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BEGIN:VEVENT
SUMMARY:Andrew Brooke-Taylor (University of Leeds)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/1
DESCRIPTION:Title: Complexity of classification problems\nby Andrew Brooke-Taylor (U
niversity of Leeds) as part of ANTLR seminar\n\nLecture held in EFRY 01.05
.\n\nAbstract\nThe notion of "Borel reducibility" gives a framework that a
llows us to compare the complexities of different classes of mathematical
objects. I will give an introduction to this framework\, including how it
has been used to show that a number of proposed classification programmes
in different areas of mathematics were impossible to realise. I'll then
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 wit
h Sheila Miller)\, and finish with a discussion of what happens when the f
ramework is extended to capture functoriality (joint work with Filippo Cal
deroni).\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (UEA)
DTSTART:20230217T120000Z
DTEND:20230217T130000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/2
DESCRIPTION:Title: Classification of charge-conserving loop braid representations\nb
y Fiona Torzewska (UEA) as part of ANTLR seminar\n\nLecture held in SCI 1.
20.\n\nAbstract\nThe loop braid category is the diagonal category made up
of loop braid groups $LB_n$\, exactly paralleling the relationship betwee
n MacLane's braid category and the Artin braid groups. A loop braid repres
entation is a monoidal functor from the loop braid category $\\mathsf{L}$
to a suitable target category\, and is $N$-charge-conserving if that targe
t is the category $\\mathrm{Match}^N$ of charge-conserving matrices.\nIn t
his talk I will discuss the classification and construction of all such re
presentations. (These representations fall into varieties indexed by a set
in bijection with the set of pairs of plane partitions of total degree $N
$.)\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamilla Rekvenyi (Imperial)
DTSTART:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/4
DESCRIPTION:Title: The Orbital Diameter of Primitive Permutation Groups\nby Kamilla
Rekvenyi (Imperial) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.0
6.\n\nAbstract\nLet G be a group acting transitively on a finite set Ω. T
hen G acts on ΩxΩ component wise. Define the orbitals to be the orbits o
f 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 grap
h with vertex set Ω and edge set (α\,β)∈ Γ with α\,β∈ Ω. If the
action of G on Ω is primitive\, then all non-diagonal orbital graphs are
connected. The orbital diameter of a primitive permutation group is the s
upremum of the diameters of its non-diagonal orbital graphs.\n\nThere has
been a lot of interest in finding bounds on the orbital diameter of primit
ive permutation groups. In my talk I will outline some important backgroun
d information and the progress made towards finding explicit bounds on the
orbital diameter. In particular\, I will discuss some results on the orbi
tal diameter of the groups of simple diagonal type and their connection to
the covering number of finite simple groups. I will also discuss some res
ults for affine groups\, which provides a nice connection to the represent
ation theory of quasisimple groups.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Martin (Earlham Institute)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/6
DESCRIPTION:Title: Dimensions of phylogenetic network varieties\nby Samuel Martin (E
arlham Institute) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\
nAbstract\nPhylogenetic networks provide a means of describing the evoluti
onary history of taxa that have undergone “horizontal” events\, such a
s hybridization or lateral gene transfer. The mutation process of a single
site in shared DNA sequence for a set of such taxa can be modelled as a M
arkov process on a phylogenetic network\, and the site-pattern probability
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 thi
s variety for a given level-1 phylogenetic network under any group-based m
odel of evolution. I will give an overview of the model from an algebraic
perspective and describe our results\, focussing on the toric fiber produc
t of two ideals\, and finish with some applications to identifiability pro
blems. Joint work with Elizabeth Gross and Robert Krone.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (Imperial)
DTSTART:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/7
DESCRIPTION:Title: Towards a theta correspondence in families for type II dual pairs
\nby Justin Trias (Imperial) as part of ANTLR seminar\n\nLecture held in Q
UEENS 1.03.\n\nAbstract\nThe classical local theta correspondence for p-ad
ic reductive dual pairs defines a bijection between prescribed subsets of
irreducible smooth complex representations coming from two groups (H\,H')\
, forming a dual pair in a symplectic group. Alberto Mínguez extended thi
s result for type II dual pairs\, i.e. when (H\,H') is made of general lin
ear groups\, to representations with coefficients in an algebraically clos
ed field of characteristic l as long as the characteristic l does not divi
de the pro-orders of H and H'. For coefficients rings like Z[1/p]\, we exp
lain how to build a theory in families for type II dual pairs that is comp
atible with reduction to residue fields of the base coefficient ring\, whe
re central to this approach is the integral Bernstein centre. We translate
some weaker properties of the classical correspondence\, such as compatib
ility with supercuspidal support\, as a morphism between the integral Bern
stein 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 expect
it to be surjective. This would result in a closed immersion between the a
ssociated affine schemes as well as a correspondence between characters of
the Bernstein centre. This is current work with Gil Moss.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Saha (Queen Mary University of London)
DTSTART:20230523T130000Z
DTEND:20230523T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/8
DESCRIPTION:Title: The Manin constant\, the modular degree\, and Fourier expansions at c
usps\nby Abhishek Saha (Queen Mary University of London) as part of AN
TLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nLet f be a normalize
d newform of weight k for $\\Gamma_0(N)$. It is a natural question to try
to understand the size (in a $p$-adic sense) of the "denominators" of the
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 abo
ut recent joint work with Kȩstutis Česnavičius and Michael Neururer whe
re we solve this problem using representation-theoretic techniques. Roughl
y speaking\, we reduce the problem to bounding $p-$adic valuations of loca
l Whittaker newforms and then use a "basic identity" (a consequence of the
Jacquet-Langlands local functional equation) to reduce to $p$-adic proper
ties of local epsilon factors of representations of $\\GL_2(\\Q_p)$. \n\n
A key application of our result is to understand the Manin constant c of a
n elliptic curve E over the rationals. The integer c scales the differenti
al determined by the normalized newform f associated to E into the pullbac
k of a N\\'{e}ron differential under a minimal modular parametrization. Ma
nin conjectured that c equals 1 or -1 for optimal parametrizations. We pro
ve that c divides the degree of the parametrization under a minor assumpti
on at the primes 2 and 3. For this result\, we establish a certain integra
lity property of $\\omega_f$ that follows from the Manin conjecture. We ex
pect that this integrability property we prove here will be necessary for
any further progress towards Manin's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (Cambridge)
DTSTART:20230425T130000Z
DTEND:20230425T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/10
DESCRIPTION:Title: Modularity in the partial weight one case\nby Hanneke Wiersema (
Cambridge) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstra
ct\nThe strong form of Serre's conjecture states that a two-dimensional mo
d p representation of the absolute Galois group of $\\mathbb{Q}$ arises fr
om a modular form of a specific weight\, level and character. Serre restri
cted to modular forms of weight at least 2\, but Edixhoven later refined t
his conjecture to include weight one modular forms. In this talk we explor
e analogues of Edixhoven's refinement for Galois representations of totall
y real fields\, extending recent work of Diamond and Sasaki. In particular
\, we show how modularity of partial weight one Hilbert modular forms can
be related to modularity of Hilbert modular forms with regular weights\, a
nd vice versa. We will also discuss the applications of this for p-adic Ho
dge theory.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (UEA)
DTSTART:20230509T130000Z
DTEND:20230509T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/12
DESCRIPTION:Title: Scopes equivalence for blocks of Ariki-Koike algebras\nby Alice
Dell'Arciprete (UEA) as part of ANTLR 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 i
ndexed by multipartitions of $n$. We examine blocks of the Ariki-Koike alg
ebra\, in an attempt to generalise the combinatorial representation theory
of the Iwahori-Hecke algebra. In particular\, we prove a sufficient condi
tion such that restriction of modules leads to a natural correspondence be
tween 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 block
$B'$\, obtained from $B$ applying a Scopes' equivalence. This gives us an
equality of decomposition numbers for the corresponding Ariki-Koike algeb
ras.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nutt Tananimit (UEA)
DTSTART:20230530T130000Z
DTEND:20230530T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/13
DESCRIPTION:Title: Consistent and Inconsistent Generalizations of Martin's Axiom and We
ak Square\nby Nutt Tananimit (UEA) as part of ANTLR seminar\n\nLecture
held in SCI 3.05.\n\nAbstract\nWe prove that the forcing axiom $\\textsf{
MA}^{1.5}_{\\aleph_2}(\\text{stratified})$ 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://stable.researchseminars.org/talk/UEAPS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Ardakov (Oxford)
DTSTART:20230328T130000Z
DTEND:20230328T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/14
DESCRIPTION:Title: The central sheaf of the category of smooth mod-$p$ representations
of $SL_2(\\mathbb{Q}_p)$\nby Konstantin Ardakov (Oxford) as part of AN
TLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nThis is work in prog
ress with Peter Schneider. The Bernstein centre of a $p$-adic reductive gr
oup plays a fundamental role in the classical local Langlands corresponden
ce. In the mod-p local Langlands program\, the naive analogue of the Berns
tein centre\, namely the centre of the category $Mod(G)$ of all smooth mod
-$p$ representations\, turns out to be too small: it is for example trivia
l whenever the group in question has trivial centre. Instead\, we consider
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 subcatego
ries that are $stable$ $under$ $injective$ $envelopes$\, this defines a sh
eaf with respect to finite coverings. In the case where $G = SL_2(\\mathbb
{Q}_p)$ and $p \\neq 2\,3$\, we use recent results by Ollivier and Schneid
er on the structure of the pro-$p$ Iwahori $Ext$-algebra to construct a ce
rtain projective variety $X$ having the property that every Zariski open s
ubset $U$ of $X$ gives rise to a stable localizing subcategory $\\mathcal{
L}_U$ of $Mod(G)$. Both connected components of $X$ are certain chains of
projective lines\, and $X$ and is closely related to the recent work of Do
tto\, Emerton and Gee.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:test
DTSTART:20230801T130000Z
DTEND:20230801T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/15
DESCRIPTION:by test as part of ANTLR seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Jones (The University of Manchester)
DTSTART:20231017T130000Z
DTEND:20231017T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/16
DESCRIPTION:Title: An effective version of a theorem of Habegger\nby Gareth Jones (
The University of Manchester) as part of ANTLR seminar\n\nLecture held in
SCI 3.05.\n\nAbstract\nHabegger showed that a subvariety of a fibre power
of the Legendre family of elliptic curves contains a Zariski-dense set of
special points if and only if it is special. I'll explain this result\, an
d discuss an effective version proved by Gal Binyamini\, Harry Schmidt\, M
argaret Thomas\, and me.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar León Sánchez (The University of Manchester)
DTSTART:20231205T140000Z
DTEND:20231205T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/17
DESCRIPTION:Title: Some remarks on differentially large fields and CODFs\nby Omar L
eón Sánchez (The University of Manchester) as part of ANTLR seminar\n\nL
ecture held in SCI 3.05.\n\nAbstract\nWe make some observations around dif
ferentially large fields (in characteristic zero). In particular\, we note
that they can be characterised as those differential fields that are exis
tentially closed in the "differential algebraic" Laurent series ring. We a
lso 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 real
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 no p
rime model. We then discuss the question of when a real closed differentia
l field has a CODF extension inside a differential closure.\nThis is a com
bination of joint work with Marcus Tressl and Anand Pillay.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Torzewski (Kings College London)
DTSTART:20231003T130000Z
DTEND:20231003T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/18
DESCRIPTION:Title: Studying points on varieties via varying families\nby Alex Torze
wski (Kings College London) as part of ANTLR seminar\n\nLecture held in EF
RY 01.05.\n\nAbstract\nWe show how Lawrence-Venkatesh's method for studyin
g points on a variety X can be applied to curves in families. In the proce
ss\, we also outline the original method. The idea is that if there exists
a family over X which varys "a lot"\, then this strongly constrains the e
xistence of points. This is an example of how topology influences arithmet
ic!\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Rockwood (Kings College London)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/19
DESCRIPTION:Title: Families of branching laws and their arithmetic applications\nby
Rob Rockwood (Kings College London) as part of ANTLR seminar\n\nLecture h
eld in EFRY 01.08.\n\nAbstract\nThe branching laws of certain special pair
s of algebraic groups $H \\to G$ are related to the $L$-functions of autom
orphic representations via the theory of period integrals\, made concrete
by the conjectures of Gan--Gross--Prasad and Ichino--Ikeda. On the algebra
ic side\, one can use branching laws for highest weight representations to
construct cohomological avatars of automorphic period integrals in the co
homology of Shimura varieties. These classes are related to $p$-adic $L$-f
unctions and Euler systems\, both of which have applications to important
arithmetic conjectures such as the Bloch--Kato conjectures. I will explain
how one constructs such avatars and will describe work of myself and Loef
fler--Zerbes on varying these classes in $p$-adic families.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Islam Foniqi (University of East Anglia)
DTSTART:20231010T130000Z
DTEND:20231010T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/20
DESCRIPTION:Title: Decision and membership problems in one-relator monoids and groups\nby Islam Foniqi (University of East Anglia) as part of ANTLR seminar\n
\nLecture held in SCI 3.05.\n\nAbstract\nMotivated by the open word proble
m for one-relator monoids\, we study decision problems for monoids and gro
ups. I will present some recent results (joint work with Robert D. Gray &
C.-F. Nyberg-Brodda) on submonoid and rational subset membership problems
in algebraic structures\, and discuss their implications and connections
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://stable.researchseminars.org/talk/UEAPS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Spriano (Oxford University)
DTSTART:20231212T140000Z
DTEND:20231212T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/21
DESCRIPTION:Title: On uniquely geodesic graphs and groups\nby Davide Spriano (Oxfor
d University) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbs
tract\nGraph with a unique geodesic between any two points are a very natu
ral object to define\, but they remain a mysterious object. In this talk w
e will discuss new results about their classifications\, and show that a g
roup with a uniquely geodesic Cayley graph needs to be virtually free. Thi
s is joint work with Elder\, Gardam\, Piggott and Townsend.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Simoes (Lancaster University)
DTSTART:20231121T140000Z
DTEND:20231121T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/22
DESCRIPTION:Title: From gentle to string algebras: a geometric model\nby Raquel Coe
lho Simoes (Lancaster University) as part of ANTLR seminar\n\n\nAbstract\n
Geometric models associated to triangulations of Riemann surfaces arose in
the context of cluster algebras and have since been used as an important
tool to study representation theory of algebras and provide connections wi
th algebraic geometry and symplectic geometry. \n\nSignificant application
s of geometric models include a description of extensions and a classifica
tion of support tau-tilting modules over gentle algebras. Gentle algebras
are a particular subclass of string algebras\, which are of tame represent
ation type\, meaning it is often possible to get a global understanding of
their representation theory.\n\nIn this talk I will describe the module c
ategory of a gentle algebra via partial triangulations of unpunctured surf
aces and explain how to extend this model to a geometric model of the modu
le category of any string algebra. This is based on joint work in progress
with Karin Baur.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (KCL)
DTSTART:20240227T140000Z
DTEND:20240227T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/23
DESCRIPTION:Title: Parametrising abelian surfaces with RM by $\\mathbb{Z}[\\sqrt{2}]$ u
sing Richelot isogenies\nby Lassina Dembélé (KCL) as part of ANTLR s
eminar\n\nLecture held in TPSC 0.1.\n\nAbstract\nIn this talk\, we describ
e a parametrisation of abelian surfaces with real multiplication by $\\mat
hbb{Z}[\\sqrt{2}]$ using Richelot isogenies\, and give some arithmetic app
lications.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Gruber (York)
DTSTART:20240312T140000Z
DTEND:20240312T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/24
DESCRIPTION:Title: Centers and centralizers in (double) affine Hecke algebras\nby J
onathan Gruber (York) as part of ANTLR seminar\n\nLecture held in Queen 01
.09.\n\nAbstract\nThe affine Hecke algebra and its center are important ob
jects of study in combinatorial\, geometric and categorical representation
theory. In this talk\, I will discuss a new commutative subalgebra of the
affine Hecke algebra of type A\, which arises from a centralizer construc
tion in the double affine Hecke algebra. This subalgebra contains the cent
er\, and it admits a canonical basis akin to the Kazhdan-Lusztig basis of
the affine Hecke algebra. I will explain how the canonical basis can be us
ed as a tool to compute composition multiplicities in Gaitsgory's central
sheaves on affine flag manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (Sheffield)
DTSTART:20240319T140000Z
DTEND:20240319T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/25
DESCRIPTION:Title: Newforms for cuspidal representations\nby Rob Kurinczuk (Sheffie
ld) as part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAbstract\nW
e will review the theory of newforms for cuspidal representations of p-adi
c general linear groups of Jacquet--Piatetski-Shapiro--Shalika\, and Matri
nge. Then compare them with the explicit functions of Paskunas-Stevens fo
r cuspidal representations in special cases. This is joint work in progre
ss with Johannes Girsch.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Prest (Manchester)
DTSTART:20240423T130000Z
DTEND:20240423T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/26
DESCRIPTION:Title: Linear algebra over general rings\nby Mike Prest (Manchester) as
part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nIn line
ar algebra we meet solution sets to systems of linear equations with coeff
icients from a field. Later\, we see that we can replace the field by a m
ore general ring\, for instance a Weyl algebra where we would be looking a
t solutions of systems of linear partial differential equations. Over gen
eral rings\, however\, such solution sets do not have nice closure propert
ies\; for instance they might not be closed under coordinate projections.
But\, if we accept projected systems of equations and their solution sets
as basic objects\, then we recover the nice closure properties that one h
as over fields and\, over general rings\, find interesting structures sitt
ing within a rich and extensive theory which ramifies into many aspects of
representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvy Anscombe (Paris)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/27
DESCRIPTION:Title: Uniformities for Hilbert's Tenth Problem in henselian valued fields<
/a>\nby Sylvy Anscombe (Paris) as part of ANTLR seminar\n\nLecture held in
NEWSCI 0.04.\n\nAbstract\nHilbert's Tenth Problem in its original form as
ks for an algorithm to determine correctly whether -- or not -- a given mu
ltivariable polynomial equation with integer coefficients has integer solu
tions.\nThe surprising resolution\, by Davis\, Putnam\, Robinson\, and fin
ished by Matiyasevich in 1970\, is that there is no such algorithm. In the
terminology of mathematical logic\, the existential theory of the ring of
integers is undecidable. I am interested in the (un?)decidability of the
existential theories of a variety of rings and fields\, especially of "lar
ge" fields\, for example those fields admitting a non-trivial valuation th
at 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 l
inks with theories of function fields.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aberdeen Powell (UEA)
DTSTART:20240206T140000Z
DTEND:20240206T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/28
DESCRIPTION:Title: Frobenius reciprocity for fiat 2-categories\nby Aberdeen Powell
(UEA) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nF
robenius reciprocity is a famous property first observed in the setting of
group representations. Representations of 2-categories is a lively and re
latively young field\, where many classic results of representation theory
reappear: the Jordan-Hölder theorem (Mackaay\, Mazorchuk\, Miemietz\, Tu
bbenhauer and Zhang\, Finitary birepresentations of fintary bicategories)\
, various properties from Morita theory (Mazorchuk and Miemietz\, Morita t
heory for finitary 2-categories)\, etc. In this talk\, we consider Frobeni
us reciprocity in the context of 2-categories.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curial Gallart Rodriguez (UEA)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/29
DESCRIPTION:Title: Current trends in set theory\nby Curial Gallart Rodriguez (UEA)
as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nNot all
questions in mathematics can be answered in ZFC by Gödel's incompletenes
s theorems. Numerous concrete examples of mathematical statements have bee
n proven to be independent from the ZFC axioms over the years. Many of the
m being non-set-theoretic in nature. Most notably\, the Whitehead problem\
, the Borel conjecture\, Kaplansky's conjecture on Banach algebras\, or th
e Brown-Douglas-Fillmore problem. Instead of accepting that there are ques
tions that don't have an answer\, the independence phenomenon lead set the
orists to search for axioms beyond ZFC that would give us a clearer pictur
e of the set theoretic (and mathematical) universe.\n\nIn this talk I will
present the main lineages of axioms that have been considered and their c
onsequences. I will describe their connections and the main methods to stu
dy them\, and I will finish by connecting all of this with my PhD thesis.\
n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Ward
DTSTART:20240507T130000Z
DTEND:20240507T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/30
DESCRIPTION:Title: Hidden dynamical zeta functions\nby Tom Ward as part of ANTLR se
minar\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 - as
it turns out\, many - sequences that arise naturally in combinatorics or n
umber theory fail to count periodic points (that is\, be the coefficients
of a dynamical zeta function) but succeed after some modest modification.
Examples include the Stirling numbers and linear recurrence sequences.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (Manchester)
DTSTART:20240213T140000Z
DTEND:20240213T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/32
DESCRIPTION:Title: You need 27 tickets to guarantee a win on the UK National Lottery (J
t with David Cushing)\nby David Stewart (Manchester) as part of ANTLR
seminar\n\nLecture held in Queen 01.09.\n\nAbstract\nThe authors came acro
ss 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\, su
ch that for any subset D of {1\,..\,n} of size p\, one finds an intersecti
on D\\cap B_i with at least t elements. In the context of a lottery\, n re
presents the. number of balls\, k the number of choices of balls on a tick
et\, p the size of a draw.\nFor the UK national lottery\, n=59\, k=p=6 and
one gets a (rather meagre) prize as long as t is at least 2.\nUsing the c
onstraint solving library in Prolog\, we calculated j for k=p=6\, t=2 and
n all the way up to 70. For example L(59\,6\,6\,2)=27. This is the second
paper where we have aimed to show the value of Prolog and constraint progr
amming in pure mathematics.\nI’ll give an overview of constraint program
ming\, logic programming in Prolog\, and describe how we used these tools
to solve the problem described in the title.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Macpherson (Instituto Superior Tecnico\, Lisbon)
DTSTART:20240318T140000Z
DTEND:20240318T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/33
DESCRIPTION:Title: Evaluation 2-functors for categorified affine sl(n)\nby James Ma
cpherson (Instituto Superior Tecnico\, Lisbon) as part of ANTLR seminar\n\
nLecture held in EFRY01.10.\n\nAbstract\nWhen studying representations of
particularly unruly\nmathematical structures\, it can often be useful to c
ompose\nrepresentations of an associated\, simpler structure with an `eval
uation'\nfunctor from the unruly structure to the better behaved one. A\np
reviously studied example is the evaluation functor from (the\nidempotente
d 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 present
the categorification of this evaluation functor\nbetween the correspondin
g 2-Kac-Moody algebras for the n=3 case\, and\nalso discuss some of the te
chniques used for an inductive construction\nof the evaluation 2-functor f
or larger n. This is joint work with Marco\nMackaay and Pedro Vaz.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan Haden (UEA)
DTSTART:20240606T100000Z
DTEND:20240606T110000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/34
DESCRIPTION:Title: 3-Preprojective Algebras of Type D\nby Jordan Haden (UEA) as par
t of ANTLR seminar\n\nLecture held in EFry 01.02.\n\nAbstract\nGiven an al
gebra with finite global dimension\, it is natural to consider two autoequ
ivalences of its bounded derived category: the Serre functor and the shift
functor. If a power of one is isomorphic to a power of the other\, we say
the algebra is fractional Calabi-Yau. Closely related are d-representatio
n-finite algebras. These are algebras whose module category contains a d-c
luster tilting subcategory\, which is “manageable” even if the algebra
has wild representation type. We will explain these concepts\, and how th
ey are connected\, before presenting an infinite family of algebras which
are both fractional Calabi-Yau and 2-representation-finite.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yujie Xu (Columbia University)
DTSTART:20240708T130000Z
DTEND:20240708T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/35
DESCRIPTION:Title: Hecke algebras for p-adic groups and explicit Local Langlands Corres
pondence\nby Yujie Xu (Columbia University) as part of ANTLR seminar\n
\n\nAbstract\nI will talk about several results on Hecke algebras attached
to Bernstein blocks of reductive p-adic groups\, where we construct a loc
al Langlands correspondence for these Bernstein blocks. Our techniques dra
w inspirations from the foundational works of Deligne\, Kazhdan\, Langland
s\, Lusztig and Shahidi.\n\n\nAs an application\, we prove the Local Langl
ands Conjecture for G_2\, which is the first known case in literature of L
LC for exceptional groups. Our correspondence satisfies an expected proper
ty on cuspidal support\, which is compatible with the generalized Springer
correspondence\, along with a list of characterizing properties including
the stabilization of character sums\, formal degree property etc. In part
icular\, we obtain (not necessarily unipotent) "mixed" L-packets containin
g "F-singular" supercuspidals and non-supercuspidals. I will give explicit
examples of such mixed L-packets in terms of Deligne-Lusztig theory and K
azhdan-Lusztig parametrization.\n\nIf time permits\, I will explain how to
pin down certain choices in the construction of the correspondence using
stability of L-packets\; one key input is a homogeneity result due to Wald
spurger and DeBacker. Moreover\, I will mention how to adapt our general s
trategy to construct explicit LLC for other reductive groups\, such as GSp
_4\, Sp_4\, etc\, generalizing the depth-zero L-packets of Lust-Stevens. S
uch explicit description of the L-packets has been useful in number-theore
tic applications\, e.g. modularity lifting questions.\n\nVarious parts of
this talk are based on joint works with various collaborators\, and attrib
utions will be made clear throughout the talk.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashot Minasyan (Southampton)
DTSTART:20241015T130000Z
DTEND:20241015T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/36
DESCRIPTION:Title: Generating RAAGs in 1-relator groups\nby Ashot Minasyan (Southam
pton) as part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\
nGiven a finite simplicial graph $\\Gamma$\, the right angled Artin group
(RAAG) $A(\\Gamma)$ is generated by the vertices of $\\Gamma$ subject to t
he relations that two vertices commute if and only if they are adjacent in
$\\Gamma$. The monoid with the same presentation is called the trace mono
id $T(\\Gamma)$. RAAGs play a significant role in Geometric Group Theory\,
while Trace monoids have important applications in Computer Science.\n\nT
he trace monoid $T(\\Gamma)$ is naturally embedded in the RAAG $A(\\Gamma)
$\, as the set of positive words. In my talk I will discuss the following
problem: suppose that a 1-relator group G contains a submonoid isomorphic
to $T(\\Gamma)$. Does $G$ also contain a copy of $A(\\Gamma)$ as a subgrou
p?\n\nThis problem is motivated by recent work of Foniqi\, Gray and Nyberg
-Brodda\, who proved that groups containing T(P_4)\, where P_4 is the path
with 4 vertices (of length 3)\, have undecidable rational subset problem.
They also exhibited 1-relator groups containing A(P_4) and asked whether
every 1-relator group which has a submonoid isomorphic to T(P_4) must also
have a subgroup isomorphic to A(P_4). I will sketch an argument\, based o
n joint work with Motiejus Valiunas\, showing that the answer to the latte
r question is positive.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım (Leeds)
DTSTART:20241112T140000Z
DTEND:20241112T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/37
DESCRIPTION:Title: Surface triangulations and friezes\nby Emine Yıldırım (Leeds)
as part of ANTLR seminar\n\nLecture held in EFRY 01.08.\n\nAbstract\nInte
rplays between representation theory of algebras and combinatorics give ri
se to new discoveries and questions. In this talk\, I will give a tour of
some of these development using friezes interpreted in different contexts
. This talk is based on a joint work with K. Baur\, L. Bittman\, E. Gunawa
n\, and G. Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Williams (Nottingham)
DTSTART:20241001T130000Z
DTEND:20241001T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/38
DESCRIPTION:Title: Congruences between eigensystems for GL(n)\nby Chris Williams (N
ottingham) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.03.\n\nAbs
tract\nIn this talk\, I will discuss congruences between modular forms\, a
nd -- more generally -- between systems of eigenvalues on GL(n)\, modular
forms being the special case $n=2$. In a broad sense\, this seeks to answe
r the following type of question: Let $p$ be prime and $f$ be a modular fo
rm 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 can
be captured geometrically via 1-dimensional families' of eigenforms (via
the eigencurve'). This geometric object has had profound consequences in I
wasawa theory and the Langlands program. In this talk\, I will attempt to
give a gentle introduction to $p$-adic families\, and describe joint work
with Daniel Barrera and Andy Graham\, where we consider some of the probl
ems in generalising them to higher dimension. Here the picture becomes mor
e 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 t
o the same automorphic representation.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Warne (UEA)
DTSTART:20241022T130000Z
DTEND:20241022T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/39
DESCRIPTION:Title: Factorisations of finitely presented special inverse monoids\nby
Jonathan Warne (UEA) as part of ANTLR seminar\n\nLecture held in JSC 2.02
.\n\nAbstract\nInverse monoids are a kind of algebraic object which model
partial bijections in the same way that groups model bijections and semigr
oups model transformations generally. A special inverse monoid is one defi
ned by a set of relations of the form $r_i = 1$. We can factorise these $r
_i$ into component words\, for instance $xyxzxy =1$ may be written $(xy)(
xz)(xy)=1$. In particular\, every special inverse monoid presentation has
a unique factorisation of its relators into minimal invertible pieces.\n\n
In 2001 Ivanov\, Margolis and Meakin produced a paper which included among
st others two important results. That the special inverse monoid's group o
f units is generated by the minimal invertible pieces and that we can deci
de the word problem of an E-unitary special inverse monoid by deciding the
word and prefix membership problems of its maximal group image. Both allo
w us to better understand an inverse monoid by studying corresponding grou
ps.\n\nIn this talk we will use these results to discuss the effects of th
e minimal invertible pieces of a special inverse monoid's relators having
certain combinatorial properties on a number of decision problems\, extend
ing results by Dolinka and Gray.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Seminar
DTSTART:20241029T140000Z
DTEND:20241029T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/40
DESCRIPTION:by No Seminar as part of ANTLR seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembele (KCL)
DTSTART:20241105T140000Z
DTEND:20241105T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/41
DESCRIPTION:Title: Parametrising abelian surfaces with RM by $\\mathbb{Z}[\\sqrt{2}]$ u
sing Richelot isogenies\nby Lassina Dembele (KCL) as part of ANTLR sem
inar\n\nLecture held in NEWSCI 0.03.\n\nAbstract\nIn this talk\, we descri
be a parametrisation of abelian surfaces with real multiplication by $\\ma
thbb{Z}[\\sqrt{2}]$ using Richelot isogenies\, and give some arithmetic ap
plications.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Cambridge)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/42
DESCRIPTION:Title: Steenrod operations via higher Bruhat orders\nby Nicholas Willia
ms (Cambridge) as part of ANTLR seminar\n\nLecture held in EFRY 01.08.\n\n
Abstract\nThe cohomology of a topological space has a ring structure via t
he cup product. The cup product is defined at the level of cochains\, wher
e it is not commutative\, but it becomes commutative at the cohomology lev
el. At the cochain level\, the lack of commutativity is resolved homotopic
ally by an infinite tower of higher products\, known as the Steenrod cup-i
products. This additional structure provides more refined information whi
ch can be used to tell apart non-homotopy-equivalent spaces. Not assuming
any background from algebraic topology\, I will explain recent work with G
uillaume Laplante-Anfossi\, where we show how conceptual proofs of the key
properties of Steenrod's cup-i products can be given using the higher Bru
hat orders of Manin and Schechtman.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Levine (UEA)
DTSTART:20241008T130000Z
DTEND:20241008T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/43
DESCRIPTION:Title: Equations with constraints in virtually abelian groups\nby Alex
Levine (UEA) as part of ANTLR seminar\n\nLecture held in SCI 1.50.\n\nAbst
ract\nThe Diophantine problem in a group G is the decision problem asking
whether there is an algorithm that decides if a system of equations in G a
dmits a solution. When considering equations in groups\, one can also add
'constraints' to the variables\, such as insisting a specific variable mus
t lie in a specific subgroup. We consider the Diophantine problem for virt
ually abelian groups\, which has long been considered 'folklore'. We look
at adding various types of constraints to equations in virtually abelian
groups.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Dmitrieva (UEA)
DTSTART:20241119T140000Z
DTEND:20241119T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/44
DESCRIPTION:Title: Generic functions and quasiminimality\nby Anna Dmitrieva (UEA) a
s part of ANTLR seminar\n\n\nAbstract\nOne of the well-known accomplishmen
ts of model theory is the study of the field of complex numbers. It posses
ses numerous nice properties\, including minimality\, i.e. any definable s
ubset is finite or cofinite. However\, adding the exponential map to the s
tructure makes it possible to define the ring of integers\, preventing min
imality and many other properties. Nevertheless\, there is still hope that
the complex exponential field is somewhat well-behaved. For instance\, Zi
lber’s quasiminimality conjecture states that the complex exponential fi
eld is quasiminimal\, i.e. every definable subset is countable or co-count
able. Analogous conjectures were made\, replacing the exponential map with
other analytical functions.\n\nIn this talk we look at the theory of a ge
neric function\, as introduced by Zilber in 2002. As the main result\, we
prove that adding an entire generic function to the complex field gives a
quasiminimal structure\, and\, moreover\, this structure is unique up to a
n isomorphism. Thus we obtain a non-trivial example of an entire function
which keeps the complex field quasiminimal.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (UEA)
DTSTART:20250225T140000Z
DTEND:20250225T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/45
DESCRIPTION:Title: Categorification in Representation Theory\nby Vanessa Miemietz (
UEA) as part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\n
I will explain some of the ideas behind the theory of finitary 2-represent
ations of finitary 2-categories\, which attempts to categorify the represe
ntation theory of finite dimensional algebras. I will illustrate these on
the example of the categorification of Hecke algebras via Soergel bimodule
s.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (Royal Holloway)
DTSTART:20250211T140000Z
DTEND:20250211T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/46
DESCRIPTION:Title: Multiplicity-free induced characters of symmetric groups\nby Pav
el Turek (Royal Holloway) as part of ANTLR seminar\n\nLecture held in EFRY
01.05.\n\nAbstract\nLet $n$ be a sufficiently large positive integer. A c
haracter is multiplicity-free if its irreducible constituents appear with
multiplicity one. Wildon in 2009 and independently Godsil and Meagher in 2
010 have found all multiplicity-free permutation characters of the symmetr
ic group $S_n$. In this talk\, we focus on a significantly more general pr
oblem when the permutation characters are replaced by induced characters o
f the form $\\rho\\!\\uparrow^{S_n}$ with $\\rho$ irreducible. \n\n
\nDespite the nature of the problem\, I expl
ain\, combining results from group theory\, representation theory and comb
inatorics\, why this problem may be feasible and present a close to full a
nswer. I also mention some of my (often surprising) results to questions a
bout conjugate partitions\, which naturally arise when solving the problem
\, and the remarkable complete classification of subgroups $G$ of $S_n$\,
which have an irreducible character which stays multiplicity-free when ind
uced to $S_n$.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niccolò Guicciardini (Università di Milano)
DTSTART:20250218T140000Z
DTEND:20250218T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/47
DESCRIPTION:Title: The status of mathematics in sixteenth-century Europe\nby Niccol
ò Guicciardini (Università di Milano) as part of ANTLR seminar\n\nLectur
e held in LT4.\n\nAbstract\nAt the dawn of the so-called scientific revolu
tion\, the mathematical sciences acquired a new status as the key to under
standing the structure of reality in a way that contradicted Aristotelian
physics and cosmology. This new role for mathematics did not come without
controversy. In this talk I will explore some of these debates\, placing t
hem in philosophical\, scientific and sociological contexts. I will begin
with Copernicus’s statements in the Preface to De revolutionibus (1543
) concerning the role of mathematics in revealing the harmony of the plan
etary system and end with Galileo’s statement in the Assayer (1623) that
the Book of Nature is written in mathematical characters and his statemen
t at the end of the first Day of the Dialogo sui due massimi sistemi del m
ondo (1632) that mathematics provides man with knowledge as certain as tha
t available to God. As we shall see these statements\, which characterise
the scientific revolution\, were controversial.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiuhua Luo (Nantong University)
DTSTART:20250204T140000Z
DTEND:20250204T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/48
DESCRIPTION:Title: The structure of separated monomorphism category and its application
s\nby Xiuhua Luo (Nantong University) as part of ANTLR seminar\n\nLect
ure held in Queens 01.09.\n\nAbstract\nInitiated by G. Birkhoff\, there is
a long history of studying (separated) monomorphism category. It was gene
ralized to finite acyclic (bounded) quiver representations over a finite-d
imensional algebra around ten year ago. It turns out that this category is
related with many mathematical branches\, such as singularity theory\, pr
eprojective algebra\, and plays an important role in relative homological
algebra.\n\nIn this talk\, firstly\, the properties of the separated monom
orphism category are given in a more general setup. Secondly\, I will expl
ain the relation between separated monomorphism category and Gorenstein-pr
ojective modules. Finally\, the construction of this category will be desc
ribed.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Bays (University of Oxford)
DTSTART:20250311T140000Z
DTEND:20250311T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/49
DESCRIPTION:Title: An asymmetric version of Elekes-Szabó via group actions\nby Mar
tin Bays (University of Oxford) as part of ANTLR seminar\n\nLecture held i
n EFRY 01.05.\n\nAbstract\nElekes and Rónyai showed that a bivariate real
polynomial f(x\,y)\nexpands\, meaning $|f(A\,A)| \\geq c|A|^{1+\\eta}$ fo
r all finite A\, unless\nf can be written as the composition of addition o
r multiplication with\nunivariate polynomials. The proof can be seen as go
ing via the group\nconfiguration theorem of model theory. I will talk abou
t recent work\nwith Tingxiang Zou\, in which we consider a more general se
tup where\nwe can apply a homogeneous space version of this group configur
ation\ntheorem\, and yet still subsequently reduce to an abelian group. We
\ndeduce asymmetric expansion $|f(A\,B)| \\geq c|A|^{1+\\eta}$ even when B
is\nallowed to be drastically smaller than A. Moreover\, we obtain a simi
lar\nresult when y is allowed to be a tuple. Allowing x to also be a tuple
\nintroduces new phenomena\, and if time permits I may mention some partia
l\nresults in this case.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorna Gregory (UEA)
DTSTART:20250318T140000Z
DTEND:20250318T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/50
DESCRIPTION:Title: Representation Type\, Decidability and Pseudofinite-dimensional Modu
les over Finite-dimensional Algebras\nby Lorna Gregory (UEA) as part o
f ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nThe representa
tion type of a finite-dimensional k-algebra is an algebraic measure of how
hard it is to classify its finite-dimensional indecomposable modules. Int
uitively\, a finite-dimensional k-algebra is of tame representation type i
f we can classify its finite-dimensional modules and wild representation t
ype if its module category contains a copy of the category of finite-dimen
sional modules of all other finite-dimensional k-algebras. An archetypical
(although not finite-dimensional) tame algebra is k[x]. The structure the
orem for finitely generated modules over a PID describes its finite-dimens
ional modules. Drozd’s famous dichotomy theorem states that all finite-d
imensional algebras are either wild or tame.\n\n\nThe (theory of) a class
of modules is said to be decidable if there is an algorithm which given a
sentence in the language of modules (a sentence is a particular kind of st
atement about modules) answers whether it is true in all modules in that c
lass. A long-standing conjecture of Mike Prest claims that the (theory of)
the class of all modules over a finite-dimensional algebra is decidable t
heory if and only if it is of tame representation type. The reverse direct
ion of this conjecture is often hard to prove even in particular examples.
One difficulty is that the conjecture talks about all modules rather than
just finite-dimensional ones. In this talk I will present work in progres
s around and in support of a new conjecture\, inspired by Prest’s conjec
ture\, which claims that the (theory of) the class of finite-dimensional m
odules over a finite-dimensional algebra is decidable if and only if it is
of tame representation type.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Angdinata (UCL)
DTSTART:20250325T140000Z
DTEND:20250325T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/51
DESCRIPTION:Title: Teaching a computer algebraic number theory\nby David Angdinata
(UCL) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nF
or most of recorded human history\, mathematics has been done with good-ol
d pen and paper. With the advent of modern computers\, lightning-fast calc
ulations and large-scale datasets have granted us unprecedented advances i
n mathematics\, both in pure and applied forms. On the other hand\, they h
ave merely been algorithmic tools for us to compute with\, while lacking t
he capacity to comprehend and formulate new ideas as we do. I will explore
recent attempts at teaching my area of arithmetic geometry to a computer\
, by formalising fundamental constructions in an interactive theorem prove
r called Lean.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlad Vankov (Bristol)
DTSTART:20250429T130000Z
DTEND:20250429T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/52
DESCRIPTION:Title: Cohomology\, groups and negatively curved geometry\nby Vlad Vank
ov (Bristol) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbst
ract\nOver the last thirty years\, hyperbolic and relatively hyperbolic gr
oups have found characterisations in terms of homological algebra in vario
us forms\, for example through bounded cohomology and bounded-valued cohom
ology. To link the algebra and the geometry\, locally finite spaces are us
ually used. This can pose issues when dealing with other generalisations o
f hyperbolicity\, such as acylindrically hyperbolic groups. To address thi
s\, in joint work with Francesco Milizia\, Nansen Petrosyan and Alessandro
Sisto\, we study a cohomology theory that detects hyperbolicity for gener
al metric spaces. As a consequence\, we are able to provide a characterisa
tion of hyperbolically embedded subgroups in terms of homological algebra.
\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caner Nazaroglu
DTSTART:20250508T120000Z
DTEND:20250508T130000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/53
DESCRIPTION:Title: Statistics for random representations of Lie algebras\nby Caner
Nazaroglu as part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAbstr
act\nHow does a typical finite-dimensional representation of a complex Lie
algebra look like? In this talk\, we address this question for the infini
te family $\\mathfrak{sl}_{r+1}(\\mathbb{C})$ with $r \\geq 2$. Specifical
ly\, we derive the asymptotic statistical properties of a representation s
ampled uniformly from all representations with a given large dimension. Th
is naturally extends similar studies on integer partitions with methods in
spired from statistical mechanics. The multivariable generalization we con
sider contains some new features compared to integer partitions\, which ha
ve been studied from a large range of points of view from combinatorics to
modularity. In the talk\, we will review those aspects familiar from inte
ger partitions\, describe the physics inspired approach to the problem\, a
nd finally detail our results for the general case. This is joint work wit
h Walter Bridges and Kathrin Bringmann.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rose Berry (UEA)
DTSTART:20250512T130000Z
DTEND:20250512T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/54
DESCRIPTION:Title: The Derived l-modular Unipotent Block of p-adic GLn\nby Rose Ber
ry (UEA) as part of ANTLR seminar\n\nLecture held in LT3.\n\nAbstract\nCom
plex representations of p-adic groups are in many ways well-understood. Th
e category has Bernstein's decomposition into blocks\, and for many groups
each block is known to be equivalent to modules over a Hecke Algebra. In
particular\, the unipotent block (the block containing the trivial represe
ntation) of GLn is equivalent to the modules over an extended affine hecke
algebra of type A. Over \\bar{Fl} the situation is more complicated in th
e general case: the Bernstein block decomposition can fail (eg for SP8)\,
and there is no longer in general an equivalence with the Hecke algebra. H
owever\, some groups\, such as GLn and its inner forms\, still have a Bern
stein decomposition. Furthermore\, Vigernas showed that the unipotent bloc
k of GLn contains a subcategory that is equivalent to modules over a mild
extension of the Hecke Algebra\, the Schur Algebra\, and this subcategory
generates the principal block under extensions. Building on this work\, we
show that the derived category of the principal block of GLn is triangula
ted-equivalent to the perfect complexes over a dg-enriched Schur algebra.
We prove this by combining general finiteness results about Schur algebras
with the well-known structure of the l-modular unipotent blocks of GLn ov
er finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Vaz (Université catholique de Louvain)
DTSTART:20250508T150000Z
DTEND:20250508T160000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/55
DESCRIPTION:Title: A tour on quantum topology and categorification\nby Pedro Vaz (U
niversité catholique de Louvain) as part of ANTLR seminar\n\nLecture held
in EFRY 01.10.\n\nAbstract\nQuantum topology is a generic term used to de
signate algebraic-topological constructions that are\, in some broad sense
\, close to the Jones polynomial and its variants.\nIn this talk\, I will
give an overview of topological quantum invariants and their categorificat
ion\, from their historical origins with the Jones polynomial to modern de
velopments. I will introduce the main concepts and present several example
s\, highlighting their multidisciplinary impact within contemporary mathem
atics.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Mackaay (Universidade do Algarve)
DTSTART:20250506T100000Z
DTEND:20250506T110000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/56
DESCRIPTION:Title: Parabolic induction and restriction play an important role in the (f
inite-dimensional) representation theory\nby Marco Mackaay (Universida
de do Algarve) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAb
stract\nParabolic induction and restriction play an important role in the
(finite-dimensional) representation theory \nof extended affine type A Hec
ke algebras\, so it is natural to look for a categorical analog in the bir
epresentation \ntheory of extended affine type A Soergel bimodules. In my
talk\, which is based on a forthcoming paper with \nV. Miemietz and P. Vaz
\, I will sketch such an analog for a maximal parabolic.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Luo
DTSTART:20250930T130000Z
DTEND:20250930T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/57
DESCRIPTION:Title: On the Local Converse Theorem for Depth 1/N Supercuspidal Representa
tions of $\\mathrm{GL}(2N\, F)$\nby David Luo as part of ANTLR seminar
\n\n\nAbstract\nIn this talk\, we use type theory to construct a family of
depth $\\frac{1}{N}$ minimax supercuspidal representations of $p$-adic $\
\GL(2N\, F)$ which we call \\textit{middle supercuspidal representations}.
These supercuspidals may be viewed as a natural generalization of simple
supercuspidal representations\, i.e. those supercuspidals of minimal posit
ive depth. Via explicit computations of twisted gamma factors\, we show th
at middle supercuspidal representations may be uniquely determined through
twisting by quasi-characters of $F^{\\times}$ and simple supercuspidal re
presentations of $\\GL(N\, F)$. Furthermore\, we give a conjecture which r
efines the local converse theorem for general supercuspidal representation
s of $\\GL(n\, F)$.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kamsma
DTSTART:20251009T130000Z
DTEND:20251009T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/58
DESCRIPTION:Title: Cofibrant generation of pure monomorphisms in presheaf categories\nby Mark Kamsma as part of ANTLR seminar\n\n\nAbstract\nThe title of thi
s talk\, and its main result\, are purely category-theoretic. However\, we
use model-theoretic methods to obtain the result. For a fixed monoid $S$\
, there is an algebraic question whether or not pure monomorphisms between
sets with an $S$-action are cofibrantly generated. In (positive) model th
eory\, we sometimes call pure monomorphisms immersions: those homomorphism
s that reflect solutions to systems of equations. An earlier result by Lie
berman\, Vasey and Rosický established an equivalence between the existen
ce of a stable independence relation on a category and cofibrant generatio
n of a certain class of morphisms. We use this equivalence\, as well as id
eas of Mustafin\, to characterise for which monoids $S$ the class of pure
monomorphisms is cofibrantly generated: those such that for every $a\, b \
\in S$ there is $c \\in S$ with $a = cb$ or $b = ca$. Our methods directly
go through in the greater generality of presheaf categories\, hence the t
itle\, and main result\, of the talk.\n\nThis is joint work with Sean Cox\
, Jonathan Feigert\, Marcos Mazari-Armida and Jiří Rosický.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Keyes (KCL)
DTSTART:20251014T130000Z
DTEND:20251014T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/59
DESCRIPTION:Title: Towards Artin’s conjecture on $p$-adic forms in low degree\nby
Chris Keyes (KCL) as part of ANTLR seminar\n\n\nAbstract\nArtin conjectur
ed that whenever $n$ is at least $d^2$\, a homogeneous polynomial $f(x_0\,
...\, x_n)$ of degree $d$ in $n+1$ variables has a nontrivial $p$-adic ze
ro\; equivalently\, the field $\\mathbb{Q}_p$ is $C_2$. This conjecture is
false\, with the first counterexample in degree 4 over $\\mathbb{Q}_2$ di
scovered by Terjanian. However\, all known counterexamples have composite
degree\, begging the question: does Artin's conjecture hold if we restrict
to prime degrees $d$? We have evidence in degrees 2 and 3 due to results
of Hasse and Lewis\, respectively\, and the celebrated Ax--Kochen theorem
establishes an asymptotic version of Artin's conjecture when $p$ is large
relative to $d$. In recent joint work with Lea Beneish\, we establish Arti
n's conjecture in degree 5 when $p > 5$ and in degree 7 when $p > 679$. In
this talk\, we will explore the ideas and techniques spanning nearly a ce
ntury behind these results\, from the Lang--Weil theorem to effective Bert
ini theorems and parallel computing.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fournier-Facio
DTSTART:20251021T130000Z
DTEND:20251021T140000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/60
DESCRIPTION:Title: First-order theory of torsion-free Tarski monsters\nby Francesco
Fournier-Facio as part of ANTLR seminar\n\n\nAbstract\nA torsion-free Tar
ski monster is a non-abelian group all of whose proper nontrivial subgroup
s are infinite cyclic. I will present joint work with Remi Coulon and Turb
o Ho\, where we construct torsion-free Tarski monsters with controlled fir
st-order theory\, something which is usually only done for groups with hyp
erbolic features. No preliminary knowledge of any of these words will be a
ssumed.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Camina
DTSTART:20251104T140000Z
DTEND:20251104T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/61
DESCRIPTION:Title: Cosets of normal subgroups: what can they tell us about the group\nby Alan Camina as part of ANTLR seminar\n\nLecture held in C. HALL 01.0
8.\n\nAbstract\nIn this talk we discuss how information about the non-triv
ial cosets of a normal subgroup can influence the structure of a finite g
roup.\n\nHere is one example:\n\nLet $G$ be a finite group with a normal s
ubgroup $N$. Assume that for each non-trivial coset $Nr$ all the elements
in $Nr$ have the same order.\n\nThen one of the following holds:\n\n1. $N
< F(G)$\, in this case $F(G)$\, and hence $N$\, is a $p$-group for some p
rime $p$.\n\n2. $N = F(G)$.\n\n3. $F(G) < N$ in this case $G/N$ is a $p$
-group.\n\nHere $F(G)$ is the Fitting subgroup of $G$.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Philipp Wächter
DTSTART:20251111T140000Z
DTEND:20251111T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/62
DESCRIPTION:Title: Equations in Wreath Products of Abelian Groups\nby Jan Philipp W
ächter as part of ANTLR seminar\n\nLecture held in NEWSCI 0.08.\n\nAbstra
ct\nSolving equations is among the most classical and fundamental question
s in\nMathematics. Typically\, equations are solved over fields of numbers
such as\nthe rational\, real or complex numbers. Solving equations over t
he ring of\nintegers (Hilbert’s 10th problem) is famously known to be un
decidable. If\,\ninstead of considering the two operations of addition and
multiplication of a\nring\, we restrict ourselves to a single one\, we ve
ry naturally arrive at the\nDiophantine problem over a group: given a syst
em of/a single equation(s)\ncontaining variables and constants (from the g
roup)\, can we decide whether we\nmay substitute the variables with some g
roup elements such that the equation\nholds? In many groups this problem i
s generally undecidable. However\, we can\nrestrict the question further a
nd consider only quadratic equations (where\nevery variable appears at mos
t twice\, counting positive and negative\ninstances).\nIn the talk\, we wi
ll discuss (ongoing) joint work with Ruiwen Dong and Leon\nPernak to solve
quadratic equations in (restricted) wreath products of abelian\ngroups. T
he talk will contain a short introduction on equations over groups\,\nthe
lamplighter group and its generalization to wreath products of abelian\ngr
oups. Then we will look at the case of nonorientable equations over these\
ngroups.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Mantova (University of Leeds)
DTSTART:20251118T140000Z
DTEND:20251118T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/63
DESCRIPTION:Title: Composition of transseries\, monotonicity\, and analyticity\nby
Vincenzo Mantova (University of Leeds) as part of ANTLR seminar\n\nLecture
held in Queens 1.03.\n\nAbstract\nTransseries generalise power series by
including exponential and logarithmic terms\, if not more\, and can be int
erpreted as germs of a non-standard Hardy field by composition (for instan
ce\, on surreal numbers). I'll discuss a few results that must 'obviously'
be true\, yet their proofs are not obvious: that composition is monotonic
in both arguments\, once claimed but not proved by Edgar for LE-series\,
that it satisfies a suitable Taylor theorem and that in fact composition i
s 'analytic with large radius of convergence' (joint with V. Bagayoko)\, s
omething which appeared before in various special forms\, but not in full
generality. I'll show how monotonicity and Taylor can be used to prove som
e fairly general normalisation results for hyperbolic transseries (joint w
ith D. Peran\, J.-P. Rolin\, T. Servi).\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie Roth (University of East Anglia)
DTSTART:20251125T140000Z
DTEND:20251125T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/64
DESCRIPTION:Title: On the unitriangularity of decomposition matrices of finite groups o
f Lie type of exceptional type\nby Marie Roth (University of East Angl
ia) as part of ANTLR seminar\n\nLecture held in SCI 0.31.\n\nAbstract\nDec
omposition matrices encode the link between ordinary and modular represent
ations of finite groups.\nIn 2020\, Brunat--Dudas--Taylor showed that the
decomposition matrix of the unipotent $\\ell$-blocks of a finite group $G$
of Lie type in good characteristic has unitriangular shape\, answering a
conjecture of Geck. Their theorem holds under some conditions on the prime
$\\ell$\, in particular when $\\ell$ is good. In this talk\, we will disc
uss how to extend this result\, firstly to $\\ell$ bad (for any $G$ simple
adjoint) and then to other blocks\, namely the isolated blocks (for $G$ s
imple adjoint of type $G_2$\, $F_4$\, and $E_6$). This work was part of my
PhD thesis under the supervision of Gunter Malle and Olivier Dudas.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gemma Crowe
DTSTART:20260217T140000Z
DTEND:20260217T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/65
DESCRIPTION:Title: The conjugacy problem in twisted right-angled Artin groups\nby G
emma Crowe as part of ANTLR seminar\n\n\nAbstract\nThere exists a vast lit
erature around the idea of constructing groups (and monoids) via some corr
espondence with finite simple graphs. One well-known example is right-angl
ed Artin groups (RAAGs)\, where edges in our graph correspond precisely to
commuting generators in our group. \nIn this talk\, we will discuss an ad
aptation of this group\, known as twisted RAAGs (T-RAAGs)\, where we intro
duce the option of ‘Klein-bottle’ relations\, which correspond to dire
cted edges of our graph. We will then survey some results about these grou
ps (including many open questions!) and show T-RAAGs have decidable conjug
acy problem. This is based on joint work with Islam Foniqi.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Norris (Queen Mary University of London)
DTSTART:20251209T140000Z
DTEND:20251209T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/66
DESCRIPTION:Title: On $p$-ordinary mod $p$ local Langlands correspondences.\nby Mir
iam Norris (Queen Mary University of London) as part of ANTLR seminar\n\nL
ecture held in NEWSCI 0.04.\n\nAbstract\nTo a suitably “nice” automorp
hic representation\, we can attach a $p$-adic representation of the absolu
te Galois group of a number field. We call a Galois representation arising
in this way automorphic. One of the goals of the Langlands programme is t
o classify the image of automorphic Galois representations within the set
of all Galois representations\, thereby establishing a correspondence.\n\n
When $n=2$ and the number field is $\\mathbb{Q}$\, such a correspondence h
as been constructed by combining mod $p$ and $p$-adic correspondences with
local–global compatibility results. In particular\, the $p$-adic corres
pondence is a representation of $GL_2(\\mathbb{Q}_p)$\, associated to a lo
cal Galois representation\, which appears in the cohomology of the modular
curve.\n\nIn work of Breuil and Herzig\, a candidate for a more general c
orrespondence for $p$-ordinary local Galois representations was constructe
d. In this talk I will discuss joint work with Shu Sasaki in which we cons
truct a framework that should generalise Breuil and Herzig's construction\
, in particular allowing for the non-generic case.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Islam Foniqi (University of East Anglia)
DTSTART:20251202T140000Z
DTEND:20251202T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/67
DESCRIPTION:Title: Droms’ theorems for twisted right-angled Artin groups.\nby Isl
am Foniqi (University of East Anglia) as part of ANTLR seminar\n\nLecture
held in LT 4.\n\nAbstract\nRight-angled Artin groups (RAAGs) form an impor
tant link between combinatorics and group theory\, since the structure of
the group is determined by its defining graph. Twisted right-angled Artin
groups (T-RAAGs) generalize this idea by adding directed edges\, which all
ow us to encode both commutation and certain “twisted’’ relations. I
n this talk\, based on joint work with Simone Blumer and Claudio Quadrelli
\, we explain how Droms’ classical theorems for RAAGs extend to this bro
ader setting. We determine exactly which T-RAAGs have the property that al
l finitely generated subgroups are again T-RAAGs\, give a graph-theoretic
criterion for coherence\, and solve the isomorphism problem for an importa
nt subclass.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katie Reilly (UEA)
DTSTART:20260203T140000Z
DTEND:20260203T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/68
DESCRIPTION:Title: One-Relator Inverse Monoids with Decidable Word Problem Are Algorith
mically Unclassifiable\nby Katie Reilly (UEA) as part of ANTLR seminar
\n\nLecture held in EFRY 01.10.\n\nAbstract\nA classical result from Combi
natorial Group Theory\, the Adian-Rabin Theorem\, states that there does n
ot exist an algorithm which takes a finitely presented group G and decides
whether G possesses a given Markov property. An example of such a propert
y is having decidable word problem. Consequently\, there is no algorithm t
hat takes a finitely presented group and decides whether the group has dec
idable word problem. On the other hand\, Magnus proved in the 1930s that e
very one-relator group has decidable word problem\, so in the one-relator
case such an algorithm (trivially) does exist.\n\nIn contrast\, in 2019\,
Gray proved that there exists a one-relator inverse monoid with undecidabl
e word problem. One key question arising from that work is whether it migh
t be possible to classify the one-relator inverse monoids with decidable w
ord problem. Related to this one can ask whether there is an algorithm tha
t takes a one-relator inverse monoid as input and decides whether or not t
hat one-relator inverse monoid has decidable word problem.\n\nIn this talk
\, I will show that there does not exist an algorithm which takes a one-re
lator inverse monoid M as input and decides whether M has decidable word p
roblem. In other words\, the one-relator inverse monoids with decidable wo
rd problem are algorithmically unclassifiable.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Kirby (UEA)
DTSTART:20260210T140000Z
DTEND:20260210T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/69
DESCRIPTION:Title: Galois groups\, differential equations\, and special functions\n
by Jonathan Kirby (UEA) as part of ANTLR seminar\n\nLecture held in NewSci
0.05.\n\nAbstract\nI will outline a path through Galois groups\, differen
tial Galois groups\, and transcendence of functions to some new applicatio
ns to old functions\, including the non-integrability in finite terms of L
ambert’s W function\, algebraic independence of solutions of Kepler’s
equation of 1607\, and exponential-algebraic independence of Bessel functi
ons. All these terms will be explained so no prior knowledge is required!\
n\n \n\nThis is joint work with Rémi Jaoui\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Broomhead (Plymouth)
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/70
DESCRIPTION:Title: Convex geometry for fans of triangulated categories\nby Nathan B
roomhead (Plymouth) as part of ANTLR seminar\n\nLecture held in EFRY 01.02
.\n\nAbstract\nFans and other convex-geometric objects have recently appea
red in homological algebra in several related contexts. For example\, as g
-fans in the silting theory of finite-dimensional algebras and as scatteri
ng diagrams in Bridgeland stability theory. I will discuss joint work with
David Pauksztello\, David Ploog and Jon Woolf on a general construction w
hich we hope will provide a natural and unifying framework.\n\nStarting wi
th a triangulated category D and a finite rank quotient lattice L of its G
rothendieck group\, we show that each heart H in D determines a closed con
vex `heart cone' in the dual vector space V=Hom(L\,R). The heart cones of
H and all its forward tilts form a `heart fan' in V. If H is `algebraic'\,
i.e. is a length category with finitely many simple objects\, then the he
art cone is simplicial and the heart fan is complete.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Nichols (UEA)
DTSTART:20260303T140000Z
DTEND:20260303T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/71
DESCRIPTION:Title: Free Shelves: Connecting Representations of Braid Groups and Forcing
over Models with Reinhardt Embeddings\nby Eric Nichols (UEA) as part
of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nSet Theory ofte
n seems very disconnected from other pure math topics like Algebra and Rep
resentation Theory. However\, if we look closer we can often find deep con
nections between these fields. In this talk we explore the connection betw
een I3 embeddings\, representations of Braid Groups\, and set theoretic fo
rcing by searching for examples of a free Shelf (or Left Distributive Magm
a). Highlighting how shelves arise out of I3 embeddings and out of algebra
\, showing that I3 embeddings provide examples of free shelves\, and the n
ecessity of these free shelves for forcing over models with Reinhardt embe
ddings.\n\nThis talk will not go into formal detail on the involved set th
eory\, instead focusing on pictorial motivations and general concepts. As
a result this talk should be accessible to all!\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny Roberts (KCL)
DTSTART:20260310T140000Z
DTEND:20260310T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/72
DESCRIPTION:Title: Newform Eisenstein congruences of local origin\nby Jenny Roberts
(KCL) as part of ANTLR seminar\n\nLecture held in QUEENS 01.09.\n\nAbstra
ct\nThe theory of Eisenstein congruences dates back to Ramanujan’s surpr
ising discovery that the Fourier coefficients of the discriminant function
are congruent to the 11th power divisor sum modulo 691. This observation
can be explained via the congruence of two modular forms of weight 12 and
level 1\; the discriminant function and the Eisenstein series\, E_{12}. Ei
senstein congruences were later used by Ribet in his proof of the converse
to Herbrand's theorem. In this talk\, I will first discuss the steps Ribe
t used in his proof and then compare these steps to work in my thesis on c
ongruences between Eisenstein series and newforms of weight k > 2\, square
free level and non-trivial character.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcus Tressl (The University of Manchester)
DTSTART:20260317T140000Z
DTEND:20260317T150000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/73
DESCRIPTION:Title: Every join-semilattice with smallest element is isomorphic to the se
milattice of compact open sets of some space.\nby Marcus Tressl (The U
niversity of Manchester) as part of ANTLR seminar\n\nLecture held in EFRY
1.01.\n\nAbstract\nThe assertion belongs to the representation theory of p
artially ordered sets\, to Non-Hausdorff topology and to domain theory\,
but is (co-)motivated by algebraic questions about the analysis of struc
tures that can be seen as global sections of a sheaf (like a ring or like
a generalized product). I will first explain my interest in the statement
of the title and then construct the asserted space in a functorial way.\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Parente
DTSTART:20260223T160000Z
DTEND:20260223T170000Z
DTSTAMP:20260404T100117Z
UID:UEAPS/74
DESCRIPTION:by Francesco Parente as part of ANTLR seminar\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/UEAPS/74/
END:VEVENT
END:VCALENDAR