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BEGIN:VEVENT
SUMMARY:Ciaran Schembri (Dartmouth College)
DTSTART:20221115T130000Z
DTEND:20221115T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/1
DESCRIPTION:Title: Torsion points on abelian surfaces with many endomorp
hisms\nby Ciaran Schembri (Dartmouth College) as part of Sheffield Num
ber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nIn
a celebrated work Mazur classified which torsion subgroups can occur for
elliptic curves defined over the rationals. A natural analogue is to consi
der surfaces with geometric endomorphisms by a quaternion order\, since th
e associated moduli space is 1-dimensional. In this talk I will discuss pr
ogress towards classifying which torsion subgroups are possible for these
surfaces. This is joint work (in progress) with Jef Laga\, Ari Shnidman an
d John Voight.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peiyi Cui (University of East Anglia)
DTSTART:20221122T130000Z
DTEND:20221122T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/2
DESCRIPTION:Title: Decompositions of the category of $\\ell$-modular rep
resentations of $SL_n(F)$\nby Peiyi Cui (University of East Anglia) as
part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Bui
lding.\n\nAbstract\nLet $F$ be a $p$-adic field\, and k an algebraically c
losed field of characteristic $\\ell$ different from $p$. In this talk\, w
e will first give a category decomposition of $Rep_k(SL_n(F))$\, the categ
ory of smooth $k$-representations of $SL_n(F)$\, with respect to the $GL_n
(F)$-equivalent supercuspidal classes of $SL_n(F)$\, which is not always a
block decomposition in general. We then give a block decomposition of the
supercuspidal subcategory\, by introducing a partition on each $GL_n(F)$-
equivalent supercuspidal class through type theory\, and we interpret this
partition by the sense of $\\ell$-blocks of finite groups. We give an exa
mple where 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 c
ase where $\\ell$ is zero. We end this talk by giving a prediction on the
block decomposition of $Rep_k(A)$ for a general $p$-adic group $A$.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Pozzi (Imperial College London)
DTSTART:20221129T130000Z
DTEND:20221129T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/3
DESCRIPTION:Title: Tame triple product periods\nby Alice Pozzi (Impe
rial College London) as part of Sheffield Number Theory Seminar\n\nLecture
held in 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" anal
ogues of triple product periods for a triple of mod p modular forms of wei
ghts (2\,1\,1). I will then present an elliptic counterpart to this conjec
ture relating a tame triple product period to a regulator for global point
s of elliptic curves. This is joint work with Henri Darmon.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadir Matringe (Université Paris Cité)
DTSTART:20221108T130000Z
DTEND:20221108T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/4
DESCRIPTION:Title: Symmetric periods for automorphic forms on unipotent
groups\nby Nadir Matringe (Université Paris Cité) as part of Sheffie
ld Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstra
ct\nLet $G$ be an algebraic group defined over a number field $k$ with rin
g of adeles $\\mathbb{A}$\, and let $\\sigma$ be a $k$-involution of $G$.
Studying the nonvanishing of (possible regularizations of) the period inte
gral \n$p: \\phi \\mapsto \\int_{G^\\sigma(k) \\backslash G^\\sigma(\\math
bb{A}}\\phi(h)dh$ on topologically irreducible submodules of $L^2(G(k) \\b
ackslash G(\\mathbb{A}))$ is a very popular topic when $G$ is reductive. H
ere I will focus on the case where $G$ is unipotent\, and explain that $p$
does not vanish on such a submodule $\\Pi$ if and only if $\\Pi^\\vee=\\P
i^\\sigma$.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (University of Sheffield)
DTSTART:20221004T120000Z
DTEND:20221004T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/5
DESCRIPTION:Title: The integral Bernstein centre\nby Rob Kurinczuk (
University of Sheffield) as part of Sheffield Number Theory Seminar\n\nLec
ture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maleeha Khawaja (University of Sheffield)
DTSTART:20221018T120000Z
DTEND:20221018T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/6
DESCRIPTION:Title: The Fermat equation over real biquadratic fields\
nby Maleeha Khawaja (University of Sheffield) as part of Sheffield Number
Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nWe wil
l take a look at an overview of the so called modular approach to Diophant
ine equations. We will particularly focus on the obstacles that arise when
applying this approach to the Fermat equation over real biquadratic field
s\, using $\\Q(\\sqrt{2}\, \\sqrt{3})$ as an illustrating example.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Newton (King's College London)
DTSTART:20221206T130000Z
DTEND:20221206T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/7
DESCRIPTION:Title: Distribution of genus numbers of abelian number field
s\nby Rachel Newton (King's College London) as part of Sheffield Numbe
r Theory 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 o
f L/K is the largest extension of L which is unramified at all places of L
and abelian as an extension of K. The genus group is its Galois group ove
r L\, which is a quotient of the class group of L\, and the genus number i
s the size of the genus group. We study the quantitative behaviour of genu
s numbers as one varies over abelian extensions L/K with fixed Galois grou
p. We give an asymptotic formula for the average value of the genus number
and show that any given genus number appears only 0% of the time. This is
joint work with Christopher Frei and Daniel Loughran.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bodan Arsovski (University College London)
DTSTART:20221214T140000Z
DTEND:20221214T150000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/8
DESCRIPTION:Title: The p-adic Kakeya conjecture\nby Bodan Arsovski (
University College London) as part of Sheffield Number Theory Seminar\n\nL
ecture held in J-11 Hicks Building.\n\nAbstract\nThe classical Kakeya conj
ecture states that all compact subsets of ℝ^n containing a line segment
of unit length in every direction have full Hausdorff dimension. In this t
alk we prove the natural analogue of the classical Kakeya conjecture over
the p-adic numbers — more specifically\, that all compact subsets of ℚ
_p^n containing a line segment of unit length in every direction have full
Hausdorff dimension — a conjecture which was first discussed in the 199
0s by James Wright. More generally\, in this talk we prove the p-adic anal
ogue of the Kakeya maximal conjecture\, which is a functional version of t
he Kakeya conjecture proposed by Jean Bourgain in the 1990s.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (Imperial College London)
DTSTART:20230328T120000Z
DTEND:20230328T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/9
DESCRIPTION:Title: Towards a theta correspondence in families for type I
I dual pairs\nby Justin Trias (Imperial College London) as part of She
ffield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAb
stract\nThis is current work with Gil Moss. The classical local theta corr
espondence for p-adic reductive dual pairs defines a bijection between pre
scribed subsets of irreducible smooth complex representations coming from
two groups (H\,H')\, forming a dual pair in a symplectic group. Alberto M
ínguez extended this result for type II dual pairs\, i.e. when (H\,H') is
made of general linear groups\, to representations with coefficients in a
n algebraically closed field of characteristic l as long as the characteri
stic l does 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 dua
l pairs that is compatible with reduction to residue fields of the base co
efficient ring\, where central to this approach is the integral Bernstein
centre. We translate some weaker properties of the classical correspondenc
e\, such as compatibility with supercuspidal support\, as a morphism betwe
en the integral Bernstein centres of H and H' and interpret it for the Wei
l representation. In general\, we only know that this morphism is finite t
hough we may expect it to be surjective. This would result in a closed imm
ersion between the associated affine schemes as well as a correspondence b
etween characters of the Bernstein centre.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksander Horawa (Oxford)
DTSTART:20230207T130000Z
DTEND:20230207T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/10
DESCRIPTION:Title: Motivic action conjectures\nby Aleksander Horawa
(Oxford) as part of Sheffield Number Theory Seminar\n\nLecture held in J-
11 Hicks Building.\n\nAbstract\nA surprising property of the cohomology of
locally symmetric spaces is that Hecke operators can act on multiple coho
mological degrees with the same eigenvalues. A recent series of conjecture
s proposes an arithmetic explanation: a hidden degree-shifting action of a
certain motivic cohomology group. We will give an overview of these conje
ctures\, focusing on the examples of GL_2 over the rational numbers\, real
quadratic fields\, and imaginary quadratic fields.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/10
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (Sheffield)
DTSTART:20230307T130000Z
DTEND:20230307T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/11
DESCRIPTION:Title: Modularity of a certain ``rank-2 attractor'' Calabi-
Yau 3-fold\nby Neil Dummigan (Sheffield) as part of Sheffield Number T
heory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nWe prov
e that the 4-dimensional Galois representations associated with a certain
Calabi-Yau threefold are reducible\, with 2-dimensional composition factor
s coming from specific modular forms of weights 2 and 4\, both level 14. T
his was essentially conjectured by Meyer and Verrill. It was revisited in
its present form by Candelas\, de la Ossa\, Elmi and van Straten\, whose c
omputations of Euler factors in a whole pencil of Calabi-Yau threefolds hi
ghlighted this fibre as one of three overwhelmingly likely to be ``rank-2
attractors''. The proof is conditional on the truth of their as yet unprov
ed conjecture about the correctness of a certain matrix entering into thei
r computations.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/11
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Berger (Sheffield)
DTSTART:20230228T130000Z
DTEND:20230228T140000Z
DTSTAMP:20260404T094532Z
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://stable.researchseminars.org/talk/SheffieldNumberTheory/12
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haluk Sengun (Sheffield)
DTSTART:20230314T130000Z
DTEND:20230314T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/13
DESCRIPTION:Title: K-theory and automorphic forms?\nby Haluk Sengun
(Sheffield) as part of Sheffield Number Theory Seminar\n\nLecture held in
J-11 Hicks Building.\n\nAbstract\nMy research in the recent years have be
en guided by the simple question: "Why not consider K-theory instead of or
dinary cohomology in the study of arithmetic groups and automorphic forms?
". Here I mean not only the topological K-theory or arithmetic manifolds b
ut also the operator K-theory of the various C*-algebras associated to ari
thmetic groups\; such as group C*-algebras\, boundary crossed product alge
bras.\n\nIn this talk\, I will sketch basics around cohomology of arithmet
ic groups and automorphic forms\, and then will give about some samples fr
om my K-theoretic works\, but I will mainly be raising questions some of w
hich I hope will lead to conversations between number theorists and algebr
aic topologists in the department.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/13
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo La Porta (Kings College London)
DTSTART:20230221T130000Z
DTEND:20230221T140000Z
DTSTAMP:20260404T094532Z
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://stable.researchseminars.org/talk/SheffieldNumberTheory/14
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Yiasemides (Nottingham)
DTSTART:20230502T120000Z
DTEND:20230502T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/17
DESCRIPTION:Title: Divisor Sums and Hankel Matrices\nby Michael Yia
semides (Nottingham) as part of Sheffield Number Theory Seminar\n\nLecture
held in 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 d
ivisor function over short intervals\, and divisor correlations. The appro
ach makes use of additive characters to translate the problem from a numbe
r theoretic one to a linear algebraic one involving Hankel matrices. I wil
l briefly discuss extensions to other Diophantine equations\, as well as i
ndicate further connections between Hankel matrices and number theory.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/17
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Håvard Damm-Johnsen (Oxford)
DTSTART:20231024T120000Z
DTEND:20231024T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/19
DESCRIPTION:Title: Diagonal Restrictions of Hilbert Eisenstein series\nby Håvard Damm-Johnsen (Oxford) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nDarmon and Vonk
's theory of rigid meromorphic cocycles\, or "RM theory"\, can be thought
of as a $p$-adic counterpart to the classical CM theory. In particular\, v
alues of certain cocycles conjecturally behave similarly to values of the
modular $j$-function at CM points.\nRecently\, Darmon\, Pozzi and Vonk pro
ved special cases of these conjectures using $p$-adic deformations of Hilb
ert Eisenstein series.\nI will describe some ongoing work extending these
results\, and how to make their constructions effectively computable.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/19
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Manning (Imperial College London)
DTSTART:20231107T130000Z
DTEND:20231107T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/20
DESCRIPTION:Title: The Wiles-Lenstra-Diamond numerical criterion over i
maginary quadratic fields\nby Jeff Manning (Imperial College London) a
s part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Bu
ilding.\n\nAbstract\nWiles' modularity lifting theorem was the central arg
ument in his proof of modularity of (semistable) elliptic curves over Q\,
and hence of Fermat's Last Theorem. His proof relied on two key components
: his "patching" argument (developed in collaboration with Taylor) and his
numerical isomorphism criterion.\n\nIn the time since Wiles' proof\, the
patching argument has been generalized extensively to prove a wide variety
of modularity lifting results. In particular Calegari and Geraghty have f
ound a way to generalize it to prove potential modularity of elliptic curv
es over imaginary quadratic fields (contingent on some standard conjecture
s). The numerical criterion on the other hand has proved far more difficul
t to generalize\, although in situations where it can be used it can prove
stronger results than what can be proven purely via patching.\n\nIn this
talk I will present joint work with Srikanth Iyengar and Chandrashekhar Kh
are which proves a generalization of the numerical criterion to the contex
t considered by Calegari and Geraghty (and contingent on the same conjectu
res). This allows us to prove integral "R=T" theorems at non-minimal level
s over imaginary quadratic fields\, which are inaccessible by Calegari and
Geraghty's method. The results provide new evidence in favor of a torsion
analog of the classical Langlands correspondence.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/20
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Rockwood (King's College London)
DTSTART:20231121T130000Z
DTEND:20231121T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/21
DESCRIPTION:Title: p-adic families of cohomology classes and Euler syst
ems for GSp4\nby Rob Rockwood (King's College London) as part of Sheff
ield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbst
ract\nIn a trio of papers Loeffler\, Zerbes and myself give a general mach
ine for constructing ‘norm-compatible’ classes in the cohomology of Sh
imura varieties (Loeffler)\, varying these classes in ordinary families (L
oeffler—R.—Zerbes) and\, most recently\, varying these classes in non-
ordinary families (R.). I will give a brief overview of these works and sh
ow how one can apply the results of these papers to construct Euler system
s for GSp4 and vary them in p-adic families.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/21
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Birkbeck (UEA)
DTSTART:20231205T130000Z
DTEND:20231205T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/22
DESCRIPTION:Title: Formalising modular forms\, Eisenstein series and th
e modularity conjecture in Lean\nby Chris Birkbeck (UEA) as part of Sh
effield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nA
bstract\nI’ll discuss some recent work on defining modular forms and Eis
enstein series in Lean. This is an interactive theorem prover which has re
cently attracted mathematicians and computer scientists who are working to
gether to create a unified digitised library of mathematics. In my talk I
will explain what Lean is\, why would one want to formalise results\, and
explain the process of taking basic definitions/examples of modular forms
and formalising them. No prior knowledge of Lean or formalisation will be
required!\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/22
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ju-Feng Wu (Warwick)
DTSTART:20231010T120000Z
DTEND:20231010T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/23
DESCRIPTION:Title: On $p$-adic adjoint $L$-functions for Bianchi cuspfo
rms: the $p$-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. Th
e geometry of the eigencurve encodes interesting arithmetic information. F
or example\, the Bellaïche—Kim method showed that there is a strong rel
ationship between the ramification locus of the (cuspidal) eigencurve over
the weight space and the adjoint $L$-value. In this talk\, based on joint
work with Pak-Hin Lee\, I will discuss a generalisation of the Bellaïche
—Kim method to the Bianchi setting. If time permits\, I will discuss an
interesting question derived from these $p$-adic adjoint $L$-functions.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/23
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Girsch (Sheffield)
DTSTART:20231128T130000Z
DTEND:20231128T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/24
DESCRIPTION:Title: On families of degenerate representations of GL_n(F)
\nby Johannes Girsch (Sheffield) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nSmooth generic
representations of GL_n(F)\, i.e. representations admitting a nondegenerat
e Whittaker model\, are an important class of representations\, for exampl
e in the setting of Rankin-Selberg integrals. However\, in recent years th
ere has been an increased interest in non-generic representations and thei
r degenerate Whittaker models. By the theory of Bernstein-Zelevinsky deriv
atives we can associate to each smooth irreducible representation of GL_n(
F) an integer partition of n\, which encodes the "degeneracy" of the repre
sentation. For each integer partition \\lambda of n\, we then construct a
family of universal degenerate representations of type \\lambda and prove
some suprising properties of these families. This is joint work with David
Helm.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/24
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Kurinczuk (Sheffield)
DTSTART:20231031T130000Z
DTEND:20231031T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/25
DESCRIPTION:Title: Blocks for classical p-adic groups\nby Robert Ku
rinczuk (Sheffield) as part of Sheffield Number Theory Seminar\n\nLecture
held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/25
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20231114T130000Z
DTEND:20231114T140000Z
DTSTAMP:20260404T094532Z
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://stable.researchseminars.org/talk/SheffieldNumberTheory/26
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beth Romano (Kings)
DTSTART:20240220T130000Z
DTEND:20240220T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/27
DESCRIPTION:Title: Epipelagic representations in the local Langlands co
rrespondence\nby Beth Romano (Kings) as part of Sheffield Number Theor
y Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe local L
anglands correspondence (LLC) is a kaleidoscope of conjectures relating lo
cal Galois theory\, complex Lie theory\, and representations of p-adic gro
ups. The LLC is divided into two parts: first\, there is the tame or depth
-zero part\, where much is known and proofs tend to be uniform for all res
idue characteristics p. Then there is the positive-depth (or wild) part of
the correspondence\, where there is much that still needs to be explored.
I will talk about recent results that build our understanding of this wil
d part of the LLC via epipelagic representations and their Langlands param
eters. I will not assume background knowledge of the LLC\, but will give a
n introduction to these ideas via examples.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/27
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Groutides (Warwick)
DTSTART:20240227T130000Z
DTEND:20240227T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/28
DESCRIPTION:Title: On integral structures in smooth $\\mathrm{GL}_2$-re
presentations and zeta integrals.\nby Alexandros Groutides (Warwick) a
s part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hicks Bu
ilding.\n\nAbstract\nWe will discuss recent work on local integral structu
res in smooth ($\\mathrm{GL}_2\\times H$)-representations\, where $H$ is a
n unramified maximal torus of $\\mathrm{GL}_2$. Inspired by work of Loeffl
er-Skinner-Zerbes\, we will introduce certain unramified Hecke modules con
taining lattices with deep integral properties. We'll see how this approac
h recovers a Gross-Prasad type multiplicity one result in this unramified
setting and present an integral variant of it with applications to zeta in
tegrals and automorphic modular forms. Finally\, we will reformulate and
answer a conjecture of Loeffler on integral unramified Hecke operators att
ached to the lattices mentioned above.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/28
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Dotto (Cambridge)
DTSTART:20240312T130000Z
DTEND:20240312T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/29
DESCRIPTION:Title: Some consequences of mod p multiplicity one for Shim
ura curves\nby Andrea Dotto (Cambridge) as part of Sheffield Number Th
eory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe mult
iplicity of Hecke eigenspaces in the mod p cohomology of Shimura curves is
a classical invariant\, which has been computed in significant generality
when the group is split at p. This talk will focus on the complementary c
ase of nonsplit quaternion algebras\, and will describe a new multiplicity
one result\, as well as some of its consequences regarding the structure
of completed cohomology. I will also discuss applications towards the cate
gorical 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://stable.researchseminars.org/talk/SheffieldNumberTheory/29
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bence Hevesi (Kings)
DTSTART:20240430T120000Z
DTEND:20240430T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/30
DESCRIPTION:Title: Local-global compatibility at l=p for torsion automo
rphic Galois representations\nby Bence Hevesi (Kings) as part of Sheff
ield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbst
ract\nSome ten years ago\, Scholze proved the existence of Galois represen
tations associated with torsion eigenclasses appearing in the cohomology o
f locally symmetric spaces for GL_n over imaginary CM fields. Since then\,
the question of local-global compatibility for these automorphic Galois r
epresentations has been an active area of research motivated by applicatio
ns towards new automorphy lifting theorems. I will report on my work on lo
cal-global compatibility at l=p in this direction\, generalising the resul
ts of the celebrated 10-author paper and Caraiani—Newton.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/30
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jay Taylor (Manchester)
DTSTART:20240507T120000Z
DTEND:20240507T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/31
DESCRIPTION:Title: Modular Reduction of Nilpotent Orbits\nby Jay Ta
ylor (Manchester) as part of Sheffield Number Theory Seminar\n\nLecture he
ld in J-11 Hicks Building.\n\nAbstract\nSuppose $𝐺_𝕜$ is a (split) c
onnected reductive algebraic $𝕜$-group where $𝕜$ is an algebraically
closed field. If $𝑉_𝕜$ is a $𝐺_𝕜$-module then\, using geometr
ic invariant 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
precisely 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 $𝔤^* = H
om(𝔤\, ℤ)$ which are both modules for $𝐺$\, that are free of finit
e 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://stable.researchseminars.org/talk/SheffieldNumberTheory/31
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Patashnick (Kings)
DTSTART:20240521T120000Z
DTEND:20240521T130000Z
DTSTAMP:20260404T094532Z
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-1
1 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 poin
ts of the Markoff surface is true for a certain class of K3 surfaces as we
ll\, namely\, the Kummer of the square of an elliptic curve without CM.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/32
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Santiago Palacios (Bordeaux)
DTSTART:20240213T130000Z
DTEND:20240213T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/33
DESCRIPTION:Title: Geometry of the Bianchi eigenvariety at non-cuspidal
points\nby Luis Santiago Palacios (Bordeaux) as part of Sheffield Num
ber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nAn
important tool to study automorphic representations in the framework of t
he Langlands program\, is to produce $p$-adic variation. Such variation is
captured geometrically in the study of certain "moduli spaces" of p-adic
automorphic forms\, called eigenvarieties.\nIn this talk\, we first introd
uce Bianchi modular forms\, that is\, automorphic forms for $\\mathrm{GL}_
2$ over an imaginary quadratic field\, and then discuss its contribution t
o the cohomology of the Bianchi threefold. After that\, we present the Bia
nchi eigenvariety and state our result about its geometry at a special non
-cuspidal point. This is a joint work in progress with Daniel Barrera (Uni
versidad de Santiago de Chile).\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/33
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis M Combes (Sheffield)
DTSTART:20240305T130000Z
DTEND:20240305T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/34
DESCRIPTION:Title: Period polynomials of level 1 Bianchi modular forms<
/a>\nby Lewis M Combes (Sheffield) as part of Sheffield Number Theory Semi
nar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nThe period polyno
mial of a classical modular form encodes important arithmetic information
about the form itself\, being made out of critical L-values and connecting
to congruences via Haberland's formula. In this talk\, we report on work
to generalise these connections to the setting of Bianchi modular forms---
those over an imaginary quadratic field. We demonstrate explicit congruenc
es between various types of Bianchi modular form\, and show how to detect
them using a pairing on period polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/34
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Droschl (Vienna)
DTSTART:20240423T120000Z
DTEND:20240423T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/35
DESCRIPTION:Title: On modular representations of $GL_n$ over a p-adic f
ield\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 repres
entations of $GL_n$. Minguez extended their definition to representations
over fields of characteristic $\\ell\\neq p$. In this talk we will finish
the computation of these L-functions for modular representations and check
that they agree with the L-function of their respective C-parameter defin
ed by Kurinczuk and Matringe. We approach the problem by extending the the
ory of square-irreducible representations\, and their derivatives\, of Lap
id and Minguez to modular representations and applying it to our setting.\
n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/35
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Plymen (Manchester)
DTSTART:20250603T120000Z
DTEND:20250603T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/36
DESCRIPTION:Title: K-theory and Langlands duality\nby Roger Plymen
(Manchester) as part of Sheffield Number Theory Seminar\n\nLecture held in
J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/36
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Torzewski (Kings College London)
DTSTART:20250225T130000Z
DTEND:20250225T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/37
DESCRIPTION:Title: How common is Galois complex multiplication?\nby
Alex Torzewski (Kings College London) as part of Sheffield Number Theory
Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/37
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Funke (Durham)
DTSTART:20250304T130000Z
DTEND:20250304T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/38
DESCRIPTION:Title: Indefinite theta series via incomplete theta integra
ls\nby Jens Funke (Durham) as part of Sheffield Number Theory Seminar\
n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/38
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Collacciani (Padova)
DTSTART:20250318T130000Z
DTEND:20250318T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/39
DESCRIPTION:Title: Extending Local Langlands framework over finite fiel
ds: a conjecture by Vogan\nby Elena Collacciani (Padova) as part of Sh
effield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/39
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rose Berry (UEA)
DTSTART:20250325T130000Z
DTEND:20250325T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/40
DESCRIPTION:Title: The Derived Unipotent Block of GLn(F)\nby Rose B
erry (UEA) as part of Sheffield Number Theory Seminar\n\nLecture held in J
-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/40
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny Roberts (Bristol)
DTSTART:20250429T120000Z
DTEND:20250429T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/41
DESCRIPTION:Title: Newform Eisenstein congruences of local origin: clas
sical and beyond\nby Jenny Roberts (Bristol) as part of Sheffield Numb
er Theory Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/41
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rawson
DTSTART:20241112T140000Z
DTEND:20241112T150000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/42
DESCRIPTION:Title: Computing Tangent Spaces to Eigenvarieties\nby J
ames Rawson as part of Sheffield Number Theory Seminar\n\nLecture held in
J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/42
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ariel Weiss
DTSTART:20241119T140000Z
DTEND:20241119T150000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/43
DESCRIPTION:Title: Stable Lattices in Galois representations and the Ge
ometry 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://stable.researchseminars.org/talk/SheffieldNumberTheory/43
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neil Dummigan (Sheffield)
DTSTART:20241126T140000Z
DTEND:20241126T150000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/44
DESCRIPTION:Title: Residual paramodularity of a certain Calabi-Yau 3-fo
ld\nby Neil Dummigan (Sheffield) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/44
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Leung Fong (Sheffield)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/45
DESCRIPTION:Title: Adjoint L-functions and my recent research\nby H
o Leung Fong (Sheffield) as part of Sheffield Number Theory Seminar\n\nLec
ture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/45
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Luo (Minnesota)
DTSTART:20251007T120000Z
DTEND:20251007T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/46
DESCRIPTION:Title: On the Local Converse Theorem for p-adic GL(2N)\
nby David Luo (Minnesota) as part of Sheffield Number Theory Seminar\n\nLe
cture held in J-11 Hicks Building.\n\nAbstract\nIn this talk\, we use type
theory to construct a family of depth 1/m minimax supercuspidal represent
ations of 𝑝-adic GL(2m\,𝐹) which we call middle supercuspidal repres
entations. These supercuspidals may be viewed as a natural generalization
of simple supercuspidal representations\, i.e. those supercuspidals of min
imal positive depth. Via explicit computations of twisted gamma factors\,
we show that middle supercuspidal representations may be uniquely determin
ed through twisting by quasi-characters of 𝐹× and simple supercuspidal
representations of GL(m\,𝐹). Furthermore\, we pose a conjecture which
refines the local converse theorem for general supercuspidal representatio
ns of GL(𝑛\,𝐹)\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/46
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Lanard (Versailles)
DTSTART:20251021T120000Z
DTEND:20251021T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/47
DESCRIPTION:Title: An algorithm for Aubert-Zelevinsky duality à la Mœ
glin-Waldspurger\nby Thomas Lanard (Versailles) as part of Sheffield N
umber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\n
The Aubert-Zelevinsky duality is an involution on the irreducible represen
tations of a p-adic group\, playing a central role in representation theor
y. For GL_n\, irreducible representations can be classified by combinatori
al objects called multisegments. In this case\, an explicit formula to com
pute the Aubert-Zelevinsky dual was given by Mœglin and Waldspurger. For
classical groups such as Sp_{2n} or SO_{2n+1}\, irreducible representation
s can be described in terms of Langlands parameters. In this talk\, I will
present a combinatorial algorithm\, inspired by the Mœglin–Waldspurger
approach\, to compute the Aubert–Zelevinsky dual in terms of Langlands
data. Interestingly\, the algorithm was discovered with the help of machin
e learning tools\, which guided us toward patterns leading to its formulat
ion. This is joint work with Alberto Mínguez.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/47
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kris Klosin (Queens College CUNY)
DTSTART:20250708T120000Z
DTEND:20250708T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/48
DESCRIPTION:Title: Klingen Eisenstein series congruences and modularity
\nby Kris Klosin (Queens College CUNY) as part of Sheffield Number The
ory Seminar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/48
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dillery (Bonn)
DTSTART:20251208T160000Z
DTEND:20251208T170000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/50
DESCRIPTION:Title: New directions in the Langlands correspondence for n
on quasi-split groups\nby Peter Dillery (Bonn) as part of Sheffield Nu
mber Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nT
he refined local Langlands correspondence is a bijection between irreducib
le representations of a reductive group and its inner forms over a local f
ield to number-theoretic data called enhanced L-parameters---the only vers
ion of this bijective correspondence that applies to arbitrary groups is t
he "rigid correspondence" due to Kaletha. This local picture can be glued
together at all primes to give formulas for the multiplicity of automorphi
c representations of a group G (over a global field) in its discrete spect
rum. The goal of this talk is two-fold: First\, explain the precise formul
ation of this bijection with an emphasis on examples and\, second\, explai
n the current progress towards expanding and geometrizing this bijective c
orrespondence and its global applications.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/50
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kilian Bönisch
DTSTART:20251118T130000Z
DTEND:20251118T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/51
DESCRIPTION:Title: Fibering out Calabi-Yau motives\nby Kilian Böni
sch as part of Sheffield Number Theory Seminar\n\nLecture held in J-11 Hic
ks Building.\n\nAbstract\nI will present a method which allows proving the
modularity of mixed periods associated with singular fibers of families o
f Calabi-Yau threefolds (e.g. the mirror quintic). This is done by "fiberi
ng out"\, i.e. by expressing these periods as integrals of periods of fami
lies of K3 surfaces and by using modularity properties of the latter. Besi
des classical 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 resid
ues as well as contours between CM points. The talk is based on the collab
oration https://arxiv.org/abs/2510.03939 with Vasily Golyshev and Albrecht
Klemm.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/51
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Dawydiak (Glasgow)
DTSTART:20260127T130000Z
DTEND:20260127T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/52
DESCRIPTION:Title: Affine and asymptotic Hecke algebras for p-adic grou
ps\nby Stefan Dawydiak (Glasgow) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nStarting from c
elebrated work of Kazhdan-Lusztig\, rich geometric and spectral pictures o
f affine Hecke algebras have emerged as a special case of the Local Langla
nds Correspondence for p-adic groups. I will report on work\, initiated by
Braverman-Kazhdan\, to extend these pictures to a slightly larger algebra
\, Lusztig's asymptotic Hecke algebra. This ring retains the connection to
the geometry of the dual group enjoyed by the affine Hecke algebra\, whic
h we will recall and use to give some formulas for certain Harish-Chandra
Schwartz functions and a geometric criterion for reducibility of certain t
empered representations.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/52
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Shotton (Durham)
DTSTART:20260421T120000Z
DTEND:20260421T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/53
DESCRIPTION:by Jack Shotton (Durham) as part of Sheffield Number Theory Se
minar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/53
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maleeha Khawaja (Warwick)
DTSTART:20260505T120000Z
DTEND:20260505T130000Z
DTSTAMP:20260404T094532Z
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://stable.researchseminars.org/talk/SheffieldNumberTheory/54
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandros Groutides (Warwick)
DTSTART:20260310T130000Z
DTEND:20260310T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/55
DESCRIPTION:Title: Arithmetic of Rankin-Selberg zeta-integrals for newf
orms\nby Alexandros Groutides (Warwick) as part of Sheffield Number Th
eory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbstract\nZeta-int
egrals of Rankin type have been a cornerstone in the representation-theore
tic approach toward the study of product L-functions. In this talk\, I wil
l first motivate the construction of this for the Rankin-Selberg convoluti
on of newforms. I will then introduce a generic notion of ''integral input
data'' at which this zeta-integral can be evaluated and mention how it re
lates to Rankin-Selberg Euler systems. Using this notion\, I will present
an integral refinement of Jacquet-Langland's GCD-result\, and If time perm
its\, I will summarize key ingredients in the approach. These include a no
vel reinterpretation of the Rankin-Selberg zeta-integral\, and works of A.
Saha and E. Assing on p-adic Whittaker newvectors.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/55
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Chambers (Sheffield)
DTSTART:20260224T130000Z
DTEND:20260224T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/56
DESCRIPTION:Title: Congruences of Modular Forms of Half-Integral Weight
(and Twisted L-Values)\nby Mark Chambers (Sheffield) as part of Sheff
ield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nAbst
ract\nWe have a classical theta lifting between weight 2k and weight k+1/2
modular forms. Specifically\, for squarefree level\, we get finitely many
lifts corresponding to classes of discriminants. A natural question to as
k is whether these lifts preserve congruences of Fourier coefficients\, wh
ich also has applications towards square roots of twisted L-Values. In ord
er to prove congruences\, we look at cohomological lifts\, which were used
by Kohnen-Zagier to construct the lift for one class of discriminants. We
extend this to all other cases using a construction of Kojima-Tokuno\, an
d prove that congruences are preserved for large non-Eisenstein primes.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/56
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Solomon (IMJ)
DTSTART:20260428T120000Z
DTEND:20260428T130000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/57
DESCRIPTION:by David Solomon (IMJ) as part of Sheffield Number Theory Semi
nar\n\nLecture held in J-11 Hicks Building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/57
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tim Berland (University of Copenhagen)
DTSTART:20260324T130000Z
DTEND:20260324T140000Z
DTSTAMP:20260404T094532Z
UID:SheffieldNumberTheory/58
DESCRIPTION:Title: Growth of torsion in the cohomology of Q-rank 1 arit
hmetic groups\nby Tim Berland (University of Copenhagen) as part of Sh
effield Number Theory Seminar\n\nLecture held in J-11 Hicks Building.\n\nA
bstract\nCohomology of arithmetic groups has long been understood to have
number theoretic significance. By the Ash conjecture\, cohomological torsi
on predicts the existence of Galois representations\, hence it is desirabl
e to know when to expect torsion\, and how much. It was conjectured by Ber
geron and Venkatesh that when the deficiency is 1\, there should be expone
ntial growth of torsion in families of congruence subgroups\, and they sho
wed this to be true for cocompact congruence subgroups with certain coeffi
cient systems. This was generalized to Q-rank 1 by Müller and Rochon. How
ever\, it is still unclear what to expect outside deficiency 1. As a step
towards remedying this\, in this talk we give subexponential bounds on tor
sion in the cohomology of Q-rank 1 congruence subgroups when the deficienc
y is not 1\, as well as bounds on second order terms for deficiency 1\, us
ing sharpened asymptotics on analytic torsion.\n
LOCATION:https://stable.researchseminars.org/talk/SheffieldNumberTheory/58
/
END:VEVENT
END:VCALENDAR