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BEGIN:VEVENT
SUMMARY:Ciaran Schembri (Dartmouth College)
DTSTART:20221115T130000Z
DTEND:20221115T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/1
DESCRIPTION:Title: Torsion points on abelian surfaces with many endomorphisms\nby Ciaran Schembri (Dartmouth College) as part of Sheffield Number The
ory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nIn a cele
brated work Mazur classified which torsion subgroups can occur for ellipti
c curves defined over the rationals. A natural analogue is to consider sur
faces with geometric endomorphisms by a quaternion order\, since the assoc
iated moduli space is 1-dimensional. In this talk I will discuss progress
towards classifying which torsion subgroups are possible for these surface
s. This is joint work (in progress) with Jef Laga\, Ari Shnidman and John
Voight.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peiyi Cui (University of East Anglia)
DTSTART:20221122T130000Z
DTEND:20221122T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/2
DESCRIPTION:Title: Decompositions of the category of $\\ell$-modular representa
tions of $SL_n(F)$\nby Peiyi Cui (University of East Anglia) as part o
f Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\
n\nAbstract\nLet $F$ be a $p$-adic field\, and k an algebraically closed f
ield of characteristic $\\ell$ different from $p$. In this talk\, we will
first give a category decomposition of $Rep_k(SL_n(F))$\, the category of
smooth $k$-representations of $SL_n(F)$\, with respect to the $GL_n(F)$-eq
uivalent supercuspidal classes of $SL_n(F)$\, which is not always a block
decomposition in general. We then give a block decomposition of the superc
uspidal subcategory\, by introducing a partition on each $GL_n(F)$-equival
ent supercuspidal class through type theory\, and we interpret this partit
ion by the sense of $\\ell$-blocks of finite groups. We give an example wh
ere a block of $Rep_k(SL_2(F))$ is defined with respect to several $SL_2(F
)$-equivalent supercuspidal classes\, which is different from the case whe
re $\\ell$ is zero. We end this talk by giving a prediction on the block d
ecomposition of $Rep_k(A)$ for a general $p$-adic group $A$.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Pozzi (Imperial College London)
DTSTART:20221129T130000Z
DTEND:20221129T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/3
DESCRIPTION:Title: Tame triple product periods\nby Alice Pozzi (Imperial Co
llege London) as part of Sheffield Number Theory Seminar\n\nLecture held i
n J-11 Hicks Building.\n\nAbstract\nA recent conjecture proposed by Harris
and Venkatesh relates the action of derived Hecke operators on the space
of weight one modular forms to certain Stark units. In this talk\, I will
explain how this can be rephrased as a conjecture about "tame" analogues o
f triple product periods for a triple of mod p modular forms of weights (2
\,1\,1). I will then present an elliptic counterpart to this conjecture re
lating a tame triple product period to a regulator for global points of el
liptic curves. This is joint work with Henri Darmon.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadir Matringe (Université Paris Cité)
DTSTART:20221108T130000Z
DTEND:20221108T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/4
DESCRIPTION:Title: Symmetric periods for automorphic forms on unipotent groups<
/a>\nby Nadir Matringe (Université Paris Cité) as part of Sheffield Numb
er Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nLet
$G$ be an algebraic group defined over a number field $k$ with ring of ad
eles $\\mathbb{A}$\, and let $\\sigma$ be a $k$-involution of $G$. Studyin
g the nonvanishing of (possible regularizations of) the period integral \n
$p: \\phi \\mapsto \\int_{G^\\sigma(k) \\backslash G^\\sigma(\\mathbb{A}}\
\phi(h)dh$ on topologically irreducible submodules of $L^2(G(k) \\backslas
h G(\\mathbb{A}))$ is a very popular topic when $G$ is reductive. Here I w
ill focus on the case where $G$ is unipotent\, and explain that $p$ does n
ot vanish on such a submodule $\\Pi$ if and only if $\\Pi^\\vee=\\Pi^\\sig
ma$.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (University of Sheffield)
DTSTART:20221004T120000Z
DTEND:20221004T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/5
DESCRIPTION:Title: The integral Bernstein centre\nby Rob Kurinczuk (Univers
ity of Sheffield) as part of Sheffield Number Theory Seminar\n\nLecture he
ld in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maleeha Khawaja (University of Sheffield)
DTSTART:20221018T120000Z
DTEND:20221018T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/6
DESCRIPTION:Title: The Fermat equation over real biquadratic fields\nby Mal
eeha Khawaja (University of Sheffield) as part of Sheffield Number Theory
Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nWe will take
a look at an overview of the so called modular approach to Diophantine equ
ations. We will particularly focus on the obstacles that arise when applyi
ng this approach to the Fermat equation over real biquadratic fields\, usi
ng $\\Q(\\sqrt{2}\, \\sqrt{3})$ as an illustrating example.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Newton (King's College London)
DTSTART:20221206T130000Z
DTEND:20221206T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/7
DESCRIPTION:Title: Distribution of genus numbers of abelian number fields\n
by Rachel Newton (King's College London) as part of Sheffield Number Theor
y Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nLet K be a
number field and let L/K be an abelian extension. The genus field of L/K i
s the largest extension of L which is unramified at all places of L and ab
elian as an extension of K. The genus group is its Galois group over L\, w
hich is a quotient of the class group of L\, and the genus number is the s
ize of the genus group. We study the quantitative behaviour of genus numbe
rs as one varies over abelian extensions L/K with fixed Galois group. We g
ive an asymptotic formula for the average value of the genus number and sh
ow that any given genus number appears only 0% of the time. This is joint
work with Christopher Frei and Daniel Loughran.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bodan Arsovski (University College London)
DTSTART:20221214T140000Z
DTEND:20221214T150000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/8
DESCRIPTION:Title: The p-adic Kakeya conjecture\nby Bodan Arsovski (Univers
ity College London) as part of Sheffield Number Theory Seminar\n\nLecture
held in J-11 Hicks Building.\n\nAbstract\nThe classical Kakeya conjecture
states that all compact subsets of ℝ^n containing a line segment of unit
length in every direction have full Hausdorff dimension. In this talk we
prove the natural analogue of the classical Kakeya conjecture over the p-a
dic numbers — more specifically\, that all compact subsets of ℚ_p^n co
ntaining a line segment of unit length in every direction have full Hausdo
rff dimension — a conjecture which was first discussed in the 1990s by J
ames Wright. More generally\, in this talk we prove the p-adic analogue of
the Kakeya maximal conjecture\, which is a functional version of the Kake
ya conjecture proposed by Jean Bourgain in the 1990s.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (Imperial College London)
DTSTART:20230328T120000Z
DTEND:20230328T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/9
DESCRIPTION:Title: Towards a theta correspondence in families for type II dual
pairs\nby Justin Trias (Imperial College London) as part of Sheffield
Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\
nThis is current work with Gil Moss. The classical local theta corresponde
nce for p-adic reductive dual pairs defines a bijection between prescribed
subsets of irreducible smooth complex representations coming from two gro
ups (H\,H')\, forming a dual pair in a symplectic group. Alberto Mínguez
extended this result for type II dual pairs\, i.e. when (H\,H') is made of
general linear groups\, to representations with coefficients in an algebr
aically closed field of characteristic l as long as the characteristic l d
oes not divide the pro-orders of H and H'. For coefficients rings like Z[1
/p]\, we explain how to build a theory in families for type II dual pairs
that is compatible with reduction to residue fields of the base coefficien
t ring\, where central to this approach is the integral Bernstein centre.
We translate some weaker properties of the classical correspondence\, such
as compatibility with supercuspidal support\, as a morphism between the i
ntegral Bernstein centres of H and H' and interpret it for the Weil repres
entation. In general\, we only know that this morphism is finite though we
may expect it to be surjective. This would result in a closed immersion b
etween the associated affine schemes as well as a correspondence between c
haracters of the Bernstein centre.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Horawa (Oxford)
DTSTART:20230207T130000Z
DTEND:20230207T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/10
DESCRIPTION:Title: Motivic action conjectures\nby Aleksander Horawa (Oxfor
d) as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hick
s Building.\n\nAbstract\nA surprising property of the cohomology of locall
y symmetric spaces is that Hecke operators can act on multiple cohomologic
al degrees with the same eigenvalues. A recent series of conjectures propo
ses an arithmetic explanation: a hidden degree-shifting action of a certai
n motivic cohomology group. We will give an overview of these conjectures\
, focusing on the examples of GL_2 over the rational numbers\, real quadra
tic fields\, and imaginary quadratic fields.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (Sheffield)
DTSTART:20230307T130000Z
DTEND:20230307T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/11
DESCRIPTION:Title: Modularity of a certain ``rank-2 attractor'' Calabi-Yau 3-f
old\nby Neil Dummigan (Sheffield) as part of Sheffield Number Theory S
eminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nWe prove that
the 4-dimensional Galois representations associated with a certain Calabi-
Yau threefold are reducible\, with 2-dimensional composition factors comin
g from specific modular forms of weights 2 and 4\, both level 14. This was
essentially conjectured by Meyer and Verrill. It was revisited in its pre
sent form by Candelas\, de la Ossa\, Elmi and van Straten\, whose computat
ions of Euler factors in a whole pencil of Calabi-Yau threefolds highlight
ed this fibre as one of three overwhelmingly likely to be ``rank-2 attract
ors''. The proof is conditional on the truth of their as yet unproved conj
ecture about the correctness of a certain matrix entering into their compu
tations.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Berger (Sheffield)
DTSTART:20230228T130000Z
DTEND:20230228T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/12
DESCRIPTION:by Tobias Berger (Sheffield) as part of Sheffield Number Theor
y Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Sengun (Sheffield)
DTSTART:20230314T130000Z
DTEND:20230314T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/13
DESCRIPTION:Title: K-theory and automorphic forms?\nby Haluk Sengun (Sheff
ield) as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 H
icks Building.\n\nAbstract\nMy research in the recent years have been guid
ed by the simple question: "Why not consider K-theory instead of ordinary
cohomology in the study of arithmetic groups and automorphic forms?". Here
I mean not only the topological K-theory or arithmetic manifolds but also
the operator K-theory of the various C*-algebras associated to arithmetic
groups\; such as group C*-algebras\, boundary crossed product algebras.\n
\nIn this talk\, I will sketch basics around cohomology of arithmetic grou
ps and automorphic forms\, and then will give about some samples from my K
-theoretic works\, but I will mainly be raising questions some of which I
hope will lead to conversations between number theorists and algebraic top
ologists in the department.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo La Porta (Kings College London)
DTSTART:20230221T130000Z
DTEND:20230221T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/14
DESCRIPTION:by Lorenzo La Porta (Kings College London) as part of Sheffiel
d Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Yiasemides (Nottingham)
DTSTART:20230502T120000Z
DTEND:20230502T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/17
DESCRIPTION:Title: Divisor Sums and Hankel Matrices\nby Michael Yiasemides
(Nottingham) as part of Sheffield Number Theory Seminar\n\nLecture held i
n J-11 Hicks Building.\n\nAbstract\nIn this talk I will demonstrate a new
approach to evaluating divisor sums\, such as the variance of the divisor
function over short intervals\, and divisor correlations. The approach mak
es use of additive characters to translate the problem from a number theor
etic one to a linear algebraic one involving Hankel matrices. I will brief
ly discuss extensions to other Diophantine equations\, as well as indicate
further connections between Hankel matrices and number theory.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Håvard Damm-Johnsen (Oxford)
DTSTART:20231024T120000Z
DTEND:20231024T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/19
DESCRIPTION:Title: Diagonal Restrictions of Hilbert Eisenstein series\nby
Håvard Damm-Johnsen (Oxford) as part of Sheffield Number Theory Seminar\n
\nLecture held in J-11 Hicks Building.\n\nAbstract\nDarmon and Vonk's theo
ry of rigid meromorphic cocycles\, or "RM theory"\, can be thought of as a
$p$-adic counterpart to the classical CM theory. In particular\, values o
f certain cocycles conjecturally behave similarly to values of the modular
$j$-function at CM points.\nRecently\, Darmon\, Pozzi and Vonk proved spe
cial cases of these conjectures using $p$-adic deformations of Hilbert Eis
enstein series.\nI will describe some ongoing work extending these results
\, and how to make their constructions effectively computable.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Manning (Imperial College London)
DTSTART:20231107T130000Z
DTEND:20231107T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/20
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion over imaginar
y quadratic fields\nby Jeff Manning (Imperial College London) as part
of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.
\n\nAbstract\nWiles' modularity lifting theorem was the central argument i
n his proof of modularity of (semistable) elliptic curves over Q\, and hen
ce of Fermat's Last Theorem. His proof relied on two key components: his "
patching" argument (developed in collaboration with Taylor) and his numeri
cal isomorphism criterion.\n\nIn the time since Wiles' proof\, the patchin
g argument has been generalized extensively to prove a wide variety of mod
ularity lifting results. In particular Calegari and Geraghty have found a
way to generalize it to prove potential modularity of elliptic curves over
imaginary quadratic fields (contingent on some standard conjectures). The
numerical criterion on the other hand has proved far more difficult to ge
neralize\, although in situations where it can be used it can prove strong
er results than what can be proven purely via patching.\n\nIn this talk I
will present joint work with Srikanth Iyengar and Chandrashekhar Khare whi
ch proves a generalization of the numerical criterion to the context consi
dered by Calegari and Geraghty (and contingent on the same conjectures). T
his allows us to prove integral "R=T" theorems at non-minimal levels over
imaginary quadratic fields\, which are inaccessible by Calegari and Geragh
ty's method. The results provide new evidence in favor of a torsion analog
of the classical Langlands correspondence.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Rockwood (King's College London)
DTSTART:20231121T130000Z
DTEND:20231121T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/21
DESCRIPTION:Title: p-adic families of cohomology classes and Euler systems for
GSp4\nby Rob Rockwood (King's College London) as part of Sheffield Nu
mber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nI
n a trio of papers Loeffler\, Zerbes and myself give a general machine for
constructing ‘norm-compatible’ classes in the cohomology of Shimura v
arieties (Loeffler)\, varying these classes in ordinary families (Loeffler
—R.—Zerbes) and\, most recently\, varying these classes in non-ordinar
y families (R.). I will give a brief overview of these works and show how
one can apply the results of these papers to construct Euler systems for G
Sp4 and vary them in p-adic families.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Birkbeck (UEA)
DTSTART:20231205T130000Z
DTEND:20231205T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/22
DESCRIPTION:Title: Formalising modular forms\, Eisenstein series and the modul
arity conjecture in Lean\nby Chris Birkbeck (UEA) as part of Sheffield
Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract
\nI’ll discuss some recent work on defining modular forms and Eisenstein
series in Lean. This is an interactive theorem prover which has recently
attracted mathematicians and computer scientists who are working together
to create a unified digitised library of mathematics. In my talk I will ex
plain what Lean is\, why would one want to formalise results\, and explain
the process of taking basic definitions/examples of modular forms and for
malising them. No prior knowledge of Lean or formalisation will be require
d!\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ju-Feng Wu (Warwick)
DTSTART:20231010T120000Z
DTEND:20231010T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/23
DESCRIPTION:Title: On $p$-adic adjoint $L$-functions for Bianchi cuspforms: th
e $p$-split case\nby Ju-Feng Wu (Warwick) as part of Sheffield Number
Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nIn the
late '90's\, Coleman and Mazur showed that finite-slope eigenforms can be
patched into a rigid analytic curve\, the so-called eigencurve. The geome
try of the eigencurve encodes interesting arithmetic information. For exam
ple\, the Bellaïche—Kim method showed that there is a strong relationsh
ip between the ramification locus of the (cuspidal) eigencurve over the we
ight space and the adjoint $L$-value. In this talk\, based on joint work w
ith Pak-Hin Lee\, I will discuss a generalisation of the Bellaïche—Kim
method to the Bianchi setting. If time permits\, I will discuss an interes
ting question derived from these $p$-adic adjoint $L$-functions.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Girsch (Sheffield)
DTSTART:20231128T130000Z
DTEND:20231128T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/24
DESCRIPTION:Title: On families of degenerate representations of GL_n(F)\nb
y Johannes Girsch (Sheffield) as part of Sheffield Number Theory Seminar\n
\nLecture held in J-11 Hicks Building.\n\nAbstract\nSmooth generic represe
ntations of GL_n(F)\, i.e. representations admitting a nondegenerate Whitt
aker model\, are an important class of representations\, for example in th
e setting of Rankin-Selberg integrals. However\, in recent years there has
been an increased interest in non-generic representations and their degen
erate Whittaker models. By the theory of Bernstein-Zelevinsky derivatives
we can associate to each smooth irreducible representation of GL_n(F) an i
nteger partition of n\, which encodes the "degeneracy" of the representati
on. For each integer partition \\lambda of n\, we then construct a family
of universal degenerate representations of type \\lambda and prove some su
prising properties of these families. This is joint work with David Helm.\
n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Kurinczuk (Sheffield)
DTSTART:20231031T130000Z
DTEND:20231031T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/25
DESCRIPTION:Title: Blocks for classical p-adic groups\nby Robert Kurinczuk
(Sheffield) as part of Sheffield Number Theory Seminar\n\nLecture held in
J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20231114T130000Z
DTEND:20231114T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/26
DESCRIPTION:by TBA as part of Sheffield Number Theory Seminar\n\nLecture h
eld in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beth Romano (Kings)
DTSTART:20240220T130000Z
DTEND:20240220T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/27
DESCRIPTION:Title: Epipelagic representations in the local Langlands correspon
dence\nby Beth Romano (Kings) as part of Sheffield Number Theory Semin
ar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe local Langland
s correspondence (LLC) is a kaleidoscope of conjectures relating local Gal
ois theory\, complex Lie theory\, and representations of p-adic groups. Th
e LLC is divided into two parts: first\, there is the tame or depth-zero p
art\, where much is known and proofs tend to be uniform for all residue ch
aracteristics p. Then there is the positive-depth (or wild) part of the co
rrespondence\, where there is much that still needs to be explored. I will
talk about recent results that build our understanding of this wild part
of the LLC via epipelagic representations and their Langlands parameters.
I will not assume background knowledge of the LLC\, but will give an intro
duction to these ideas via examples.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Groutides (Warwick)
DTSTART:20240227T130000Z
DTEND:20240227T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/28
DESCRIPTION:Title: On integral structures in smooth $\\mathrm{GL}_2$-represent
ations and zeta integrals.\nby Alexandros Groutides (Warwick) as part
of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.
\n\nAbstract\nWe will discuss recent work on local integral structures in
smooth ($\\mathrm{GL}_2\\times H$)-representations\, where $H$ is an unram
ified maximal torus of $\\mathrm{GL}_2$. Inspired by work of Loeffler-Skin
ner-Zerbes\, we will introduce certain unramified Hecke modules containing
lattices with deep integral properties. We'll see how this approach recov
ers a Gross-Prasad type multiplicity one result in this unramified setting
and present an integral variant of it with applications to zeta integrals
and automorphic modular forms. Finally\, we will reformulate and answer
a conjecture of Loeffler on integral unramified Hecke operators attached t
o the lattices mentioned above.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Dotto (Cambridge)
DTSTART:20240312T130000Z
DTEND:20240312T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/29
DESCRIPTION:Title: Some consequences of mod p multiplicity one for Shimura cur
ves\nby Andrea Dotto (Cambridge) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe multiplicit
y of Hecke eigenspaces in the mod p cohomology of Shimura curves is a clas
sical invariant\, which has been computed in significant generality when t
he group is split at p. This talk will focus on the complementary case of
nonsplit quaternion algebras\, and will describe a new multiplicity one re
sult\, as well as some of its consequences regarding the structure of comp
leted cohomology. I will also discuss applications towards the categorical
mod p Langlands correspondence for the nonsplit inner form of GL_2(Q_p).
Part of the talk will comprise a joint work in progress with Bao Le Hung.\
n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bence Hevesi (Kings)
DTSTART:20240430T120000Z
DTEND:20240430T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/30
DESCRIPTION:Title: Local-global compatibility at l=p for torsion automorphic G
alois representations\nby Bence Hevesi (Kings) as part of Sheffield Nu
mber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nS
ome ten years ago\, Scholze proved the existence of Galois representations
associated with torsion eigenclasses appearing in the cohomology of local
ly symmetric spaces for GL_n over imaginary CM fields. Since then\, the qu
estion of local-global compatibility for these automorphic Galois represen
tations has been an active area of research motivated by applications towa
rds new automorphy lifting theorems. I will report on my work on local-glo
bal compatibility at l=p in this direction\, generalising the results of t
he celebrated 10-author paper and Caraiani—Newton.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Taylor (Manchester)
DTSTART:20240507T120000Z
DTEND:20240507T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/31
DESCRIPTION:Title: Modular Reduction of Nilpotent Orbits\nby Jay Taylor (M
anchester) as part of Sheffield Number Theory Seminar\n\nLecture held in J
-11 Hicks Building.\n\nAbstract\nSuppose $𝐺_𝕜$ is a (split) connecte
d reductive algebraic $𝕜$-group where $𝕜$ is an algebraically closed
field. If $𝑉_𝕜$ is a $𝐺_𝕜$-module then\, using geometric inva
riant theory\, Kempf has defined the nullcone $𝒩(𝑉_𝕜)$ of $𝑉_
𝕜$. For the Lie algebra $𝔤_𝕜 = Lie(𝐺_𝕜)$\, viewed as a $
𝐺_𝕜$-module via the adjoint action\, we have $𝒩(𝔤_𝕜)$ is pr
ecisely the set of nilpotent elements.\n\nWe may assume that our group $
𝐺_𝕜 = 𝐺 ×_ℤ 𝕜$ is obtained by base-change from a suitable $
ℤ$-form 𝐺. Suppose $𝑉$ is $𝔤 = Lie(G)$ or its dual $𝔤^* = Ho
m(𝔤\, ℤ)$ which are both modules for $𝐺$\, that are free of finite
rank as $ℤ$-modules. Then $𝑉 ⨂_ℤ 𝕜$\, as a module for $𝐺_
𝕜$\, is $𝔤_𝕜$ or $𝔤_𝕜^*$ respectively.\n\nIt is known that
each $𝐺_ℂ$ -orbit $𝒪 ⊆ 𝒩(𝑉_ℂ)$ contains a representative
$ξ ∈ 𝑉$ in the $ℤ$-form. Reducing $ξ$ one gets an element $ξ_
𝕜 ∈ 𝑉_𝕜$ for any algebraically closed $𝕜$. In this talk we w
ill explain ways in which we might want $ξ$ to have “good reduction”
and how one can find elements with these properties. Given time\, we will
also discuss the relationship to Lusztig’s special orbits.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Patashnick (Kings)
DTSTART:20240521T120000Z
DTEND:20240521T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/32
DESCRIPTION:Title: Aut we to act? a mod p story\nby Owen Patashnick (Kings
) as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks
Building.\n\nAbstract\nIn this talk\, we will show that an analogy for a
result about the action of the automorphism group on the mod p points of t
he Markoff surface is true for a certain class of K3 surfaces as well\, na
mely\, the Kummer of the square of an elliptic curve without CM.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Santiago Palacios (Bordeaux)
DTSTART:20240213T130000Z
DTEND:20240213T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/33
DESCRIPTION:Title: Geometry of the Bianchi eigenvariety at non-cuspidal points
\nby Luis Santiago Palacios (Bordeaux) as part of Sheffield Number The
ory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nAn import
ant tool to study automorphic representations in the framework of the Lang
lands program\, is to produce $p$-adic variation. Such variation is captur
ed geometrically in the study of certain "moduli spaces" of p-adic automor
phic forms\, called eigenvarieties.\nIn this talk\, we first introduce Bia
nchi modular forms\, that is\, automorphic forms for $\\mathrm{GL}_2$ over
an imaginary quadratic field\, and then discuss its contribution to the c
ohomology of the Bianchi threefold. After that\, we present the Bianchi ei
genvariety and state our result about its geometry at a special non-cuspid
al point. This is a joint work in progress with Daniel Barrera (Universida
d de Santiago de Chile).\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis M Combes (Sheffield)
DTSTART:20240305T130000Z
DTEND:20240305T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/34
DESCRIPTION:Title: Period polynomials of level 1 Bianchi modular forms\nby
Lewis M Combes (Sheffield) as part of Sheffield Number Theory Seminar\n\n
Lecture held in J-11 Hicks Building.\n\nAbstract\nThe period polynomial of
a classical modular form encodes important arithmetic information about t
he form itself\, being made out of critical L-values and connecting to con
gruences via Haberland's formula. In this talk\, we report on work to gene
ralise these connections to the setting of Bianchi modular forms---those o
ver an imaginary quadratic field. We demonstrate explicit congruences betw
een various types of Bianchi modular form\, and show how to detect them us
ing a pairing on period polynomials.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Droschl (Vienna)
DTSTART:20240423T120000Z
DTEND:20240423T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/35
DESCRIPTION:Title: On modular representations of $GL_n$ over a p-adic field\nby Johannes Droschl (Vienna) as part of Sheffield Number Theory Seminar
\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe Godement-Jacquet
L-function is a classical invariant attached to irreducible representatio
ns of $GL_n$. Minguez extended their definition to representations over fi
elds of characteristic $\\ell\\neq p$. In this talk we will finish the com
putation of these L-functions for modular representations and check that t
hey agree with the L-function of their respective C-parameter defined by K
urinczuk and Matringe. We approach the problem by extending the theory of
square-irreducible representations\, and their derivatives\, of Lapid and
Minguez to modular representations and applying it to our setting.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Plymen (Manchester)
DTSTART:20250603T120000Z
DTEND:20250603T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/36
DESCRIPTION:Title: K-theory and Langlands duality\nby Roger Plymen (Manche
ster) as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 H
icks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Torzewski (Kings College London)
DTSTART:20250225T130000Z
DTEND:20250225T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/37
DESCRIPTION:Title: How common is Galois complex multiplication?\nby Alex T
orzewski (Kings College London) as part of Sheffield Number Theory Seminar
\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Funke (Durham)
DTSTART:20250304T130000Z
DTEND:20250304T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/38
DESCRIPTION:Title: Indefinite theta series via incomplete theta integrals\
nby Jens Funke (Durham) as part of Sheffield Number Theory Seminar\n\nLect
ure held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Collacciani (Padova)
DTSTART:20250318T130000Z
DTEND:20250318T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/39
DESCRIPTION:Title: Extending Local Langlands framework over finite fields: a c
onjecture by Vogan\nby Elena Collacciani (Padova) as part of Sheffield
Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rose Berry (UEA)
DTSTART:20250325T130000Z
DTEND:20250325T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/40
DESCRIPTION:Title: The Derived Unipotent Block of GLn(F)\nby Rose Berry (U
EA) as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hic
ks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny Roberts (Bristol)
DTSTART:20250429T120000Z
DTEND:20250429T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/41
DESCRIPTION:Title: Newform Eisenstein congruences of local origin: classical a
nd beyond\nby Jenny Roberts (Bristol) as part of Sheffield Number Theo
ry Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rawson
DTSTART:20241112T140000Z
DTEND:20241112T150000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/42
DESCRIPTION:Title: Computing Tangent Spaces to Eigenvarieties\nby James Ra
wson as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hi
cks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Weiss
DTSTART:20241119T140000Z
DTEND:20241119T150000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/43
DESCRIPTION:Title: Stable Lattices in Galois representations and the Geometry
of Bruhat–Tits Buildings\nby Ariel Weiss as part of Sheffield Number
Theory Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (Sheffield)
DTSTART:20241126T140000Z
DTEND:20241126T150000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/44
DESCRIPTION:Title: Residual paramodularity of a certain Calabi-Yau 3-fold\
nby Neil Dummigan (Sheffield) as part of Sheffield Number Theory Seminar\n
\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Leung Fong (Sheffield)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/45
DESCRIPTION:Title: Adjoint L-functions and my recent research\nby Ho Leung
Fong (Sheffield) as part of Sheffield Number Theory Seminar\n\nLecture he
ld in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Luo (Minnesota)
DTSTART:20251007T120000Z
DTEND:20251007T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/46
DESCRIPTION:Title: On the Local Converse Theorem for p-adic GL(2N)\nby Dav
id Luo (Minnesota) as part of Sheffield Number Theory Seminar\n\nLecture h
eld in J-11 Hicks Building.\n\nAbstract\nIn this talk\, we use type theory
to construct a family of depth 1/m minimax supercuspidal representations
of 𝑝-adic GL(2m\,𝐹) which we call middle supercuspidal representatio
ns. These supercuspidals may be viewed as a natural generalization of simp
le supercuspidal representations\, i.e. those supercuspidals of minimal po
sitive depth. Via explicit computations of twisted gamma factors\, we show
that middle supercuspidal representations may be uniquely determined thro
ugh twisting by quasi-characters of 𝐹× and simple supercuspidal repres
entations of GL(m\,𝐹). Furthermore\, we pose a conjecture which refines
the local converse theorem for general supercuspidal representations of G
L(𝑛\,𝐹)\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lanard (Versailles)
DTSTART:20251021T120000Z
DTEND:20251021T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/47
DESCRIPTION:Title: An algorithm for Aubert-Zelevinsky duality à la Mœglin-Wa
ldspurger\nby Thomas Lanard (Versailles) as part of Sheffield Number T
heory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe Aub
ert-Zelevinsky duality is an involution on the irreducible representations
of a p-adic group\, playing a central role in representation theory. For
GL_n\, irreducible representations can be classified by combinatorial obje
cts called multisegments. In this case\, an explicit formula to compute th
e Aubert-Zelevinsky dual was given by Mœglin and Waldspurger. For classic
al groups such as Sp_{2n} or SO_{2n+1}\, irreducible representations can b
e described in terms of Langlands parameters. In this talk\, I will presen
t a combinatorial algorithm\, inspired by the Mœglin–Waldspurger approa
ch\, to compute the Aubert–Zelevinsky dual in terms of Langlands data. I
nterestingly\, the algorithm was discovered with the help of machine learn
ing tools\, which guided us toward patterns leading to its formulation. Th
is is joint work with Alberto Mínguez.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Klosin (Queens College CUNY)
DTSTART:20250708T120000Z
DTEND:20250708T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/48
DESCRIPTION:Title: Klingen Eisenstein series congruences and modularity\nb
y Kris Klosin (Queens College CUNY) as part of Sheffield Number Theory Sem
inar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (Bonn)
DTSTART:20251208T160000Z
DTEND:20251208T170000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/50
DESCRIPTION:Title: New directions in the Langlands correspondence for non quas
i-split groups\nby Peter Dillery (Bonn) as part of Sheffield Number Th
eory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe refi
ned local Langlands correspondence is a bijection between irreducible repr
esentations of a reductive group and its inner forms over a local field to
number-theoretic data called enhanced L-parameters---the only version of
this bijective correspondence that applies to arbitrary groups is the "rig
id correspondence" due to Kaletha. This local picture can be glued togethe
r at all primes to give formulas for the multiplicity of automorphic repre
sentations of a group G (over a global field) in its discrete spectrum. Th
e goal of this talk is two-fold: First\, explain the precise formulation o
f this bijection with an emphasis on examples and\, second\, explain the c
urrent progress towards expanding and geometrizing this bijective correspo
ndence and its global applications.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kilian Bönisch
DTSTART:20251118T130000Z
DTEND:20251118T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/51
DESCRIPTION:Title: Fibering out Calabi-Yau motives\nby Kilian Bönisch as
part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Buil
ding.\n\nAbstract\nI will present a method which allows proving the modula
rity of mixed periods associated with singular fibers of families of Calab
i-Yau threefolds (e.g. the mirror quintic). This is done by "fibering out"
\, i.e. by expressing these periods as integrals of periods of families of
K3 surfaces and by using modularity properties of the latter. Besides cla
ssical periods of holomorphic modular forms and meromorphic modular forms
with vanishing residues\, the computations lead to new interesting periods
associated with meromorphic modular forms with non-vanishing residues as
well as contours between CM points. The talk is based on the collaboration
https://arxiv.org/abs/2510.03939 with Vasily Golyshev and Albrecht Klemm.
\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Dawydiak (Glasgow)
DTSTART:20260127T130000Z
DTEND:20260127T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/52
DESCRIPTION:Title: Affine and asymptotic Hecke algebras for p-adic groups\
nby Stefan Dawydiak (Glasgow) as part of Sheffield Number Theory Seminar\n
\nLecture held in J-11 Hicks Building.\n\nAbstract\nStarting from celebrat
ed work of Kazhdan-Lusztig\, rich geometric and spectral pictures of affin
e Hecke algebras have emerged as a special case of the Local Langlands Cor
respondence for p-adic groups. I will report on work\, initiated by Braver
man-Kazhdan\, to extend these pictures to a slightly larger algebra\, Lusz
tig's asymptotic Hecke algebra. This ring retains the connection to the ge
ometry of the dual group enjoyed by the affine Hecke algebra\, which we wi
ll recall and use to give some formulas for certain Harish-Chandra Schwart
z functions and a geometric criterion for reducibility of certain tempered
representations.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Shotton (Durham)
DTSTART:20260421T120000Z
DTEND:20260421T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/53
DESCRIPTION:Title: Invariant Factors\, Adelic Images\, and Coincidences\nb
y Jack Shotton (Durham) as part of Sheffield Number Theory Seminar\n\nLect
ure held in J-11 Hicks Building.\n\nAbstract\nFor a rational elliptic curv
e E/Q\, we ask whether there are infinitely many primes p for which the sm
allest invariant factor of E(F_p) is equal to a given integer j. This is (
conditionally) governed by whether a constant C_{E\,j} is zero\, by work o
f Cojocaru and Murty. In this talk I will explain how to interpret this co
nstant in terms of the adelic image of the associated Galois representatio
n and give new criteria for it to be nonzero. I will also discuss experime
ntal evidence that C_{E\,j} = 0 --- so that the answer to our original que
stion is "no" --- only when there is a `coincidence' of division fields. T
his is joint work with Alexander Milner (Edinburgh).\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maleeha Khawaja (Warwick)
DTSTART:20260505T120000Z
DTEND:20260505T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/54
DESCRIPTION:by Maleeha Khawaja (Warwick) as part of Sheffield Number Theor
y Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Groutides (Warwick)
DTSTART:20260310T130000Z
DTEND:20260310T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/55
DESCRIPTION:Title: Arithmetic of Rankin-Selberg zeta-integrals for newforms\nby Alexandros Groutides (Warwick) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nZeta-integrals
of Rankin type have been a cornerstone in the representation-theoretic app
roach toward the study of product L-functions. In this talk\, I will first
motivate the construction of this for the Rankin-Selberg convolution of n
ewforms. I will then introduce a generic notion of ''integral input data''
at which this zeta-integral can be evaluated and mention how it relates t
o Rankin-Selberg Euler systems. Using this notion\, I will present an inte
gral refinement of Jacquet-Langland's GCD-result\, and If time permits\, I
will summarize key ingredients in the approach. These include a novel rei
nterpretation of the Rankin-Selberg zeta-integral\, and works of A. Saha a
nd E. Assing on p-adic Whittaker newvectors.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Chambers (Sheffield)
DTSTART:20260224T130000Z
DTEND:20260224T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/56
DESCRIPTION:Title: Congruences of Modular Forms of Half-Integral Weight (and T
wisted L-Values)\nby Mark Chambers (Sheffield) as part of Sheffield Nu
mber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nW
e have a classical theta lifting between weight 2k and weight k+1/2 modula
r forms. Specifically\, for squarefree level\, we get finitely many lifts
corresponding to classes of discriminants. A natural question to ask is wh
ether these lifts preserve congruences of Fourier coefficients\, which als
o has applications towards square roots of twisted L-Values. In order to p
rove congruences\, we look at cohomological lifts\, which were used by Koh
nen-Zagier to construct the lift for one class of discriminants. We extend
this to all other cases using a construction of Kojima-Tokuno\, and prove
that congruences are preserved for large non-Eisenstein primes.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Solomon (IMJ)
DTSTART:20260428T120000Z
DTEND:20260428T130000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/57
DESCRIPTION:Title: Heisenberg SICs\, Stark Units and Weil Representations\
nby David Solomon (IMJ) as part of Sheffield Number Theory Seminar\n\nLect
ure held in J-11 Hicks Building.\n\nAbstract\nSICs\, also known as equiang
ular tight frames\, are configurations of $d^2$ equiangular lines in $\\ma
thbb{C}^d$ whose applications in signal processing and quantum physics hav
e been known and studied for more than 30 years. More recently\, numerical
investigations of so-called Heisenberg SICs (which have an action of $\\m
athcal{H}(\\mathbb{Z}/d\\mathbb{Z})$ via its Schr\\¨odinger representatio
n) have revealed surprising\, heuristic connections with conjectural ``Sta
rk units'' and hence with Hilbert’s 12th Problem over real-quadratic fie
lds. Just as intriguingly\, the action of Galois on these units seems to b
e connected to the action of $\\mathrm{SL}_2(\\mathbb{Z}/d\\mathbb{Z})$ on
the set of Heisenberg SICs via its $d$-dimensional Weil representation as
a subgroup of the automorphism group of $\\mathcal{H}(\\mathbb{Z}/d\\math
bb{Z})$. In my talk\, I will first give an overview of recent SIC-related
research\, as well as the Stark Conjectures (which date from the 1970s but
are still largely unproven). I will explain the experimental evidence con
necting SICs with Stark-Units over the field $\\mathbb{Q}(\\sqrt{(d−1)(d
+3)})$. On a more specialised note and as time permits\, I will outline my
recent work on the lifted Weil representation in the case $d = p^n$ and p
ossible connections to a $p$-adic theory of SICs.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Berland (University of Copenhagen)
DTSTART:20260324T130000Z
DTEND:20260324T140000Z
DTSTAMP:20260422T142041Z
UID:SheffieldNumberTheory/58
DESCRIPTION:Title: Growth of torsion in the cohomology of Q-rank 1 arithmetic
groups\nby Tim Berland (University of Copenhagen) as part of Sheffield
Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract
\nCohomology of arithmetic groups has long been understood to have number
theoretic significance. By the Ash conjecture\, cohomological torsion pred
icts the existence of Galois representations\, hence it is desirable to kn
ow when to expect torsion\, and how much. It was conjectured by Bergeron a
nd Venkatesh that when the deficiency is 1\, there should be exponential g
rowth of torsion in families of congruence subgroups\, and they showed thi
s to be true for cocompact congruence subgroups with certain coefficient s
ystems. This was generalized to Q-rank 1 by Müller and Rochon. However\,
it is still unclear what to expect outside deficiency 1. As a step towards
remedying this\, in this talk we give subexponential bounds on torsion in
the cohomology of Q-rank 1 congruence subgroups when the deficiency is no
t 1\, as well as bounds on second order terms for deficiency 1\, using sha
rpened asymptotics on analytic torsion.\n
LOCATION:https://researchseminars.org/talk/SheffieldNumberTheory/58/
END:VEVENT
END:VCALENDAR