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BEGIN:VEVENT
SUMMARY:Andrew Brooke-Taylor (University of Leeds)
DTSTART;VALUE=DATE-TIME:20230207T140000Z
DTEND;VALUE=DATE-TIME:20230207T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/1
DESCRIPTION:Title: Co
mplexity of classification problems\nby Andrew Brooke-Taylor (Universi
ty of Leeds) as part of UEA pure maths seminar\n\nLecture held in EFRY 01.
05.\n\nAbstract\nThe notion of "Borel reducibility" gives a framework that
allows us to compare the complexities of different classes of mathematica
l objects. I will give an introduction to this framework\, including how
it has been used to show that a number of proposed classification programm
es in different areas of mathematics were impossible to realise. I'll the
n talk about using the framework to explain why the knot invariants called
"quandles" are often considered to be too hard to work with (joint work w
ith Sheila Miller)\, and finish with a discussion of what happens when the
framework is extended to capture functoriality (joint work with Filippo C
alderoni).\n
LOCATION:https://researchseminars.org/talk/UEAPS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (UEA)
DTSTART;VALUE=DATE-TIME:20230217T120000Z
DTEND;VALUE=DATE-TIME:20230217T130000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/2
DESCRIPTION:Title: Cl
assification of charge-conserving loop braid representations\nby Fiona
Torzewska (UEA) as part of UEA pure maths seminar\n\nLecture held in SCI
1.20.\n\nAbstract\nThe loop braid category is the diagonal category made u
p of loop braid groups $LB_n$\, exactly paralleling the relationship betw
een MacLane's braid category and the Artin braid groups. A loop braid repr
esentation is a monoidal functor from the loop braid category $\\mathsf{L}
$ to a suitable target category\, and is $N$-charge-conserving if that tar
get is the category $\\mathrm{Match}^N$ of charge-conserving matrices.\nIn
this talk I will discuss the classification and construction of all such
representations. (These representations fall into varieties indexed by a s
et in bijection with the set of pairs of plane partitions of total degree
$N$.)\n
LOCATION:https://researchseminars.org/talk/UEAPS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamilla Rekvenyi (Imperial)
DTSTART;VALUE=DATE-TIME:20230314T140000Z
DTEND;VALUE=DATE-TIME:20230314T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/4
DESCRIPTION:Title: Th
e Orbital Diameter of Primitive Permutation Groups\nby Kamilla Rekveny
i (Imperial) as part of UEA pure maths seminar\n\nLecture held in NEWSCI 0
.06.\n\nAbstract\nLet G be a group acting transitively on a finite set Ω.
Then G acts on ΩxΩ component wise. Define the orbitals to be the orbits
of G on ΩxΩ. The diagonal orbital is the orbital of the form ∆ = {(α
\, α)|α ∈ Ω}. The others are called non-diagonal orbitals. Let Γ be
a non-diagonal orbital. Define an orbital graph to be the non-directed gr
aph with vertex set Ω and edge set (α\,β)∈ Γ with α\,β∈ Ω. If t
he action of G on Ω is primitive\, then all non-diagonal orbital graphs a
re connected. The orbital diameter of a primitive permutation group is the
supremum of the diameters of its non-diagonal orbital graphs.\n\nThere ha
s been a lot of interest in finding bounds on the orbital diameter of prim
itive permutation groups. In my talk I will outline some important backgro
und information and the progress made towards finding explicit bounds on t
he orbital diameter. In particular\, I will discuss some results on the or
bital diameter of the groups of simple diagonal type and their connection
to the covering number of finite simple groups. I will also discuss some r
esults for affine groups\, which provides a nice connection to the represe
ntation theory of quasisimple groups.\n
LOCATION:https://researchseminars.org/talk/UEAPS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Martin (Earlham Institute)
DTSTART;VALUE=DATE-TIME:20230502T130000Z
DTEND;VALUE=DATE-TIME:20230502T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/6
DESCRIPTION:Title: Di
mensions of phylogenetic network varieties\nby Samuel Martin (Earlham
Institute) as part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\
n\nAbstract\nPhylogenetic networks provide a means of describing the evolu
tionary history of taxa that have undergone “horizontal” events\, such
as hybridization or lateral gene transfer. The mutation process of a sing
le site in shared DNA sequence for a set of such taxa can be modelled as a
Markov process on a phylogenetic network\, and the site-pattern probabili
ty distributions from such a model can be viewed as a projective variety.
In this work\, we have given an explicit description of the dimension of t
his variety for a given level-1 phylogenetic network under any group-based
model of evolution. I will give an overview of the model from an algebrai
c perspective and describe our results\, focussing on the toric fiber prod
uct of two ideals\, and finish with some applications to identifiability p
roblems. Joint work with Elizabeth Gross and Robert Krone.\n
LOCATION:https://researchseminars.org/talk/UEAPS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (Imperial)
DTSTART;VALUE=DATE-TIME:20230516T130000Z
DTEND;VALUE=DATE-TIME:20230516T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/7
DESCRIPTION:Title: To
wards a theta correspondence in families for type II dual pairs\nby Ju
stin Trias (Imperial) as part of UEA pure maths seminar\n\nLecture held in
QUEENS 1.03.\n\nAbstract\nThe classical local theta correspondence for p-
adic reductive dual pairs defines a bijection between prescribed subsets o
f irreducible smooth complex representations coming from two groups (H\,H'
)\, forming a dual pair in a symplectic group. Alberto Mínguez extended t
his result for type II dual pairs\, i.e. when (H\,H') is made of general l
inear groups\, to representations with coefficients in an algebraically cl
osed field of characteristic l as long as the characteristic l does not di
vide the pro-orders of H and H'. For coefficients rings like Z[1/p]\, we e
xplain how to build a theory in families for type II dual pairs that is co
mpatible with reduction to residue fields of the base coefficient ring\, w
here central to this approach is the integral Bernstein centre. We transla
te some weaker properties of the classical correspondence\, such as compat
ibility with supercuspidal support\, as a morphism between the integral Be
rnstein centres of H and H' and interpret it for the Weil representation.
In general\, we only know that this morphism is finite though we may expec
t it to be surjective. This would result in a closed immersion between the
associated affine schemes as well as a correspondence between characters
of the Bernstein centre. This is current work with Gil Moss.\n
LOCATION:https://researchseminars.org/talk/UEAPS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Saha (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20230523T130000Z
DTEND;VALUE=DATE-TIME:20230523T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/8
DESCRIPTION:Title: Th
e Manin constant\, the modular degree\, and Fourier expansions at cusps\nby Abhishek Saha (Queen Mary University of London) as part of UEA pure
maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nLet f be a normali
zed newform of weight k for $\\Gamma_0(N)$. It is a natural question to tr
y to understand the size (in a $p$-adic sense) of the "denominators" of th
e Fourier expansions of f at a cusp of $X_0(N)$. The problem is easy if N
is square-free but is delicate when N is highly square-full. I will talk a
bout recent joint work with Kȩstutis Česnavičius and Michael Neururer w
here we solve this problem using representation-theoretic techniques. Roug
hly speaking\, we reduce the problem to bounding $p-$adic valuations of lo
cal Whittaker newforms and then use a "basic identity" (a consequence of t
he Jacquet-Langlands local functional equation) to reduce to $p$-adic prop
erties of local epsilon factors of representations of $\\GL_2(\\Q_p)$. \n
\nA key application of our result is to understand the Manin constant c of
an elliptic curve E over the rationals. The integer c scales the differen
tial determined by the normalized newform f associated to E into the pullb
ack of a N\\'{e}ron differential under a minimal modular parametrization.
Manin conjectured that c equals 1 or -1 for optimal parametrizations. We p
rove that c divides the degree of the parametrization under a minor assump
tion at the primes 2 and 3. For this result\, we establish a certain integ
rality property of $\\omega_f$ that follows from the Manin conjecture. We
expect that this integrability property we prove here will be necessary fo
r any further progress towards Manin's conjecture.\n
LOCATION:https://researchseminars.org/talk/UEAPS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (Cambridge)
DTSTART;VALUE=DATE-TIME:20230425T130000Z
DTEND;VALUE=DATE-TIME:20230425T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/10
DESCRIPTION:Title: M
odularity in the partial weight one case\nby Hanneke Wiersema (Cambrid
ge) as part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\n\nAbst
ract\nThe strong form of Serre's conjecture states that a two-dimensional
mod p representation of the absolute Galois group of $\\mathbb{Q}$ arises
from a modular form of a specific weight\, level and character. Serre rest
ricted to modular forms of weight at least 2\, but Edixhoven later refined
this conjecture to include weight one modular forms. In this talk we expl
ore analogues of Edixhoven's refinement for Galois representations of tota
lly real fields\, extending recent work of Diamond and Sasaki. In particul
ar\, we show how modularity of partial weight one Hilbert modular forms ca
n be related to modularity of Hilbert modular forms with regular weights\,
and vice versa. We will also discuss the applications of this for p-adic
Hodge theory.\n
LOCATION:https://researchseminars.org/talk/UEAPS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (UEA)
DTSTART;VALUE=DATE-TIME:20230509T130000Z
DTEND;VALUE=DATE-TIME:20230509T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/12
DESCRIPTION:Title: S
copes equivalence for blocks of Ariki-Koike algebras\nby Alice Dell'Ar
ciprete (UEA) as part of UEA pure maths seminar\n\nLecture held in NEWSCI
0.06.\n\nAbstract\nWe consider representations of the Ariki-Koike algebra\
, a $q$-deformation of the group algebra of the complex reflection group $
C_r\\wr\\mathfrak{S}_n$. The representations of this algebra are naturally
indexed by multipartitions of $n$. We examine blocks of the Ariki-Koike a
lgebra\, in an attempt to generalise the combinatorial representation theo
ry of the Iwahori-Hecke algebra. In particular\, we prove a sufficient con
dition such that restriction of modules leads to a natural correspondence
between the multipartitions of $n$ whose Specht modules belong to a block
$B$ and those of $n−\\delta_i(B)$ whose Specht modules belong to the blo
ck $B'$\, obtained from $B$ applying a Scopes' equivalence. This gives us
an equality of decomposition numbers for the corresponding Ariki-Koike alg
ebras.\n
LOCATION:https://researchseminars.org/talk/UEAPS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nutt Tananimit (UEA)
DTSTART;VALUE=DATE-TIME:20230530T130000Z
DTEND;VALUE=DATE-TIME:20230530T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/13
DESCRIPTION:Title: C
onsistent and Inconsistent Generalizations of Martin's Axiom and Weak Squa
re\nby Nutt Tananimit (UEA) as part of UEA pure maths seminar\n\nLectu
re held in SCI 3.05.\n\nAbstract\nWe prove that the forcing axiom $\\texts
f{MA}^{1.5}_{\\aleph_2}(\\text{stratified})$ implies $\\square_{\\omega_1\
, \\omega_1}$. \nUsing this implication\, we show that the forcing axiom $
\\textsf{MM}_{\\aleph_2}(\\aleph_2\\text{-c.c.})$ is inconsistent.\n
LOCATION:https://researchseminars.org/talk/UEAPS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Ardakov (Oxford)
DTSTART;VALUE=DATE-TIME:20230328T130000Z
DTEND;VALUE=DATE-TIME:20230328T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/14
DESCRIPTION:Title: T
he central sheaf of the category of smooth mod-$p$ representations of $SL_
2(\\mathbb{Q}_p)$\nby Konstantin Ardakov (Oxford) as part of UEA pure
maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nThis is work in pr
ogress with Peter Schneider. The Bernstein centre of a $p$-adic reductive
group plays a fundamental role in the classical local Langlands correspond
ence. In the mod-p local Langlands program\, the naive analogue of the Ber
nstein centre\, namely the centre of the category $Mod(G)$ of all smooth m
od-$p$ representations\, turns out to be too small: it is for example triv
ial whenever the group in question has trivial centre. Instead\, we consid
er the centres $Z(Mod(G)/\\mathcal{L})$ of the quotient categories $Mod(G)
/\\mathcal{L}$\, as $\\mathcal{L}$ runs over all localizing subcategories
of $Mod(G)$. We show that provided one restricts to the localizing subcate
gories that are $stable$ $under$ $injective$ $envelopes$\, this defines a
sheaf with respect to finite coverings. In the case where $G = SL_2(\\math
bb{Q}_p)$ and $p \\neq 2\,3$\, we use recent results by Ollivier and Schne
ider on the structure of the pro-$p$ Iwahori $Ext$-algebra to construct a
certain projective variety $X$ having the property that every Zariski open
subset $U$ of $X$ gives rise to a stable localizing subcategory $\\mathca
l{L}_U$ of $Mod(G)$. Both connected components of $X$ are certain chains o
f projective lines\, and $X$ and is closely related to the recent work of
Dotto\, Emerton and Gee.\n
LOCATION:https://researchseminars.org/talk/UEAPS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:test
DTSTART;VALUE=DATE-TIME:20230801T130000Z
DTEND;VALUE=DATE-TIME:20230801T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/15
DESCRIPTION:by test as part of UEA pure maths seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Jones (The University of Manchester)
DTSTART;VALUE=DATE-TIME:20231017T130000Z
DTEND;VALUE=DATE-TIME:20231017T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/16
DESCRIPTION:Title: A
n effective version of a theorem of Habegger\nby Gareth Jones (The Uni
versity of Manchester) as part of UEA pure maths seminar\n\nLecture held i
n SCI 3.05.\n\nAbstract\nHabegger showed that a subvariety of a fibre powe
r of the Legendre family of elliptic curves contains a Zariski-dense set o
f special points if and only if it is special. I'll explain this result\,
and discuss an effective version proved by Gal Binyamini\, Harry Schmidt\,
Margaret Thomas\, and me.\n
LOCATION:https://researchseminars.org/talk/UEAPS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar León Sánchez (The University of Manchester)
DTSTART;VALUE=DATE-TIME:20231205T140000Z
DTEND;VALUE=DATE-TIME:20231205T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/17
DESCRIPTION:Title: S
ome remarks on differentially large fields and CODFs\nby Omar León S
ánchez (The University of Manchester) as part of UEA pure maths seminar\n
\nLecture held in SCI 3.05.\n\nAbstract\nWe make some observations around
differentially large fields (in characteristic zero). In particular\, we n
ote that they can be characterised as those differential fields that are e
xistentially closed in the "differential algebraic" Laurent series ring. W
e also note that a field admits a differentially large structure iff it is
of infinite transcendence degree (over Q). We then turn our attention to
the theory CODF (closed ordered differential fields). We observe that a re
al closed differential field has a prime model extension (in CODF) iff it
is already a CODF. This extends a result of Singer showing that CODF has n
o prime model. We then discuss the question of when a real closed differen
tial field has a CODF extension inside a differential closure.\nThis is a
combination of joint work with Marcus Tressl and Anand Pillay.\n
LOCATION:https://researchseminars.org/talk/UEAPS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Torzewski (Kings College London)
DTSTART;VALUE=DATE-TIME:20231003T130000Z
DTEND;VALUE=DATE-TIME:20231003T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/18
DESCRIPTION:Title: S
tudying points on varieties via varying families\nby Alex Torzewski (K
ings College London) as part of UEA pure maths seminar\n\nLecture held in
EFRY 01.05.\n\nAbstract\nWe show how Lawrence-Venkatesh's method for study
ing points on a variety X can be applied to curves in families. In the pro
cess\, we also outline the original method. The idea is that if there exis
ts a family over X which varys "a lot"\, then this strongly constrains the
existence of points. This is an example of how topology influences arithm
etic!\n
LOCATION:https://researchseminars.org/talk/UEAPS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Rockwood (Kings College London)
DTSTART;VALUE=DATE-TIME:20231024T130000Z
DTEND;VALUE=DATE-TIME:20231024T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/19
DESCRIPTION:Title: F
amilies of branching laws and their arithmetic applications\nby Rob Ro
ckwood (Kings College London) as part of UEA pure maths seminar\n\nLecture
held in EFRY 01.08.\n\nAbstract\nThe branching laws of certain special pa
irs of algebraic groups $H \\to G$ are related to the $L$-functions of aut
omorphic representations via the theory of period integrals\, made concret
e by the conjectures of Gan--Gross--Prasad and Ichino--Ikeda. On the algeb
raic side\, one can use branching laws for highest weight representations
to construct cohomological avatars of automorphic period integrals in the
cohomology of Shimura varieties. These classes are related to $p$-adic $L$
-functions and Euler systems\, both of which have applications to importan
t arithmetic conjectures such as the Bloch--Kato conjectures. I will expla
in how one constructs such avatars and will describe work of myself and Lo
effler--Zerbes on varying these classes in $p$-adic families.\n
LOCATION:https://researchseminars.org/talk/UEAPS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Islam Foniqi (University of East Anglia)
DTSTART;VALUE=DATE-TIME:20231010T130000Z
DTEND;VALUE=DATE-TIME:20231010T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/20
DESCRIPTION:Title: D
ecision and membership problems in one-relator monoids and groups\nby
Islam Foniqi (University of East Anglia) as part of UEA pure maths seminar
\n\nLecture held in SCI 3.05.\n\nAbstract\nMotivated by the open word prob
lem for one-relator monoids\, we study decision problems for monoids and g
roups. I will present some recent results (joint work with Robert D. Gray
& C.-F. Nyberg-Brodda) on submonoid and rational subset membership proble
ms in algebraic structures\, and discuss their implications and connection
s with the word problem. Right-angled Artin groups and trace monoids play
a major role in this context\, and I will highlight their use in our work.
\n
LOCATION:https://researchseminars.org/talk/UEAPS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Spriano (Oxford University)
DTSTART;VALUE=DATE-TIME:20231212T140000Z
DTEND;VALUE=DATE-TIME:20231212T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/21
DESCRIPTION:Title: O
n uniquely geodesic graphs and groups\nby Davide Spriano (Oxford Unive
rsity) as part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\n\nA
bstract\nGraph with a unique geodesic between any two points are a very na
tural object to define\, but they remain a mysterious object. In this talk
we will discuss new results about their classifications\, and show that a
group with a uniquely geodesic Cayley graph needs to be virtually free. T
his is joint work with Elder\, Gardam\, Piggott and Townsend.\n
LOCATION:https://researchseminars.org/talk/UEAPS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Simoes (Lancaster University)
DTSTART;VALUE=DATE-TIME:20231121T140000Z
DTEND;VALUE=DATE-TIME:20231121T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/22
DESCRIPTION:Title: F
rom gentle to string algebras: a geometric model\nby Raquel Coelho Sim
oes (Lancaster University) as part of UEA pure maths seminar\n\n\nAbstract
\nGeometric models associated to triangulations of Riemann surfaces arose
in the context of cluster algebras and have since been used as an importan
t tool to study representation theory of algebras and provide connections
with algebraic geometry and symplectic geometry. \n\nSignificant applicati
ons of geometric models include a description of extensions and a classifi
cation of support tau-tilting modules over gentle algebras. Gentle algebra
s are a particular subclass of string algebras\, which are of tame represe
ntation type\, meaning it is often possible to get a global understanding
of their representation theory.\n\nIn this talk I will describe the module
category of a gentle algebra via partial triangulations of unpunctured su
rfaces and explain how to extend this model to a geometric model of the mo
dule category of any string algebra. This is based on joint work in progre
ss with Karin Baur.\n
LOCATION:https://researchseminars.org/talk/UEAPS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (KCL)
DTSTART;VALUE=DATE-TIME:20240227T140000Z
DTEND;VALUE=DATE-TIME:20240227T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/23
DESCRIPTION:Title: P
arametrising abelian surfaces with RM by $\\mathbb{Z}[\\sqrt{2}]$ using Ri
chelot isogenies\nby Lassina Dembélé (KCL) as part of UEA pure maths
seminar\n\nLecture held in TPSC 0.1.\n\nAbstract\nIn this talk\, we descr
ibe a parametrisation of abelian surfaces with real multiplication by $\\m
athbb{Z}[\\sqrt{2}]$ using Richelot isogenies\, and give some arithmetic a
pplications.\n
LOCATION:https://researchseminars.org/talk/UEAPS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Gruber (York)
DTSTART;VALUE=DATE-TIME:20240312T140000Z
DTEND;VALUE=DATE-TIME:20240312T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/24
DESCRIPTION:Title: C
enters and centralizers in (double) affine Hecke algebras\nby Jonathan
Gruber (York) as part of UEA pure maths seminar\n\nLecture held in Queen
01.09.\n\nAbstract\nThe affine Hecke algebra and its center are important
objects of study in combinatorial\, geometric and categorical representati
on theory. In this talk\, I will discuss a new commutative subalgebra of t
he affine Hecke algebra of type A\, which arises from a centralizer constr
uction in the double affine Hecke algebra. This subalgebra contains the ce
nter\, and it admits a canonical basis akin to the Kazhdan-Lusztig basis o
f the affine Hecke algebra. I will explain how the canonical basis can be
used as a tool to compute composition multiplicities in Gaitsgory's centra
l sheaves on affine flag manifolds.\n
LOCATION:https://researchseminars.org/talk/UEAPS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (Sheffield)
DTSTART;VALUE=DATE-TIME:20240319T140000Z
DTEND;VALUE=DATE-TIME:20240319T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/25
DESCRIPTION:Title: N
ewforms for cuspidal representations\nby Rob Kurinczuk (Sheffield) as
part of UEA pure maths seminar\n\nLecture held in EFRY 01.02.\n\nAbstract\
nWe will review the theory of newforms for cuspidal representations of p-a
dic general linear groups of Jacquet--Piatetski-Shapiro--Shalika\, and Mat
ringe. Then compare them with the explicit functions of Paskunas-Stevens
for cuspidal representations in special cases. This is joint work in prog
ress with Johannes Girsch.\n
LOCATION:https://researchseminars.org/talk/UEAPS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Prest (Manchester)
DTSTART;VALUE=DATE-TIME:20240423T130000Z
DTEND;VALUE=DATE-TIME:20240423T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/26
DESCRIPTION:Title: L
inear algebra over general rings\nby Mike Prest (Manchester) as part o
f UEA pure maths seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nIn li
near algebra we meet solution sets to systems of linear equations with coe
fficients from a field. Later\, we see that we can replace the field by a
more general ring\, for instance a Weyl algebra where we would be looking
at solutions of systems of linear partial differential equations. Over g
eneral rings\, however\, such solution sets do not have nice closure prope
rties\; for instance they might not be closed under coordinate projections
. But\, if we accept projected systems of equations and their solution se
ts as basic objects\, then we recover the nice closure properties that one
has over fields and\, over general rings\, find interesting structures si
tting within a rich and extensive theory which ramifies into many aspects
of representation theory.\n
LOCATION:https://researchseminars.org/talk/UEAPS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvy Anscombe (Paris)
DTSTART;VALUE=DATE-TIME:20240430T130000Z
DTEND;VALUE=DATE-TIME:20240430T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/27
DESCRIPTION:Title: U
niformities for Hilbert's Tenth Problem in henselian valued fields\nby
Sylvy Anscombe (Paris) as part of UEA pure maths seminar\n\nLecture held
in NEWSCI 0.04.\n\nAbstract\nHilbert's Tenth Problem in its original form
asks for an algorithm to determine correctly whether -- or not -- a given
multivariable polynomial equation with integer coefficients has integer so
lutions.\nThe surprising resolution\, by Davis\, Putnam\, Robinson\, and f
inished by Matiyasevich in 1970\, is that there is no such algorithm. In t
he terminology of mathematical logic\, the existential theory of the ring
of integers is undecidable. I am interested in the (un?)decidability of th
e existential theories of a variety of rings and fields\, especially of "l
arge" fields\, for example those fields admitting a non-trivial valuation
that satisfies "Hensel's Lemma"\, a weak form of completion. In this talk
I'll describe work in this direction (joint with Dittmann\, Fehm\, Jahnke\
, and others\, in various combinations)\, new "uniform" results\, and some
links with theories of function fields.\n
LOCATION:https://researchseminars.org/talk/UEAPS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aberdeen Powell (UEA)
DTSTART;VALUE=DATE-TIME:20240206T140000Z
DTEND;VALUE=DATE-TIME:20240206T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/28
DESCRIPTION:Title: F
robenius reciprocity for fiat 2-categories\nby Aberdeen Powell (UEA) a
s part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\
nFrobenius reciprocity is a famous property first observed in the setting
of group representations. Representations of 2-categories is a lively and
relatively young field\, where many classic results of representation theo
ry reappear: the Jordan-Hölder theorem (Mackaay\, Mazorchuk\, Miemietz\,
Tubbenhauer and Zhang\, Finitary birepresentations of fintary bicategories
)\, various properties from Morita theory (Mazorchuk and Miemietz\, Morita
theory for finitary 2-categories)\, etc. In this talk\, we consider Frobe
nius reciprocity in the context of 2-categories.\n
LOCATION:https://researchseminars.org/talk/UEAPS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curial Gallart Rodriguez (UEA)
DTSTART;VALUE=DATE-TIME:20240514T130000Z
DTEND;VALUE=DATE-TIME:20240514T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/29
DESCRIPTION:Title: C
urrent trends in set theory\nby Curial Gallart Rodriguez (UEA) as part
of UEA pure maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nNot a
ll questions in mathematics can be answered in ZFC by Gödel's incompleten
ess theorems. Numerous concrete examples of mathematical statements have b
een proven to be independent from the ZFC axioms over the years. Many of t
hem being non-set-theoretic in nature. Most notably\, the Whitehead proble
m\, the Borel conjecture\, Kaplansky's conjecture on Banach algebras\, or
the Brown-Douglas-Fillmore problem. Instead of accepting that there are qu
estions that don't have an answer\, the independence phenomenon lead set t
heorists to search for axioms beyond ZFC that would give us a clearer pict
ure of the set theoretic (and mathematical) universe.\n\nIn this talk I wi
ll present the main lineages of axioms that have been considered and their
consequences. I will describe their connections and the main methods to s
tudy them\, and I will finish by connecting all of this with my PhD thesis
.\n
LOCATION:https://researchseminars.org/talk/UEAPS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ward
DTSTART;VALUE=DATE-TIME:20240507T130000Z
DTEND;VALUE=DATE-TIME:20240507T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/30
DESCRIPTION:Title: H
idden dynamical zeta functions\nby Tom Ward as part of UEA pure maths
seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nI will discuss examples
of a phenomenon first observed (to my knowledge) by Yash Puri. Certain - a
s it turns out\, many - sequences that arise naturally in combinatorics or
number theory fail to count periodic points (that is\, be the coefficient
s of a dynamical zeta function) but succeed after some modest modification
. Examples include the Stirling numbers and linear recurrence sequences.\n
LOCATION:https://researchseminars.org/talk/UEAPS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (Manchester)
DTSTART;VALUE=DATE-TIME:20240213T140000Z
DTEND;VALUE=DATE-TIME:20240213T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/32
DESCRIPTION:Title: Y
ou need 27 tickets to guarantee a win on the UK National Lottery (Jt with
David Cushing)\nby David Stewart (Manchester) as part of UEA pure math
s seminar\n\nLecture held in Queen 01.09.\n\nAbstract\nThe authors came ac
ross the problem of finding minimal lottery design numbers j=L(n\,k\,p\,t)
\; that is\, a set B_1\, …\, B_j subsets of {1\,..\,n} each of size k\,
such that for any subset D of {1\,..\,n} of size p\, one finds an intersec
tion D\\cap B_i with at least t elements. In the context of a lottery\, n
represents the. number of balls\, k the number of choices of balls on a ti
cket\, p the size of a draw.\nFor the UK national lottery\, n=59\, k=p=6 a
nd one gets a (rather meagre) prize as long as t is at least 2.\nUsing the
constraint solving library in Prolog\, we calculated j for k=p=6\, t=2 an
d n all the way up to 70. For example L(59\,6\,6\,2)=27. This is the secon
d paper where we have aimed to show the value of Prolog and constraint pro
gramming in pure mathematics.\nI’ll give an overview of constraint progr
amming\, logic programming in Prolog\, and describe how we used these tool
s to solve the problem described in the title.\n
LOCATION:https://researchseminars.org/talk/UEAPS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Macpherson (Instituto Superior Tecnico\, Lisbon)
DTSTART;VALUE=DATE-TIME:20240318T140000Z
DTEND;VALUE=DATE-TIME:20240318T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/33
DESCRIPTION:Title: E
valuation 2-functors for categorified affine sl(n)\nby James Macpherso
n (Instituto Superior Tecnico\, Lisbon) as part of UEA pure maths seminar\
n\nLecture held in EFRY01.10.\n\nAbstract\nWhen studying representations o
f particularly unruly\nmathematical structures\, it can often be useful to
compose\nrepresentations of an associated\, simpler structure with an `ev
aluation'\nfunctor from the unruly structure to the better behaved one. A\
npreviously studied example is the evaluation functor from (the\nidempoten
ted universal enveloping algebra of) affine type sl(n) to\nfinite type sl(
n). In this talk I will explain this example in detail. I\nwill then prese
nt the categorification of this evaluation functor\nbetween the correspond
ing 2-Kac-Moody algebras for the n=3 case\, and\nalso discuss some of the
techniques used for an inductive construction\nof the evaluation 2-functor
for larger n. This is joint work with Marco\nMackaay and Pedro Vaz.\n
LOCATION:https://researchseminars.org/talk/UEAPS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan Haden (UEA)
DTSTART;VALUE=DATE-TIME:20240606T100000Z
DTEND;VALUE=DATE-TIME:20240606T110000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/34
DESCRIPTION:Title: 3
-Preprojective Algebras of Type D\nby Jordan Haden (UEA) as part of UE
A pure maths seminar\n\nLecture held in EFry 01.02.\n\nAbstract\nGiven an
algebra with finite global dimension\, it is natural to consider two autoe
quivalences of its bounded derived category: the Serre functor and the shi
ft functor. If a power of one is isomorphic to a power of the other\, we s
ay the algebra is fractional Calabi-Yau. Closely related are d-representat
ion-finite algebras. These are algebras whose module category contains a d
-cluster tilting subcategory\, which is “manageable” even if the algeb
ra has wild representation type. We will explain these concepts\, and how
they are connected\, before presenting an infinite family of algebras whic
h are both fractional Calabi-Yau and 2-representation-finite.\n
LOCATION:https://researchseminars.org/talk/UEAPS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (Columbia University)
DTSTART;VALUE=DATE-TIME:20240708T130000Z
DTEND;VALUE=DATE-TIME:20240708T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/35
DESCRIPTION:Title: H
ecke algebras for p-adic groups and explicit Local Langlands Correspondenc
e\nby Yujie Xu (Columbia University) as part of UEA pure maths seminar
\n\n\nAbstract\nI will talk about several results on Hecke algebras attach
ed to Bernstein blocks of reductive p-adic groups\, where we construct a l
ocal Langlands correspondence for these Bernstein blocks. Our techniques d
raw inspirations from the foundational works of Deligne\, Kazhdan\, Langla
nds\, Lusztig and Shahidi.\n\n\nAs an application\, we prove the Local Lan
glands Conjecture for G_2\, which is the first known case in literature of
LLC for exceptional groups. Our correspondence satisfies an expected prop
erty on cuspidal support\, which is compatible with the generalized Spring
er correspondence\, along with a list of characterizing properties includi
ng the stabilization of character sums\, formal degree property etc. In pa
rticular\, we obtain (not necessarily unipotent) "mixed" L-packets contain
ing "F-singular" supercuspidals and non-supercuspidals. I will give explic
it examples of such mixed L-packets in terms of Deligne-Lusztig theory and
Kazhdan-Lusztig parametrization.\n\nIf time permits\, I will explain how
to pin down certain choices in the construction of the correspondence usin
g stability of L-packets\; one key input is a homogeneity result due to Wa
ldspurger and DeBacker. Moreover\, I will mention how to adapt our general
strategy to construct explicit LLC for other reductive groups\, such as G
Sp_4\, Sp_4\, etc\, generalizing the depth-zero L-packets of Lust-Stevens.
Such explicit description of the L-packets has been useful in number-theo
retic applications\, e.g. modularity lifting questions.\n\nVarious parts o
f this talk are based on joint works with various collaborators\, and attr
ibutions will be made clear throughout the talk.\n
LOCATION:https://researchseminars.org/talk/UEAPS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashot Minasyan (Southampton)
DTSTART;VALUE=DATE-TIME:20241015T130000Z
DTEND;VALUE=DATE-TIME:20241015T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/36
DESCRIPTION:Title: G
enerating RAAGs in 1-relator groups\nby Ashot Minasyan (Southampton) a
s part of UEA pure maths seminar\n\nLecture held in EFRY 01.05.\n\nAbstrac
t\nGiven a finite simplicial graph $\\Gamma$\, the right angled Artin grou
p (RAAG) $A(\\Gamma)$ is generated by the vertices of $\\Gamma$ subject to
the relations that two vertices commute if and only if they are adjacent
in $\\Gamma$. The monoid with the same presentation is called the trace mo
noid $T(\\Gamma)$. RAAGs play a significant role in Geometric Group Theory
\, while Trace monoids have important applications in Computer Science.\n\
nThe trace monoid $T(\\Gamma)$ is naturally embedded in the RAAG $A(\\Gamm
a)$\, as the set of positive words. In my talk I will discuss the followin
g problem: suppose that a 1-relator group G contains a submonoid isomorphi
c to $T(\\Gamma)$. Does $G$ also contain a copy of $A(\\Gamma)$ as a subgr
oup?\n\nThis problem is motivated by recent work of Foniqi\, Gray and Nybe
rg-Brodda\, who proved that groups containing T(P_4)\, where P_4 is the pa
th with 4 vertices (of length 3)\, have undecidable rational subset proble
m. They also exhibited 1-relator groups containing A(P_4) and asked whethe
r every 1-relator group which has a submonoid isomorphic to T(P_4) must al
so have a subgroup isomorphic to A(P_4). I will sketch an argument\, based
on joint work with Motiejus Valiunas\, showing that the answer to the lat
ter question is positive.\n
LOCATION:https://researchseminars.org/talk/UEAPS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım (Leeds)
DTSTART;VALUE=DATE-TIME:20241112T140000Z
DTEND;VALUE=DATE-TIME:20241112T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/37
DESCRIPTION:by Emine Yıldırım (Leeds) as part of UEA pure maths seminar
\n\nLecture held in EFRY 01.08.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Williams (Nottingham)
DTSTART;VALUE=DATE-TIME:20241001T130000Z
DTEND;VALUE=DATE-TIME:20241001T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/38
DESCRIPTION:Title: C
ongruences between eigensystems for GL(n)\nby Chris Williams (Nottingh
am) as part of UEA pure maths seminar\n\nLecture held in NEWSCI 0.03.\n\nA
bstract\nIn this talk\, I will discuss congruences between modular forms\,
and -- more generally -- between systems of eigenvalues on GL(n)\, modula
r forms being the special case $n=2$. In a broad sense\, this seeks to ans
wer the following type of question: Let $p$ be prime and $f$ be a modular
form of level $\\Gamma_0(M)$ where $p$ divides $M$. For a given integer $m
$\, does there exist another eigenform $g$ congruent to $f$ modulo $p^m$?\
n\nFor modular forms\, the answer is yes. Even better\, such congruences c
an be captured geometrically via 1-dimensional families' of eigenforms (vi
a the eigencurve'). This geometric object has had profound consequences in
Iwasawa theory and the Langlands program. In this talk\, I will attempt t
o give a gentle introduction to $p$-adic families\, and describe joint wo
rk with Daniel Barrera and Andy Graham\, where we consider some of the pro
blems in generalising them to higher dimension. Here the picture becomes m
ore subtle -- whilst all families for GL(2) are $1$-dimensional\, for GL(4
)\, there can be classical families of dimension $0\, 1$\, or $2$ attached
to the same automorphic representation.\n
LOCATION:https://researchseminars.org/talk/UEAPS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Warne (UEA)
DTSTART;VALUE=DATE-TIME:20241022T130000Z
DTEND;VALUE=DATE-TIME:20241022T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/39
DESCRIPTION:by Jonathan Warne (UEA) as part of UEA pure maths seminar\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Seminar
DTSTART;VALUE=DATE-TIME:20241029T140000Z
DTEND;VALUE=DATE-TIME:20241029T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/40
DESCRIPTION:by No Seminar as part of UEA pure maths seminar\n\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/UEAPS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembele (KCL)
DTSTART;VALUE=DATE-TIME:20241105T140000Z
DTEND;VALUE=DATE-TIME:20241105T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/41
DESCRIPTION:by Lassina Dembele (KCL) as part of UEA pure maths seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Cambridge)
DTSTART;VALUE=DATE-TIME:20241203T140000Z
DTEND;VALUE=DATE-TIME:20241203T150000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/42
DESCRIPTION:by Nicholas Williams (Cambridge) as part of UEA pure maths sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Levine (UEA)
DTSTART;VALUE=DATE-TIME:20241008T130000Z
DTEND;VALUE=DATE-TIME:20241008T140000Z
DTSTAMP;VALUE=DATE-TIME:20241013T130934Z
UID:UEAPS/43
DESCRIPTION:Title: E
quations with constraints in virtually abelian groups\nby Alex Levine
(UEA) as part of UEA pure maths seminar\n\nLecture held in SCI 1.50.\n\nAb
stract\nThe Diophantine problem in a group G is the decision problem askin
g whether there is an algorithm that decides if a system of equations in G
admits a solution. When considering equations in groups\, one can also ad
d 'constraints' to the variables\, such as insisting a specific variable m
ust lie in a specific subgroup. We consider the Diophantine problem for vi
rtually abelian groups\, which has long been considered 'folklore'. We lo
ok at adding various types of constraints to equations in virtually abelia
n groups.\n
LOCATION:https://researchseminars.org/talk/UEAPS/43/
END:VEVENT
END:VCALENDAR