forms with slow growing behavior could describe the
elliptic genus of a CFT whose symmetric orbifold exhibits a slow supergra
vity-like growth. In this talk\, we investigate the space of weak Jacobi f
orms that lead to slow growth. We provide analytic and numerical evidence
for the conjecture that there are such slow growing forms for any index.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yihang Zhu (Univ. of Maryland)
DTSTART:20210420T210000Z
DTEND:20210420T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/18
DESCRIPTION:Title: Irreducible components of affine Deligne-Lusztig varieties\nby
Yihang Zhu (Univ. of Maryland) as part of University of Arizona Algebra an
d Number Theory Seminar\n\n\nAbstract\nAffine Deligne-Lusztig varieties na
turally arise from the study of Shimura varieties. We prove a formula for
the number of their irreducible components\, which was a conjecture of Mia
ofen Chen and Xinwen Zhu. Our method is to count the number of F_q points\
, and to relate it to certain twisted orbital integrals. We then study th
e growth rate of these integrals using the Base Change Fundamental Lemma o
f Clozel and Labesse. In an ongoing work we also give the number of irredu
cible components in the basic Newton stratum of a Shimura variety. This is
joint work with Rong Zhou and Xuhua He.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiuya Wang (Duke Univ.)
DTSTART:20210504T210000Z
DTEND:20210504T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/19
DESCRIPTION:Title: Average of $3$-torsion in class groups of $2$-extensions\nby Ji
uya Wang (Duke Univ.) as part of University of Arizona Algebra and Number
Theory Seminar\n\n\nAbstract\nIn 1971\, Davenport and Heilbronn prove the
celebrated theorem\ndetermining the average of $3$-torsion in class groups
of quadratic\nextensions. In this talk\, we will study the average of $3$
-torsion in\nclass groups of $2$-extensions\, which are towers of relative
quadratic\nextensions. As an example\, we determine the average of $3$-to
rsion in\nclass groups of $D_4$ quartic extension. This is a joint work wi
th\nRobert J. Lemke Oliver and Melanie Matchett Wood.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanshuai Qin (UC Berkeley)
DTSTART:20210302T210000Z
DTEND:20210302T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/20
DESCRIPTION:Title: A relation between Brauer groups and Tate-Shafarevich groups for hi
gh dimensional fibrations\nby Yanshuai Qin (UC Berkeley) as part of Un
iversity of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nLet $
\\mathcal{X} \\rightarrow C$ be a dominant morphism between smooth geomet
rically connected varieties over a finitely generated field such that the
generic fiber $X/K$ is smooth\, projective and geometrically connected. W
e prove a relation between the Tate-Shafarevich group of $Pic^0_{X/K}$ an
d the geometric Brauer groups of $ \\mathcal{X}$\, $X$ and $C$\, generaliz
ing a theorem of Artin and Grothendieck for fibered surfaces to arbitrary
relative dimension.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Schwein (Univ. of Cambridge)
DTSTART:20210831T210000Z
DTEND:20210831T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/21
DESCRIPTION:Title: Recent progress on the formal degree conjecture\nby David Schwe
in (Univ. of Cambridge) as part of University of Arizona Algebra and Numbe
r Theory Seminar\n\n\nAbstract\nThe local Langlands correspondence is more
than a\ncorrespondence: it promises an extensive dictionary between the\n
representation theory of reductive p-adic groups and the arithmetic of\nth
eir L-parameters. One entry in this dictionary is a conjectural\nformula o
f Hiraga\, Ichino\, and Ikeda for the size of a discrete series\nrepresent
ation – its “formal degree” – in terms of a gamma factor of\nits L
-parameter. In the first part of the talk\, I’ll explain why the\nconjec
ture is true for almost all supercuspidal representations. In\nthe second
part\, I’ll compute the sign of the gamma factor\, verifying\na conjectu
re of Gross and Reeder.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huajie Li (Aix-Marseille Univ.)
DTSTART:20210914T170000Z
DTEND:20210914T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/22
DESCRIPTION:Title: On the comparison of an infinitesimal variant of Guo-Jacquet trace
formulae\nby Huajie Li (Aix-Marseille Univ.) as part of University of
Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nGuo-Jacquet have
proposed a comparison of two relative trace formulae in order to gernerali
se Waldspurger’s well-known theorem relating toric periods to central va
lues of automorphic L-functions for $GL(2)$. In our previous works\, we ha
ve established an infinitesimal variant of Guo-Jacquet trace formulae and
the weighted fundamental lemma in this case. In this talk\, we shall expla
in several local results for the comparison of regular semi-simple terms.
In particular\, we shall talk about certain identities between Fourier tra
nsforms of local weighted orbital integrals\, which are proved by Waldspur
ger’s global method on the endoscopic transfer. During the proof\, we sh
all also need some results in local harmonic analysis such as local trace
formulae for certain $p$-adic infinitesimal symmetric spaces.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anwesh Ray (University of British Columbia)
DTSTART:20210921T210000Z
DTEND:20210921T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/23
DESCRIPTION:Title: Rank jumps and growth of Tate-Shafarevich groups of elliptic curves
\nby Anwesh Ray (University of British Columbia) as part of University
of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nWe use techni
ques from Iwasawa theory to study the growth of the Mordell Weil group and
Tate-Shafarevich groups of elliptic curves in cyclic extensions of prime
degree. This is joint work with Lea Beneish and Debanjana Kundu.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Feng (MIT)
DTSTART:20211005T210000Z
DTEND:20211005T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/24
DESCRIPTION:Title: Higher arithmetic theta series\nby Tony Feng (MIT) as part of U
niversity of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nArit
hmetic theta series are incarnations of theta functions in arithmetic alge
braic geometry. The first examples were constructed by Kudla as generating
series of special cycles on Shimura varieties. Their conjectural key feat
ures are (1) modularity of the generating series\, and (2) the arithmetic
Siegel-Weil formula\, relating their enumerative geometry to the first der
ivative of Eisenstein series at special values. In joint work with Zhiwei
Yun and Wei Zhang\, we construct "higher" arithmetic theta series on modul
i spaces of shtukas\, which we conjecture to also enjoy (1) modularity and
(2) a higher arithmetic Siegel-Weil formula relating their enumerative ge
ometry to all derivatives of Eisenstein series at special values. We prove
several results towards these conjectures\, drawing upon ideas from Ngo's
proof of the Fundamental Lemma in addition to new ingredients from Spring
er theory and derived algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yousheng Shi (Univ. of Wisconsin)
DTSTART:20211026T210000Z
DTEND:20211026T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/25
DESCRIPTION:Title: Kudla-Rapoport conjecture at a ramified prime\nby Yousheng Shi
(Univ. of Wisconsin) as part of University of Arizona Algebra and Number T
heory Seminar\n\n\nAbstract\nKudla-Rapoport conjecture predicts that there
is an identity between the intersection number of special cycles on unita
ry Rapoport-Zink space and the derivative of local density of certain Herm
itian form. However\, the original conjecture was only formulated for RZ s
pace with hyperspecial level structure over unramified primes . In this ta
lk\, I will motivate the original conjecture and discuss how to modify it
at a ramified prime. Finally\, I will sketch how to verify the modified co
njecture for n=3. This is a joint work with Qiao He and Tonghai Yang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shizhang Li (Univ. of Michigan)
DTSTART:20211109T210000Z
DTEND:20211109T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/26
DESCRIPTION:Title: On u-power torsions in prismatic cohomology\nby Shizhang Li (Un
iv. of Michigan) as part of University of Arizona Algebra and Number Theor
y Seminar\n\n\nAbstract\nI will report a joint work with Tong\, concerning
the structure of a certain submodule inside prismatic cohomology of a smo
oth proper scheme over a p-adic ring of integers. I will explain how this
part of prismatic cohomology causes various pathologies\, then say a few c
orresponding consequences of our structural result. If time permits\, I sh
all also mention an interesting example.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Baril Boudreau (Western Univ.)
DTSTART:20211102T210000Z
DTEND:20211102T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/27
DESCRIPTION:Title: Computing an L-function modulo a prime\nby Felix Baril Boudreau
(Western Univ.) as part of University of Arizona Algebra and Number Theor
y Seminar\n\n\nAbstract\nLet $E$ be an elliptic curve with non-constant $j
$-invariant over a function field $K$ with constant field of size an odd p
rime power $q$. Its $L$-function $L(T\,E/K)$ belongs to $1 + T\\mathbb{Z}[
T]$. Inspired by the algorithms of Schoof and Pila for computing zeta func
tions of curves over finite fields\, we propose an approach to compute $L(
T\,E/K)$. The idea is to compute\, for sufficiently many primes $\\ell$ co
prime with $q$\, the reduction $L(T\,E/K) \\bmod{\\ell}$. The $L$-function
is then recovered via the Chinese remainder theorem. When $E(K)$ has a su
bgroup of order $N \\geq 2$ coprime with $q$\, Chris Hall showed how to ex
plicitly calculate $L(T\,E/K) \\bmod{N}$. We present novel theorems going
beyond Hall's.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (UCL)
DTSTART:20211123T210000Z
DTEND:20211123T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/28
DESCRIPTION:Title: Eisenstein cocycles and values of L-functions\nby Luis Garcia (
UCL) as part of University of Arizona Algebra and Number Theory Seminar\n\
n\nAbstract\nThere are several recent constructions by many authors of Eis
enstein cocycles of arithmetic groups. I will discuss a point of view on t
hese constructions using equivariant cohomology and equivariant differenti
al forms. The resulting objects behave like theta kernels relating the hom
ology of arithmetic groups to algebraic objects. As an application\, I wil
l explain the proof of some conjectures of Sczech and Colmez on critical v
alues of Hecke L-functions. The talk is based on joint work with Nicolas B
ergeron and Pierre Charollois.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aparna Upadhyay (Univ. of Arizona)
DTSTART:20211019T210000Z
DTEND:20211019T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/29
DESCRIPTION:Title: The non-projective part of modular representations of finite groups
\nby Aparna Upadhyay (Univ. of Arizona) as part of University of Arizo
na Algebra and Number Theory Seminar\n\n\nAbstract\nIn a recent paper\, Da
ve Benson and Peter Symonds introduced a new invariant for modular represe
ntations of a finite group. This invariant is a result of studying the asy
mptotics of the direct sum decomposition of the non-projective part of ten
sor powers of a finite dimensional representation of a finite group in pri
me characteristic. In this talk\, we will see some interesting properties
of this invariant. We will obtain a closed formula for computing the invar
iant for a family of modules of the symmetric group and for trivial source
modules of a finite group. Benson and Symonds conjectured that the growth
of the non-projective part of tensor powers of a module is linear recursi
ve. We will also see some results towards this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serin Hong (Univ. of Michigan)
DTSTART:20211207T210000Z
DTEND:20211207T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/30
DESCRIPTION:Title: Classification theorems for vector bundles on the Fargues-Fontaine
curve\nby Serin Hong (Univ. of Michigan) as part of University of Ariz
ona Algebra and Number Theory Seminar\n\n\nAbstract\nThe Fargues-Fontaine
curve has played a pivotal role in the recent development of arithmetic ge
ometry. Most notably\, the work of Fargues-Scholze constructs the local La
nglands correspondence in a form of the geometric Langlands correspondence
for the Fargues-Fontaine curve. In addition\, Fargues shows that the Farg
ues-Fontaine curve provides a geometric interpretation for Galois cohomolo
gy of local fields and much of the classical p-adic Hodge theory. \n\nIn t
his talk\, we discuss several classification theorems for vector bundles o
n the Fargues-Fontaine curve. In particular\, we give a complete classific
ation of all subsheaves\, quotients\, and minuscule modifications of a giv
en vector bundle on the Fargues-Fontaine curve. We also discuss some appli
cations of these theorems in the context of the local Langlands correspond
ence.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darlayne Addabbo (Univ. of Arizona)
DTSTART:20211116T210000Z
DTEND:20211116T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/31
DESCRIPTION:Title: Zhu algebras and their applications\nby Darlayne Addabbo (Univ.
of Arizona) as part of University of Arizona Algebra and Number Theory Se
minar\n\n\nAbstract\nZhu algebras and their generalizations\, higher level
Zhu algebras\, are associative algebras that are important in the study o
f vertex operator algebras. In this talk\, I will define Zhu algebras and
higher level Zhu algebras and discuss motivation for their study. This tal
k will be expository and prior knowledge of vertex operator algebras will
not be assumed. (Based on joint work with Barron\, Batistelli\, Orosz-Hunz
iker\, Pedi\\'{c}\, and Yamskulna.)\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayan Maiti (Oklahoma State Univ.)
DTSTART:20211130T210000Z
DTEND:20211130T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/32
DESCRIPTION:Title: WEYL’S LAW FOR CUSP FORMS OF ARBITRARY $K_{\\infty}$-TYPE\nby
Ayan Maiti (Oklahoma State Univ.) as part of University of Arizona Algebr
a and Number Theory Seminar\n\n\nAbstract\nLet $M$ be a compact Riemannian
manifold. It was proved by Weyl that number of\nLaplacian eigenvalues les
s than $T$\, is asymptotic to $C(M)T^{dim(M)/2}$\, where $C(M)$ is the\npr
oduct of the volume of $M$\, volume of the unit ball and $(2π)^{−dim(M)
}$. Let $\\Gamma$ be an\narithmetic subgroup of $SL_2(\\mathbb{Z})$ and \\
mathbb{H}^2 be an upper-half plane. When $M = \\Gamma \\backslash \\mathbb
{H}^2$\, Weyl’sasymptotic holds true for the discrete spectrum of Laplac
ian. It was proved by Selberg\, who used his celebrated trace formula.\nLe
t $G$ be a semisimple algebraic group of Adjoint and split type over $\\ma
thbb{Q}$. Let $G(\\mathbb{R})$ be\nthe set of $\\mathbb{R}$-points of $G$.
For simplicity of this exposition let us assume that $\\Gamma \\subset G(
\\mathbb{R})$ be an torsion free arithmetic subgroup. Let $K_{\\infty}$ be
the maximal compact subgroup.\nLet $L^2(\\Gamma \\backslash G(\\mathbb{R}
)$ be space of square integrable $\\Gamma$ invariant functions on $G(\\mat
hbb{R})$. Let $L^2_{cusp}(\\Gamma \\backslash G(\\mathbb{R})$ be the cuspi
dal subspace. Let $M = \\Gamma \\backslash G(\\mathbb{R})/K_{\\infty}$ be
a locally symmetric space. Suppose $d = dim(\\Gamma \\backslash G(\\mathbb
{R})/K_{\\infty})$. Then it was proved by Lindenstrauss and Venkatesh\,\nt
hat number of spherical\, i.e. bi-$K_{\\infty}$ invariant cuspidal Laplaci
an eigenfunctions\, whose\neigenvalues are less than T is asymptotic to $C
(M)T^{dim(M)/2}$\, where $C(M)$ is the same\nconstant as above.\nWe are go
ing to prove the same Weyl’s asymptotic estimates for $K_{\\infty}$-fini
te cusp forms for\nthe above space.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Coupek (Purdue University)
DTSTART:20220201T210000Z
DTEND:20220201T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/33
DESCRIPTION:Title: Crystalline condition for Ainf-cohomology and ramification bounds\nby Pavel Coupek (Purdue University) as part of University of Arizona A
lgebra and Number Theory Seminar\n\n\nAbstract\nLet $p>2$ be a prime and l
et $X$ be a proper smooth formal scheme over $\\mathcal{O}_K$ where $K/\\m
athbb{Q}_p$ is a local number field. In this talk\, we describe a series o
f conditions $(\\mathrm{Cr}_s)$ that provide control on the Galois action
on the Breuil--Kisin cohomology $\\mathrm{R}\\Gamma_{\\Delta}(X/\\mathfrak
{S})$ inside the $A_{\\inf}$--cohomology $\\mathrm{R}\\Gamma_{\\Delta}(X_{
\\mathbb{C}_K}/A_{\\inf})$. When $s=0$\, the resulting condition is essent
ially the crystallinity criterion of Gee and Liu for Breuil--Kisin--Fargue
s $G_K$--modules\, and it leads to an alternative proof of crystallinity o
f the $p$--adic \\'{e}tale cohomology $H^i_{\\mathrm{et}}(X_{\\mathbb{C}_K
}\, \\mathbb{Q}_p)$. Adapting a strategy of Caruso and Liu\, the condition
s $(\\mathrm{Cr}_s)$ for higher $s$ then lead to upper bounds on ramificat
ion of the mod $p$ \\'{e}tale cohomology $H^i_{\\mathrm{et}}(X_{\\mathbb{C
}_K}\, \\mathbb{Z}/p\\mathbb{Z})$\, expressed in terms of $i\, p$ and $e=e
(K/\\mathbb{Q}_p)$ that work without any restrictions on the size of $i$ a
nd $e$.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tarun Dalal (IIT)
DTSTART:20220208T210000Z
DTEND:20220208T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/34
DESCRIPTION:Title: The structure of Drinfeld modular forms of level $\\Gamma_0(T)$ and
applications\nby Tarun Dalal (IIT) as part of University of Arizona A
lgebra and Number Theory Seminar\n\n\nAbstract\nLet $q$ be a power of an o
dd prime $p$. Let $A:=\\mathbb{F}_q[T]$ and $C$ denote the completion of a
n algebraic closure of $\\mathbb{F}_q((\\frac{1}{T}))$. For any ring $R$ w
ith $A \\subseteq R \\subseteq C$\, we let $M(\\Gamma_0(\\mathfrak{n}))_R$
denote the ring of Drinfeld modular forms of level $\\Gamma_0(\\mathfrak{
n})$ with coefficients in $R$.\nIn 1988\, Gekeler showed that the $C$-alge
bra $M(\\mathrm{GL}_2(A))_C$ is isomorphic to $C[X\,Y]$. As a result\, the
properties of the weight filtration for Drinfeld modular forms for $\\mat
hrm{GL}_2(A)$ are studied by Gekeler in 1988 and by Vincent in 2010.\n\nIn
this talk\, we discuss about the structure of the $R$-algebra $M(\\Gamma_
0(T))_R$ and study the properties of the weight filtration for Drinfeld mo
dular forms of level $\\Gamma_0(T)$. As an application\, we prove a result
on mod-$\\mathfrak{p}$ congruences for Drinfeld modular forms of level $\
\Gamma_0(\\mathfrak{p} T)$ for $\\mathfrak{p} \\neq (T)$. This is a joint
work with Narasimha Kumar.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhixiang Wu (Paris-Saclay)
DTSTART:20220215T210000Z
DTEND:20220215T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/35
DESCRIPTION:Title: Companion forms with non-regular weights\nby Zhixiang Wu (Paris
-Saclay) as part of University of Arizona Algebra and Number Theory Semina
r\n\n\nAbstract\nIn general\, for an overconvergent p-adic automorphic for
m of a definite unitary group\, there exist other p-adic automorphic forms
with possibly different weights which are associated with the same Galois
representation (the companion forms). Under the Taylor-Wiles hypothesis\,
we determine all the companion forms whose associated Galois representati
ons are generic crystalline over p and with Hodge-Tate weights possibly no
n-regular. This generalizes the result of Breuil-Hellmann-Schraen in regul
ar cases.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zahi Hazan (Tel Aviv Univ.)
DTSTART:20220125T210000Z
DTEND:20220125T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/36
DESCRIPTION:Title: An Identity Relating Eisenstein Series on General Linear Groups
\nby Zahi Hazan (Tel Aviv Univ.) as part of University of Arizona Algebra
and Number Theory Seminar\n\n\nAbstract\nEisenstein series are key objects
in the theory of automorphic forms. They play an important role in the st
udy of automorphic $L$-functions\, and they figure out in the spectral dec
omposition of the $L^2$-space of automorphic forms. In recent years\, new
constructions of global integrals generating identities relating Eisenstei
n series were discovered. In 2018 Ginzburg and Soudry introduced two gener
al identities relating Eisenstein series on split classical groups (genera
lizing Mœglin 1997\, Ginzburg-Piatetski-Shapiro-Rallis 1997\, and Cai-Fri
edberg-Ginzburg-Kaplan 2016)\, as well as double covers of symplectic grou
ps (generalizing Ikeda 1994\, and Ginzburg-Rallis-Soudry 2011).\n\nWe cons
ider the Kronecker product embedding of two general linear groups\, $\\mat
hrm{GL}{m}(\\mathbb{A})$ and $\\mathrm{GL}{n}(\\mathbb{A})$\, in $\\mathrm
{GL}{mn}(\\mathbb{A})$. Now\, similarly to Ginzburg and Soudry's construct
ion\, we use a degenerate Eisenstein series of $\\mathrm{GL}{mn}(\\mathbb{
A})$ as a kernel function on $\\mathrm{GL}{m}(\\mathbb{A}) \\otimes \\math
rm{GL}{n}(\\mathbb{A})$. Integrating it against a cusp form on $\\mathrm{G
L}{n}(\\mathbb{A})$\, we obtain a 'semi-degenerate' Eisenstein series on $
\\mathrm{GL}{m}(\\mathbb{A})$. Locally\, we find an interesting relation t
o the local Godement-Jacquet integral.\n\nThis construction demonstrates t
he rise of interesting $L$-functions from integrals of doubling type\, as
suggested by the philosophy of Ginzburg and Soudry.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Phillips (University of Arizona)
DTSTART:20220222T210000Z
DTEND:20220222T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/37
DESCRIPTION:Title: Counting Elliptic Curves over Number Fields\nby Tristan Phillip
s (University of Arizona) as part of University of Arizona Algebra and Num
ber Theory Seminar\n\n\nAbstract\nIn this talk I will discuss some results
on counting elliptic curves over number fields. In particular\, I will gi
ve asymptotics for the number of isomorphism classes of elliptic curves ov
er arbitrary number fields with certain prescribed level structures and pr
escribed local conditions. This is done by counting the number of points o
f bounded height on genus zero modular curves which are isomorphic to a w
eighted projective space. This includes the cases of X(N) for N\\in\\{1\,2
\,3\,4\,5\\}\, X_1(N) for N\\in\\{1\,2\,\\dots\,10\,12\\}\, and X_0(N) for
N\\in\\{1\,2\,4\,6\,8\,9\,12\,16\,18\\}. Using these results for counting
elliptic curves over number fields with a prescribed local condition\, on
e can show that the average analytic rank of elliptic curves over any numb
er field K is bounded above by 3\\text{deg}(K)+1/2\, under the assumptions
that all elliptic curves over K are modular and have L-functions which sa
tisfy the Generalized Riemann Hypothesis\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shichen Tang (UC Irvine)
DTSTART:20220412T210000Z
DTEND:20220412T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/38
DESCRIPTION:Title: Slope stability for higher rank Artin--Schreier--Witt towers\nb
y Shichen Tang (UC Irvine) as part of University of Arizona Algebra and Nu
mber Theory Seminar\n\n\nAbstract\nFor a curve in characteristic p\, consi
der the p-adic valuations of the reciprocal roots of its zeta function. Th
ese are rational numbers between 0 and 1\, and they are also the slopes of
the p-adic Newton polygon of the numerator polynomial of the zeta functio
n. In general\, these numbers depend on the curve\, and all we have is an
upper bound and a lower bound for the Newton polygon. But for curves in an
Artin--Schreier--Witt tower satisfying certain conditions\, the slopes be
have in a stable way. It can be shown that the data of the slopes of the N
ewton polygon for all the curves in the tower is determined by the data fo
r finitely many curves\, and for each curve\, the slopes can be explicitly
written as a union of finitely many arithmetic progressions.\n\nLet d be
the rank of the Galois group of this tower as a free Z_p-module. In rank d
=1 case\, this was proved by Kosters--Zhu in 2017. In this talk\, we will
explain the proof for the higher rank case.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keerthi Madapusi (Boston College)
DTSTART:20220315T210000Z
DTEND:20220315T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/39
DESCRIPTION:Title: Derived homomorphisms of abelian varieties and special cycles on Sh
imura varieties\nby Keerthi Madapusi (Boston College) as part of Unive
rsity of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nI will p
resent a 'derived' version of homomorphisms between abelian varieties that
in a sense explains their deformation theory\, and will give some indicat
ion of how this can be applied to give a uniform construction of special c
ycle classes on Shimura varieties of Hodge type using methods from derived
algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyu Zhang (MIT)
DTSTART:20220405T210000Z
DTEND:20220405T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/40
DESCRIPTION:Title: Modularity and Bruhat--Tits stratification\nby Zhiyu Zhang (MIT
) as part of University of Arizona Algebra and Number Theory Seminar\n\n\n
Abstract\nIt is well-known that the theta series of a positive definite qu
adratic lattice is a modular form. In this talk\, I will present new modul
arity results for arithmetic theta series of some “parahoric" hermitian
lattices of sign (n-1\,1)\, which live on unitary Shimura varieties. One k
ey step is to understand a local analog of the story\, which happens on un
itary Rapoport-Zink spaces. I will explain the use of Bruhat-Tits stratifi
cation studied by S. Cho in the computation.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiao He (University of Wisconsin-Madison)
DTSTART:20220426T210000Z
DTEND:20220426T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/41
DESCRIPTION:Title: Kudla-Rapoport conjecture at a ramified prime.\nby Qiao He (Uni
versity of Wisconsin-Madison) as part of University of Arizona Algebra and
Number Theory Seminar\n\n\nAbstract\nKudla-Rapoport conjecture predicts t
hat there is an identity between the intersection number of special cycles
on unitary Rapoport-Zink space and the derivative of local density of cer
tain Hermitian form. However\, the original conjecture was only formulated
for RZ space with hyperspecial level structure over unramified primes. In
this talk\, I will motivate the original conjecture and discuss how to mo
dify it at a ramified prime. Finally\, I will sketch a surprisingly simpl
e proof of the modified conjecture by taking partial Fourier transform. Th
is is a joint work with Chao Li\, Yousheng Shi and Tonghai Yang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Fox (University of Oregon)
DTSTART:20220503T210000Z
DTEND:20220503T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/42
DESCRIPTION:Title: Supersingular Loci of Unitary (2\,m-2) Shimura Varieties\nby Ma
ria Fox (University of Oregon) as part of University of Arizona Algebra an
d Number Theory Seminar\n\n\nAbstract\nThe supersingular locus of a Unitar
y (2\,m-2) Shimura variety parametrizes supersingular abelian varieties of
dimension m\, with an action of a quadratic imaginary field meeting the "
signature (2\,m-2)" condition.\nIn some cases\, for example when m=3 or m=
4\, every irreducible component of the supersingular locus is isomorphic t
o a Deligne-Lusztig variety\, and the intersection combinatorics are gover
ned by a Bruhat-Tits building. We'll consider these cases for motivation\,
and then see how the structure of the supersingular locus becomes very di
fferent for m>4. (The new result in this talk is joint with Naoki Imai.)\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elad Zelingher (Yale University)
DTSTART:20220510T210000Z
DTEND:20220510T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/43
DESCRIPTION:Title: On regularization of integrals of matrix coefficients associated to
spherical Bessel models\nby Elad Zelingher (Yale University) as part
of University of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\n
The Gan-Gross-Prasad conjecture relates a special value of an L-function o
f two cuspidal automorphic representations to the non-vanishing of a certa
in period. The Ichino-Ikeda conjecture is a refinement of this conjecture.
It roughly states that the absolute value of the square of the period in
question can be expressed as a product of the special value of the L-funct
ion and a product of normalized local periods. However\, in order to formu
late this conjecture\, one needs to assume that the representations in que
stion are tempered everywhere\, or else the convergence of the local perio
ds is not guaranteed. The generalized Ramanujan conjecture speculates that
the representations in question (cuspidal automorphic representations lyi
ng in generic packets) are already tempered everywhere. However\, the gene
ralized Ramanujan conjecture is far from being known. In this talk\, I wil
l explain how to drop the assumption that the representations are tempered
almost everywhere. I will explain how to extend the definition of the nor
malized local periods for places where the local components are given by p
rincipal series representations.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Yang (UW-Madison)
DTSTART:20220913T210000Z
DTEND:20220913T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/44
DESCRIPTION:Title: The Tate Conjecture over Finite Fields for Varieties with $h^{2\,0}
=1$.\nby Ziquan Yang (UW-Madison) as part of University of Arizona Alg
ebra and Number Theory Seminar\n\n\nAbstract\nThe past decade has witnesse
d a great advancement on the Tate conjecture for varieties with Hodge numb
er $h^{2\,0}=1$. Charles\, Madapusi-Pera and Maulik completely settled the
conjecture for K3 surfaces over finite fields\, and Moonen proved the Mum
ford-Tate (and hence also Tate) conjecture for more or less\narbitrary $h^
{2\,0}=1$ varieties in characteristic $0$.\nIn this talk\, I will explain
that the Tate conjecture is true for mod $p$ reductions of complex project
ive $h^{2\,0}=1$ varieties when $p >> 0$\, under a mild assumption on modu
li. By refining this general result\, we prove that in characteristic $p \
\geq 5$ the BSD conjecture holds for a height 1 elliptic curve E over a fu
nction field of genus 1\, as long as E is subject to the generic condition
that all singular fibers in its minimal compactification are irreducible.
We also prove the Tate conjecture over finite fields for a class of surfa
ces of general type and a class of Fano varieties. The overall philosophy
is that the connection between the Tate conjecture over finite fields and
the Lefschetz (1\, 1)-theorem over C is very robust for $h^{2\,0}=1$ varie
ties\, and works well beyond the hyperkähler world.\nThis is based on joi
nt work with Paul Hamacher and Xiaolei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pan Yan (U of Arizona)
DTSTART:20220830T210000Z
DTEND:20220830T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/45
DESCRIPTION:Title: L-function for Sp(4)xGL(2) via a non-unique model\nby Pan Yan (
U of Arizona) as part of University of Arizona Algebra and Number Theory S
eminar\n\nLecture held in ENR2 S395.\n\nAbstract\nThe theory of L-function
s of automorphic forms or automorphic representations is a central topic i
n modern number theory. A fruitful way to study L-functions is through an
integral formula\, commonly referred to as an integral representation. The
most common examples of Eulerian integrals are the ones which unfold to a
unique model such as the Whittaker model. Integrals which unfold to non-u
nique models fall outside of this paradigm\, and there are only a few such
examples which are known to represent L-functions. In this talk\, we prov
e a conjecture of Ginzburg and Soudry [IMRN\, 2020] on an integral represe
ntation for the tensor product partial L-function for Sp(4)×GL(2) which i
s derived from the twisted doubling method of Cai\, Friedberg\, Ginzburg\,
and Kaplan. We show that the integral unfolds to a non-unique model and a
nalyze it using the New Way method of Piatetski-Shapiro and Rallis.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Hazeltine (Purdue University)
DTSTART:20220920T210000Z
DTEND:20220920T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/46
DESCRIPTION:Title: Intersections of local Arthur packets for classical groups\nby
Alexander Hazeltine (Purdue University) as part of University of Arizona A
lgebra and Number Theory Seminar\n\n\nAbstract\nRecently\, Atobe gave a re
finement of Moeglin's construction of local Arthur packets for symplectic
and split odd special orthogonal groups. In joint work with Baiying Liu an
d Chi-Heng Lo\, using Atobe's refinement\, we define certain operators whi
ch determine when two local Arthur packets intersect. From these operators
\, we can define an ordering on the set of all local Arthur packets contai
ning a fixed representation for which there is a unique maximal and minima
l element. In this talk\, we will discuss Atobe's construction\, introduce
the operators\, define the unique maximal and minimal element\, and discu
ss how these elements behave with respect to other orderings.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Suresh (U of Arizona)
DTSTART:20220906T210000Z
DTEND:20220906T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/47
DESCRIPTION:Title: Curves with large rank via the PTE problem\nby Arvind Suresh (U
of Arizona) as part of University of Arizona Algebra and Number Theory Se
minar\n\nLecture held in ENR2 S395.\n\nAbstract\nIt is an open question wh
ether the rank of a curve X/Q (i.e. the Mordell--Weil rank of the group of
rational points of the Jacobian J/Q) is bounded in terms of the genus g o
f X. Shioda extended a construction of Mestre to produce infinite families
of g>1 curves over Q with rank at least 4g+7. \nIn this talk\, I will pre
sent a refinement of the Mestre--Shioda construction which leads to some i
nteresting families of curves over Q (and over cyclotomic fields) with ran
k larger than 4g+7. These families are parametrized by certain highly symm
etric rational varieties associated to the Prouhet--Tarry--Escott (PTE) pr
oblem\, a classical problem in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jialiang Zou (University of Michigan)
DTSTART:20221101T210000Z
DTEND:20221101T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/48
DESCRIPTION:Title: On some Hecke algebra modules arising from theta correspondence and
its deformation\nby Jialiang Zou (University of Michigan) as part of
University of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nThi
s talk is based on the joint work with Jiajun Ma and Congling Qiu on theta
correspondence of type I dual pairs over a finite field $F_q$. We study
the Hecke algebra modules arising from theta correspondence between certai
n Harish-Chandra series for these dual pairs. We first show that the norma
lization of the corresponding Hecke algebra is related to the first occurr
ence index\, which leads to proof of the conservation relation. We then st
udy the deformation of this Hecke algebra module at $q=1$ and generalize t
he results of Aubert-Michel-Rouquier and Pan on theta correspondence betwe
en unipotent representations along this way.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Ovenhouse (Yale)
DTSTART:20221108T210000Z
DTEND:20221108T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/49
DESCRIPTION:Title: Super Ptolemy Relation and Double Dimer Covers\nby Nicholas Ove
nhouse (Yale) as part of University of Arizona Algebra and Number Theory S
eminar\n\nLecture held in ENR2-S395.\n\nAbstract\nGiven a quadrilateral in
scribed in a circle\, Ptolemy's Theorem relates the lengths of the diagona
ls and sides. In general\, for an inscribed polygon\, Ptolemy's relation a
llows one to write the length of any diagonal as a Laurent polynomial in t
erms of the lengths of the diagonals coming from some fixed triangulation.
Schiffler and Musiker showed that these Laurent polynomials can be writte
n in terms of perfect matchings (or "dimer covers") of some planar graph.
Recently\, Penner and Zeitlin defined a super-symmetric version of Ptolemy
's relation\, involving anti-commuting variables. In recent work with Musi
ker and Zhang\, we showed that iterated applications of the super Ptolemy
relation gives a sum over double dimer covers of the same planar graph.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soumya Sankar (Ohio State University)
DTSTART:20221115T210000Z
DTEND:20221115T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/50
DESCRIPTION:Title: Counting elliptic curves with a rational N-isogeny\nby Soumya S
ankar (Ohio State University) as part of University of Arizona Algebra and
Number Theory Seminar\n\n\nAbstract\nThe classical problem of counting el
liptic curves with a rational N-isogeny can be phrased in terms of countin
g rational points on certain moduli stacks of elliptic curves. Counting po
ints on stacks poses various challenges\, and I will discuss these along w
ith a few ways to overcome them. I will also talk about height functions o
n certain stacks\, focusing on the theory of heights on stacks developed i
n recent work of Ellenberg\, Satriano and Zureick-Brown. I will then use t
heir framework to count elliptic curves with an N-isogeny for certain N. T
he talk assumes no prior knowledge of stacks and is based on joint work wi
th Brandon Boggess.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Landesman (MIT)
DTSTART:20221014T200000Z
DTEND:20221014T210000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/51
DESCRIPTION:Title: Arithmetic representations on generic curves\nby Aaron Landesma
n (MIT) as part of University of Arizona Algebra and Number Theory Seminar
\n\n\nAbstract\nOver the last century\, the Hodge and Tate conjectures hav
e inspired much activity in algebraic and arithmetic geometry. These conje
ctures give predictions for when certain topological objects come from geo
metry. Simpson and Fontaine-Mazur introduced non-abelian analogs of these
conjectures. In joint work with Daniel Litt\, we prove these analogs for l
ow rank local systems on generic curves\, resolving conjectures of Esnault
-Kerz and Budur-Wang as well as answering questions of Kisin and Whang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heidi Goodson (Brooklyn College (CUNY))
DTSTART:20221129T210000Z
DTEND:20221129T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/52
DESCRIPTION:Title: Degeneracy and Sato-Tate Groups in Dimension Greater than 3\nby
Heidi Goodson (Brooklyn College (CUNY)) as part of University of Arizona
Algebra and Number Theory Seminar\n\n\nAbstract\nThe term degenerate is us
ed to describe abelian varieties whose Hodge rings contain exceptional cyc
les -- Hodge cycles that are not generated by divisor classes. We can see
the effect of the exceptional cycles on the structure of an abelian variet
y through its Mumford-Tate group\, Hodge group\, and Sato-Tate group. In t
his talk I will discuss degeneracy through these different but related len
ses\, specializing to Jacobians of hyperelliptic curves of the form $y^2=x
^m−1$. Together\, we will explore the various forms of degeneracy for se
veral examples\, each illustrating different phenomena that can occur.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Disegni (Ben-Gurion Univ. of the Negev)
DTSTART:20221018T170000Z
DTEND:20221018T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/53
DESCRIPTION:Title: Theta cycles\nby Daniel Disegni (Ben-Gurion Univ. of the Negev)
as part of University of Arizona Algebra and Number Theory Seminar\n\n\nA
bstract\nI will introduce ‘canonical’ algebraic cycles for motives M e
njoying a certain symmetry - for instance\, some symmetric powers of elli
ptic curves. The construction is based on works of Kudla and Liu on some (
conjecturally modular) theta series valued in Chow groups of Shimura varie
ties. The cycles have Heegner-point-like features that allow\, under some
assumptions\, to establish an analogue of the BSD conjecture for M at an o
rdinary prime p. Namely\, if the p-adic L-function of M vanishes at 0 to o
rder exactly 1\, then the Selmer group of M has rank 1 and it is generated
by classes of algebraic cycles. Partly joint work with Yifeng Liu.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Wan (Rutgers University – Newark)
DTSTART:20230112T210000Z
DTEND:20230112T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/54
DESCRIPTION:Title: Period integrals and multiplicities for some strongly tempered sphe
rical varieties\nby Chen Wan (Rutgers University – Newark) as part o
f University of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nI
n this talk I will discuss the local and global conjectures for some stron
gly tempered spherical varieties. Both conjectures are very similar to the
Gan-Gross-Prasad models. More specifically\, globally the square of the p
eriod integrals should be related to the central value of some L-functions
of symplectic type. Locally each tempered L-packet should contain a uniqu
e distinguished element with multiplicity one and the unique distinguished
element should be determined by certain epsilon factors (i.e. epsilon dic
hotomy). I will also discuss the proof of the local conjecture in many cas
es. This is a joint work with Lei Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baiying Liu (Purdue)
DTSTART:20230221T210000Z
DTEND:20230221T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/55
DESCRIPTION:Title: Recent progress on certain problems related to local Arthur packets
of classical groups\nby Baiying Liu (Purdue) as part of University of
Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nIn this talk\, I
will introduce recent progress made on certain problems related to local
Arthur packets of classical groups. First\, I will introduce my joint work
with Freydoon Shahidi towards Jiang's conjecture on the wave front sets o
f representations in local Arthur packets of classical groups\, which is a
natural generalization of Shahidi's conjecture\, confirming the relation
between the structure of wave front sets and the local Arthur parameters.
Then\, I will introduce my joint work with my students Alexander Hazeltine
and Chi-Heng Lo on the intersection problem of local Arthur packets for s
ymplectic and split odd special orthogonal groups\, with applications to t
he Enhanced Shahidi's conjecture and the closure relation conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Gao (UC Santa Cruz)
DTSTART:20230131T210000Z
DTEND:20230131T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/56
DESCRIPTION:Title: p-adic representations and simplicial balls in Bruhat-Tits building
s\nby Xu Gao (UC Santa Cruz) as part of University of Arizona Algebra
and Number Theory Seminar\n\n\nAbstract\np-adic representations are import
ant objects in number theory\, and stable lattices serve as a connection b
etween the study of ordinary and modular representations. These stable lat
tices can be understood as stable vertices in Bruhat-Tits buildings. From
this viewpoint\, the study of fixed point sets in these buildings can aid
research on p-adic representations. The simplicial balls\, in particular\,
hold an important role as they possess the most symmetry and fastest grow
th\, and are closely related to the Moy-Prasad filtrations. In this talk\,
I'll explain those new findings\, provide a characterization of such simp
licial balls\, and compute their simplicial volume under certain condition
s.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20230228T210000Z
DTEND:20230228T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/57
DESCRIPTION:Title: Tate Classes and Endoscopy for GSp4\nby Naomi Sweeting (Harvard
) as part of University of Arizona Algebra and Number Theory Seminar\n\nLe
cture held in ENR2 S395.\n\nAbstract\nWeissauer proved using the theory of
endoscopy that the Galois representations associated to classical modular
forms of weight two appear in the middle cohomology of both a modular cur
ve and a Siegel modular threefold. Correspondingly\, there are large famil
ies of Tate classes on the product of these two Shimura varieties\, and it
is natural to ask whether one can construct algebraic cycles giving rise
to these Tate classes. It turns out that a natural algebraic cycle generat
es some\, but not all\, of the Tate classes: to be precise\, it generates
exactly the Tate classes which are associated to generic members of the en
doscopic L-packets on GSp4. In the non-generic case\, one can at least sho
w that all the Tate classes arise from Hodge cycles. I'll explain these re
sults and sketch their proofs\, which rely on the theta correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cheng Chen (University of Minnesota)
DTSTART:20230214T210000Z
DTEND:20230214T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/58
DESCRIPTION:Title: On the local Gross-Prasad conjecture over archimedean local fields<
/a>\nby Cheng Chen (University of Minnesota) as part of University of Ariz
ona Algebra and Number Theory Seminar\n\n\nAbstract\nThe local Gross-Prasa
d conjecture was introduced by Gross and Prasad in the 1990s. The conjectu
re for tempered parameters over non-archimedean local fields was proved by
Waldspurger using the trace formula and twisted formula\, and the conject
ure for generic parameters over non-archimedean local fields was later pro
ved by Mœglin and Waldspurger. I will present my proof for the conjecture
for generic parameters over archimedean local fields\, together with a mu
ltiplicity formula for future applications\, and part of the work (tempere
d cases) is joint with Z. Luo.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danielle Wang (MIT)
DTSTART:20230328T210000Z
DTEND:20230328T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/59
DESCRIPTION:Title: Global twisted GGP conjecture for unramified quadratic extensions\nby Danielle Wang (MIT) as part of University of Arizona Algebra and Nu
mber Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nThe twisted
Gan--Gross--Prasad conjectures consider the restriction of representation
s from GL_n to a unitary group over a quadratic extension E/F. In this tal
k\, I will explain the adaptation of the relative trace formula comparison
used in previous work on the global GGP conjecture for unitary groups\, t
o this twisted version. In particular\, I will discuss the fundamental lem
ma that arises\, which can be used to obtain the global twisted GGP conjec
ture (under some local assumptions) in the case that everything is unramif
ied\, and how it can be reduced to the Jacquet--Rallis fundamental lemma.\
n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Groen (University of Warwick)
DTSTART:20230117T210000Z
DTEND:20230117T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/60
DESCRIPTION:Title: p-Torsion of Abelian varieties in characteristic p\nby Steven G
roen (University of Warwick) as part of University of Arizona Algebra and
Number Theory Seminar\n\n\nAbstract\nLet A be an Abelian variety of dimens
ion g over an algebraically closed field k. We are interested in the group
scheme A[p]\, consisting of the elements of A whose order divides p. If t
he characteristic of k is not p\, then there is only one possibility for A
[p]: as a group it consists of 2g copies of Z/pZ. On the other hand\, if k
has characteristic p\, then there are several distinct possibilities for
A[p]\, called Ekedahl-Oort strata. In particular\, the group will consist
of at most g copies of Z/pZ. An example of an Ekedahl-Oort stratification
is the distinction between ordinary and supersingular elliptic curves. If
the dimension g is higher\, it is natural to ask which Ekedahl-Oort strata
arise from the Jacobian of a curve. In this talk\, we treat both previous
ly known results and new results in this area. In many cases\, we add the
restriction that the curves in question are Artin-Schreier covers.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Yang (RIMS\, Kyoto University)
DTSTART:20230322T010000Z
DTEND:20230322T020000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/61
DESCRIPTION:Title: Moduli spaces of fundamental groups in positive characteristic\
nby Yu Yang (RIMS\, Kyoto University) as part of University of Arizona Alg
ebra and Number Theory Seminar\n\n\nAbstract\nIn the 1980s\, A. Grothendie
ck suggested a theory of arithmetic geometry called "anabelian geometry".
This theory focuses on the following fundamental question: How much inform
ation about algebraic varieties can be carried by their algebraic fundamen
tal groups? The conjectures based on this question are called Grothendieck
's anabelian conjectures which have been studied deeply when the base fiel
ds are arithmetic (e.g. number fields\, p-adic fields\, finite fields\, et
c.) since the 1990s\, and the non-trivial Galois representations play vita
l roles. \n\nOn the other hand\, in 1996\, A. Tamagawa discovered surpri
singly that anabelian phenomena also exist for curves over algebraically c
losed fields of characteristic p>0 (i.e.\, no Galois actions). In this tal
k\, I will explain these kinds of anabelian phenomena from the point of vi
ew of "moduli spaces of fundamental groups" introduced by the speaker\, wh
ich gives a general framework for describing the anabelian phenomena for c
urves over algebraically closed fields of characteristic p.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuhiro Wakabayashi (Osaka Univ.)
DTSTART:20230315T010000Z
DTEND:20230315T020000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/62
DESCRIPTION:Title: Dormant opers and canonical diagonal liftings\nby Yasuhiro Waka
bayashi (Osaka Univ.) as part of University of Arizona Algebra and Number
Theory Seminar\n\n\nAbstract\nIn this talk\, we will discuss dormant opers
\, which are certain flat bundles on an algebraic curve in positive charac
teristic related to linear differential equations having a full set of sol
utions. The moduli theory of such objects (in special cases) has been stud
ied in the context of p-adic Teichmüller theory\, and has many different
aspects\, including the connections with the intersection theory of Quot s
chemes and the combinatorics of colored graphs\, as well as rational polyt
opes. One goal of my research is to solve the counting problem of dormant
opers while deepening our understanding of these connections. As an approa
ch to that problem in the case of prime-power characteristic\, I have rece
ntly been thinking about a kind of arithmetic lifting of dormant opers\, w
hich I call “canonical diagonal lifting”. I would like to talk about t
hat topic\, starting with some basics on flat bundles.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radu Laza (Stony Brook)
DTSTART:20230502T210000Z
DTEND:20230502T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/64
DESCRIPTION:Title: Deformations of mildly singular Calabi-Yau varieties\nby Radu L
aza (Stony Brook) as part of University of Arizona Algebra and Number Theo
ry Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nThe well-known Bogom
olov-Tian-Todorov theorem says that the deformations of Calabi-Yau manifol
ds are unobstructed. The unobstructedness of deformations continues to hol
d Calabi-Yau varieties with ordinary nodal singularities (Kawamata\, Ran\,
Tian)\, but surprisingly the smoothability of such varieties is subject t
o topological constrains. These obstructions to the existence of smoothing
s are linear in dimension 3 (Friedman)\, and non-linear in higher dimensio
ns (Rollenske-Thomas).\n\nIn this talk\, I will give vast generalizations
to both the unobstructedness of deformations for mildly singular Calabi-Ya
u varieties\, and to the constraints on the existence of smoothings for ce
rtain classes of singular Calabi-Yau varieties. Additionally\, I will esta
blish the proper context for these results: the Hodge theory of degenerati
ons with prescribed singularities (specifically higher rational/higher Du
Bois and liminal singularities).\n\nThis is joint work with Robert Friedma
n.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arvind Suresh (U of Arizona)
DTSTART:20230418T210000Z
DTEND:20230418T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/65
DESCRIPTION:Title: Realizing Galois representations in abelian varieties by specializa
tion\nby Arvind Suresh (U of Arizona) as part of University of Arizona
Algebra and Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstra
ct\nWe present a strategy for constructing abelian varieties J/K which rea
lize a given rational Galois representation $\\rho : G_K \\to GL_n(Q)$\, i
.e. such that $\\rho$ is a subrep of $J(\\Kbar)\\otimes \\Q$. When $\\rho$
is the trivial rep.\, then $J/K$ realizes $\\rho$ if and only if $J(K)$ i
s of rank at least $n$\, and such families are usually constructed by the
specialization method pioneered by Neron. Our strategy consists in taking
an already existing construction of abelian varieties with large rank and\
, provided there is enough symmetry\, twisting the construction to obtain
non-trivial Galois actions on the points. After twisting\, we use a simple
generalization of the classical Neron specialization theorem (from trivia
l reps. to non-trivial reps.) We apply this procedure to a construction of
Mestre and Shioda to prove the following: Given a representation $\\rho:
G_K \\to GL_n(\\Q)$\, there exist infinitely many absolutely simple absolu
tely abelian varieties $J/K$ (which are in fact Jacobians of hyperelliptic
curves) such that $\\rho$ is a subrep. of the $G_K$ rep on $J(\\Kbar) \\o
times_{\\Z} \\Q$.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Wear (University of Utah)
DTSTART:20230411T210000Z
DTEND:20230411T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/67
DESCRIPTION:Title: The conjugate uniformization via 1-motives\nby Peter Wear (Univ
ersity of Utah) as part of University of Arizona Algebra and Number Theory
Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nGiven an abelian varie
ty $A$ over a finite extension $K$ of $\\mathbb{Q}_p$\, Fontaine construct
ed an integration map from the Tate module of A to its Lie algebra. This m
ap gives the splitting of the Hodge-Tate short exact sequence. Recent work
of Iovita-Morrow-Zaharescu extends this integration map to the $\\overlin
e{K}$ points of the perfectoid universal cover of $A$. They used this resu
lt to give a uniformization of the $\\mathcal{O}_{\\overline K}$ points of
the underlying $p$-divisible group. In this talk\, we explain joint work
with Sean Howe and Jackson Morrow in which we give a different perspective
on this uniformization using 1-motives. We will first give some intuition
from the complex uniformization of semi-abelian varieties and some backgr
ound and motivation on $p$-divisible groups. Then we will explain how to c
onstruct the $p$-divisible group of a 1-motive and how this gives the desi
red uniformization. Finally\, we will point out some interesting geometric
features of this map: it embeds the rigid analytic points of a $p$-divisi
ble group into an etale cover of a negative Banach-Colmez space.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liyang Yang (Princeton)
DTSTART:20230829T210000Z
DTEND:20230829T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/68
DESCRIPTION:Title: Bessel Periods for $U(3)\\times U(2)$: Nonvanishing and Equidistrib
ution\nby Liyang Yang (Princeton) as part of University of Arizona Alg
ebra and Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\n
We will introduce a simple relative trace formula to compute the second mo
ment of Bessel periods associated to $U(3)\\times U(2)$. Moreover\, we exp
lore its arithmetic implications\, addressing the quantitative nonvanishin
g problem\, and the distribution in the weighted vertical Sato-Tate contex
t. This is joint work with Dinakar Ramakrishnan and Philippe Michel.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Zhang (MIT)
DTSTART:20231121T210000Z
DTEND:20231121T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/69
DESCRIPTION:Title: Harris–Venkatesh plus Stark\nby Robin Zhang (MIT) as part of
University of Arizona Algebra and Number Theory Seminar\n\nLecture held in
ENR2 S395.\n\nAbstract\nThe class number formula describes the behavior o
f the Dedekind zeta function at $s = 0$ and $s = 1$. The Stark and Gross c
onjectures extend the class number formula\, describing the behavior of Ar
tin $L$-functions and $p$-adic $L$-functions at $s = 0$ and $s = 1$ in ter
ms of units. The Harris–Venkatesh conjecture describes the residue of St
ark units modulo $p$\, giving a modular analogue to the Stark and Gross co
njectures while also serving as the first verifiable part of the broader c
onjectures of Venkatesh\, Prasanna\, and Galatius. In this talk\, I will d
raw an introductory picture\, formulate a unified conjecture combining Har
ris–Venkatesh and Stark for weight one modular forms\, and describe the
proof of this in the imaginary dihedral case.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finn McGlade (UCSD)
DTSTART:20231114T210000Z
DTEND:20231114T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/70
DESCRIPTION:Title: A Level 1 Maass Spezialschar for Modular Forms on $\\mathrm{SO}_8$<
/a>\nby Finn McGlade (UCSD) as part of University of Arizona Algebra and N
umber Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nThe classi
cal Spezialschar is the subspace of the space of holomorphic modular forms
on $\\mathrm{Sp}_4(\\mathbb{Z})$ whose Fourier coefficients satisfy a par
ticular system of linear equations. An equivalent characterization of the
Spezialschar can be obtained by combining work of Maass\, Andrianov\, and
Zagier\, whose work identifies the Spezialschar in terms of a theta-lift f
rom $\\widetilde{\\mathrm{SL}_2}$. Inspired by work of Gan-Gross-Savin\, W
eissman and Pollack have developed a theory of modular forms on the split
adjoint group of type D_4. In this setting we describe an analogue of the
classical Spezialschar\, in which Fourier coefficients are used to charact
erize those modular forms which arise as theta lifts from holomorphic form
s on $\\mathrm{Sp}_4(\\mathbb{Z})$.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serin Hong (University of Arizona)
DTSTART:20230905T210000Z
DTEND:20230905T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/71
DESCRIPTION:Title: Newton stratification on the $B_{dR}^+$-Grassmannian\nby Serin
Hong (University of Arizona) as part of University of Arizona Algebra and
Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nThe $B_{d
R}^+$-Grassmannian is a p-adic (perfectoid) analogue of the classical affi
ne Grassmannian. It plays an important role in the geometrization of the l
ocal Langlands program and the study of Shimura varieties. In this talk\,
we discuss its geometry in terms of a natural stratification called the Ne
wton stratification\, with a particular focus on the case where the underl
ying group is GLn.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junehyuk Jung (Brown)
DTSTART:20231107T210000Z
DTEND:20231107T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/72
DESCRIPTION:Title: Zelditch’s trace formula and effective Bowen’s theorem\nby
Junehyuk Jung (Brown) as part of University of Arizona Algebra and Number
Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nIn 1989\, Zeldit
ch considered the trace of an invariant operator composed with a pseudo-di
fferential operator. The resulting trace formula turned out to be extremel
y useful in studying the distribution of closed geodesics on hyperbolic su
rfaces. I will demonstrate the simplest case of the proof\, and discuss ho
w things can be generalized to higher dimensional hyperbolic manifolds. Th
is is a joint work with Insung Park.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230912T210000Z
DTEND:20230912T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/73
DESCRIPTION:by TBA as part of University of Arizona Algebra and Number The
ory Seminar\n\nLecture held in ENR2 S395.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230919T210000Z
DTEND:20230919T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/74
DESCRIPTION:by TBA as part of University of Arizona Algebra and Number The
ory Seminar\n\nLecture held in ENR2 S395.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirti Joshi (University of Arizona)
DTSTART:20231003T210000Z
DTEND:20231003T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/76
DESCRIPTION:Title: Construction of Arithmetic Teichmuller Spaces and applications to M
ochizuki's Theory\nby Kirti Joshi (University of Arizona) as part of U
niversity of Arizona Algebra and Number Theory Seminar\n\nLecture held in
ENR2 S395.\n\nAbstract\nThis talk is intended as an semi-informal introduc
tion to my recent work on Arithmetic Teichmuller Spaces and its relationsh
ip to Mochizuki's Inter Universal Teichmuller Theory which is at the cente
r of his work on the abc-conjecture. My work establishes a p-adic analog o
f classical Teichmuller Theory of Riemann surfaces. Notably in this theory
\, the etale fundamental group remains fixed (just as in the classical the
ory of Riemann surfaces) while the holomorphic structure varies. Given the
nature of this work and its close relationship to Mochizuki's work\, I ha
ve intentionally divided this talk into two talks on (10/3/2023) and (10/
10/2023) both to provide a gentle introduction to my ideas and also to all
ow for plenty of questions. [There will be plenty of technical material pr
esented as well but the emphasis will be on providing an introduction to m
y ideas.] I will also include a discussion of Mochizuki-Scholze-Stix issu
es in the context of Mochizuki's Theory (and answer any questions in this
context).\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kirti Joshi (University of Arizona)
DTSTART:20231010T210000Z
DTEND:20231010T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/77
DESCRIPTION:Title: Construction of Arithmetic Teichmuller Spaces and applications to M
ochizuki's Theory\nby Kirti Joshi (University of Arizona) as part of U
niversity of Arizona Algebra and Number Theory Seminar\n\nLecture held in
ENR2 S395.\n\nAbstract\nThis talk is intended as an semi-informal introduc
tion to my recent work on Arithmetic Teichmuller Spaces and its relationsh
ip to Mochizuki's Inter Universal Teichmuller Theory which is at the cente
r of his work on the abc-conjecture. My work establishes a p-adic analog o
f classical Teichmuller Theory of Riemann surfaces. Notably in this theory
\, the etale fundamental group remains fixed (just as in the classical the
ory of Riemann surfaces) while the holomorphic structure varies. Given the
nature of this work and its close relationship to Mochizuki's work\, I ha
ve intentionally divided this talk into two talks on (10/3/2023) and (10/
10/2023) both to provide a gentle introduction to my ideas and also to all
ow for plenty of questions. [There will be plenty of technical material pr
esented as well but the emphasis will be on providing an introduction to m
y ideas.] I will also include a discussion of Mochizuki-Scholze-Stix issu
es in the context of Mochizuki's Theory (and answer any questions in this
context).\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Fu (California Institute of Technology)
DTSTART:20231031T210000Z
DTEND:20231031T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/78
DESCRIPTION:Title: How do generic properties spread?\nby Yu Fu (California Institu
te of Technology) as part of University of Arizona Algebra and Number Theo
ry Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nGiven a family of al
gebraic varieties\, a natural question to ask is what type of properties o
f the generic fiber\, and how those properties extend to other fibers. Let
's explore this topic from an arithmetic point of view by looking at the
scenario: Suppose we have a 1-dimensional family of pairs of elliptic cur
ves over a number field $K$\, with the generic fiber of this family bein
g a pair of non-isogenous elliptic curves. Furthermore\, suppose the (proj
ective) height of the parametrizer is less than or equal to $B$. One may a
sk how does the property of "being isogenous" extends to the special fiber
s. Can we give a quantitative estimation for the number of specializations
of height at most $B$\, such that the two elliptic curves at the speciali
zations are isogenous?\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Eischen (University of Oregon)
DTSTART:20240312T210000Z
DTEND:20240312T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/79
DESCRIPTION:Title: Algebraic and p-adic aspects of L-functions\, with a view toward Sp
in L-functions for GSp_6\nby Ellen Eischen (University of Oregon) as p
art of University of Arizona Algebra and Number Theory Seminar\n\nLecture
held in ENR2 S395.\n\nAbstract\nI will discuss recent developments and ong
oing work for algebraic and p-adic aspects of L-functions. Interest in p-a
dic properties of values of L-functions originated with Kummer’s study o
f congruences between values of the Riemann zeta function at negative odd
integers\, as part of his attempt to understand class numbers of cyclotomi
c extensions. After presenting an approach to studying analogous congruenc
es for more general classes of L-functions\, I will conclude by introducin
g ongoing joint work of G. Rosso\, S. Shah\, and myself (concerning Spin L
-functions for GSp 6). I will explain how this work fits into the context
of earlier developments\, while also indicating where new technical challe
nges arise. All who are curious about this topic are welcome at this talk\
, even without prior experience with p-adic L-functions or Spin L-function
s.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bhawesh Mishra (University of Memphis)
DTSTART:20231205T210000Z
DTEND:20231205T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/81
DESCRIPTION:Title: A Generalization of the Grunwald-Wang Theorem for $n^{th}$ Powers\nby Bhawesh Mishra (University of Memphis) as part of University of Ari
zona Algebra and Number Theory Seminar\n\n\nAbstract\nThe Grunwald-Wang th
eorem for $n^{th}$ powers states that a rational number $a$ is an $n^{th}$
power in $\\mathbb{Q}_{p}$ for almost every prime $p$ if and only if eith
er $a$ is a perfect $n^{th}$ power in rationals or $8 \\mid n$ and $a = 2^
{\\frac{n}{2}} \\cdot b^{n}$ for some rational $b$. We will discuss an app
ropriate generalization of this theorem from a single rational number to a
subset $A$ of rational numbers. Let $n$ be an odd number and $q$ be the s
mallest prime dividing $n$. A finite subset $A$ of rationals with cardinal
ity $\\leq q$ contains a $n^{th}$ power in $\\mathbb{Q}_{p}$ for almost ev
ery prime $p$ if and only if $A$ contains a perfect $n^{th}$ power. For ev
en $n$\, the result is analogous - up to a short list of exceptions\, as e
vident in the Grunwald-Wang theorem. \n\nIf time permits\, we will also sh
ow that this generalization is optimal\, i.e.\, for every $n \\geq 2$\, th
ere are infinitely many subsets $A$ of rationals of cardinality $q+1$ that
contain a $n^{th}$ power in $\\mathbb{Q}_{p}$ for almost every prime $p$
but neither contain a perfect $n^{th}$ power nor fall under the finite lis
t of exceptions.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandi Schaeffer Fry (University of Denver)
DTSTART:20240402T210000Z
DTEND:20240402T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/82
DESCRIPTION:by Mandi Schaeffer Fry (University of Denver) as part of Unive
rsity of Arizona Algebra and Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Miller (UC Santa Cruz)
DTSTART:20240116T210000Z
DTEND:20240116T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/83
DESCRIPTION:by Sam Miller (UC Santa Cruz) as part of University of Arizona
Algebra and Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryden Cais (University of Arizona)
DTSTART:20240123T210000Z
DTEND:20240123T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/84
DESCRIPTION:Title: Iwasawa theory for class group schemes in characteristic p\nby
Bryden Cais (University of Arizona) as part of University of Arizona Algeb
ra and Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nIn
a landmark 1959 paper\, Iwasawa studied the growth of class groups in Z_p
-towers of number fields\, establishing a remarkable formula for the exact
power of p dividing the order of the class group of the n-th layer of the
tower. Iwasawa's work was inspired by a profound analogy between number f
ields and function fields over finite fields. In this setting\, the direct
analogue of Iwasawa theory is the study of class groups in Z_p-towers of
global function fields over finite fields k of characteristic p\, and an a
nalogous formula for the order of p dividing the class group was establish
ed by Mazur and Wiles in 1983. An extraordinary feature of this function f
ield setting is that the class group can be realized as the k-rational poi
nts of an algebraic variety---the Jacobian. We will briefly survey some o
f this history\, and introduce a novel analogue of Iwasawa theory for func
tion fields by studying not just the k-points of these Jacobians\, but the
ir full p-torsion group schemes\, which are much richer\, geometric object
s having no analogue in the number field setting.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doug Ulmer (University of Arizona)
DTSTART:20240130T210000Z
DTEND:20240130T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/85
DESCRIPTION:Title: p-torsion for p-covers\nby Doug Ulmer (University of Arizona) a
s part of University of Arizona Algebra and Number Theory Seminar\n\nLectu
re held in ENR2 S395.\n\nAbstract\nWe consider Z/pZ covers of curves in ch
aracteristic p and the p-torsion group schemes of their Jacobians. Such c
overs are the building blocks of the towers Bryden Cais spoke about last w
eek. Our aim is to understand the full Dieudonne structure\, not just the
kernel of Frobenius.\n\nWe will give more details on groups schemes kille
d by p and their Dieudonne modules\, introduce the Ekedahl-Oort stratifica
tion of Ag\, the moduli space of abelian varieties\, and state basic quest
ions on how it interacts with the locus of Jacobians in Ag. (This gives a
n introduction to the AWS2024 courses of Karemaker and Pries.) We end by
stating a structural result on Dieudonne modules of p-covers and some of t
he restrictions it places on group schemes.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (University of Maryland)
DTSTART:20240416T210000Z
DTEND:20240416T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/86
DESCRIPTION:Title: Comparing local Langlands correspondences\nby Peter Dillery (Un
iversity of Maryland) as part of University of Arizona Algebra and Number
Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nBroadly speaking
\, for G a connected reductive group over a local field F\, the Langlands
program is the endeavor of relating Galois representations (more precisely
\, "L-parameters"---certain homomorphisms from the Weil-Deligne group of F
to the dual group of G) to admissible smooth representations of G(F). The
re is conjectured to be a finite-to-one map from irreducible smooth repres
entations of G(F) to L-parameters\, and there are many different approache
s to parametrizing the fibers of such a map. \n\nThe goal of this talk is
to explain some of these approaches\; a special focus will be placed on t
he so-called "isocrystal" and "rigid" local Langlands correspondences. The
former is best suited for building on the recent breakthroughs of Fargues
-Scholze\, while the latter is the broadest and is well-suited to endoscop
y (a version of functoriality). We will discuss a proof of the equivalence
of these two approaches\, initiated by Kaletha for p-adic fields and exte
nded to arbitrary nonarchimedean local fields in my recent work.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Kaplan (University of California\, Irvine)
DTSTART:20240328T170000Z
DTEND:20240328T180000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/87
DESCRIPTION:Title: Codes from varieties over finite fields\nby Nathan Kaplan (Univ
ersity of California\, Irvine) as part of University of Arizona Algebra an
d Number Theory Seminar\n\nLecture held in ENR2 N595.\n\nAbstract\nThere a
re $q^{20}$ homogeneous cubic polynomials in four variables with coefficie
nts in the finite field $F_q$. How many of them define a cubic surface wit
h $q^2+7q+1$ $F_q$-rational points? What about other numbers of rational p
oints? How many of the $q^{20}$ pairs of homogeneous cubic polynomials in
three variables define cubic curves that intersect in 9 $F_q$-rational poi
nts? The goal of this talk is to explain how ideas from the theory of erro
r-correcting codes can be used to study families of varieties over a fixed
finite field. We will not assume any previous familiarity with coding the
ory. We will start from the basics and emphasize examples.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Garcia (University College London)
DTSTART:20240409T210000Z
DTEND:20240409T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/88
DESCRIPTION:Title: Elliptic units for complex cubic fields\nby Luis Garcia (Univer
sity College London) as part of University of Arizona Algebra and Number T
heory Seminar\n\n\nAbstract\nThe elliptic Gamma function — a generalizat
ion of the q-Gamma function\, which is itself the q-analog of the ordinary
Gamma function — is a meromorphic special function in several variables
that mathematical physicists have shown to satisfy modular functional equ
ations under SL(3\,Z). In this talk I will present evidence (numerical and
theoretical) that products of values of this function are often algebraic
numbers that satisfy explicit reciprocity laws and are related to derivat
ives of Hecke L-functions of cubic fields at s=0. We will discuss the rela
tion to Stark's conjectures and will see that this function conjecturally
allows to extend the theory of complex multiplication to complex cubic fie
lds as envisioned by Hilbert's 12th problem. This is joint work with Nicol
as Bergeron and Pierre Charollois.\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linli Shi (University of Connecticut)
DTSTART:20241015T210000Z
DTEND:20241015T220000Z
DTSTAMP:20260404T095735Z
UID:UAANTS/89
DESCRIPTION:by Linli Shi (University of Connecticut) as part of University
of Arizona Algebra and Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UAANTS/89/
END:VEVENT
END:VCALENDAR