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BEGIN:VEVENT
SUMMARY:Andrew Brooke-Taylor (University of Leeds)
DTSTART:20230207T140000Z
DTEND:20230207T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/1
DESCRIPTION:Title: Co
mplexity of classification problems\nby Andrew Brooke-Taylor (Universi
ty of Leeds) as part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAb
stract\nThe notion of "Borel reducibility" gives a framework that allows u
s to compare the complexities of different classes of mathematical objects
. I will give an introduction to this framework\, including how it has be
en used to show that a number of proposed classification programmes in dif
ferent areas of mathematics were impossible to realise. I'll then talk ab
out using the framework to explain why the knot invariants called "quandle
s" are often considered to be too hard to work with (joint work with Sheil
a Miller)\, and finish with a discussion of what happens when the framewor
k is extended to capture functoriality (joint work with Filippo Calderoni)
.\n
LOCATION:https://researchseminars.org/talk/UEAPS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (UEA)
DTSTART:20230217T120000Z
DTEND:20230217T130000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/2
DESCRIPTION:Title: Cl
assification of charge-conserving loop braid representations\nby Fiona
Torzewska (UEA) as part of ANTLR seminar\n\nLecture held in SCI 1.20.\n\n
Abstract\nThe loop braid category is the diagonal category made up of loop
braid groups $LB_n$\, exactly paralleling the relationship between MacLa
ne's braid category and the Artin braid groups. A loop braid representatio
n is a monoidal functor from the loop braid category $\\mathsf{L}$ to a su
itable target category\, and is $N$-charge-conserving if that target is th
e category $\\mathrm{Match}^N$ of charge-conserving matrices.\nIn this tal
k I will discuss the classification and construction of all such represent
ations. (These representations fall into varieties indexed by a set in bij
ection 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:20230314T140000Z
DTEND:20230314T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/4
DESCRIPTION:Title: Th
e Orbital Diameter of Primitive Permutation Groups\nby Kamilla Rekveny
i (Imperial) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.06.\n\nA
bstract\nLet G be a group acting transitively on a finite set Ω. Then G a
cts 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-di
agonal orbital. Define an orbital graph to be the non-directed graph 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 connec
ted. The orbital diameter of a primitive permutation group is the supremum
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 primitive per
mutation groups. In my talk I will outline some important background infor
mation and the progress made towards finding explicit bounds on the orbita
l diameter. In particular\, I will discuss some results on the orbital dia
meter of the groups of simple diagonal type and their connection to the co
vering number of finite simple groups. I will also discuss some results fo
r affine groups\, which provides a nice connection to the representation t
heory of quasisimple groups.\n
LOCATION:https://researchseminars.org/talk/UEAPS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Martin (Earlham Institute)
DTSTART:20230502T130000Z
DTEND:20230502T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/6
DESCRIPTION:Title: Di
mensions of phylogenetic network varieties\nby Samuel Martin (Earlham
Institute) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstra
ct\nPhylogenetic networks provide a means of describing the evolutionary h
istory of taxa that have undergone “horizontal” events\, such as hybri
dization or lateral gene transfer. The mutation process of a single site i
n shared DNA sequence for a set of such taxa can be modelled as a Markov p
rocess on a phylogenetic network\, and the site-pattern probability distri
butions from such a model can be viewed as a projective variety. In this w
ork\, we have given an explicit description of the dimension of this varie
ty for a given level-1 phylogenetic network under any group-based model of
evolution. I will give an overview of the model from an algebraic perspec
tive and describe our results\, focussing on the toric fiber product of tw
o ideals\, and finish with some applications to identifiability problems.
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:20230516T130000Z
DTEND:20230516T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLecture held in QUEENS 1
.03.\n\nAbstract\nThe classical local theta correspondence for p-adic redu
ctive dual pairs defines a bijection between prescribed subsets of irreduc
ible smooth complex representations coming from two groups (H\,H')\, formi
ng a dual pair in a symplectic group. Alberto Mínguez extended this resul
t for type II dual pairs\, i.e. when (H\,H') is made of general linear gro
ups\, to representations with coefficients in an algebraically closed fiel
d of characteristic l as long as the characteristic l does not divide the
pro-orders of H and H'. For coefficients rings like Z[1/p]\, we explain ho
w to build a theory in families for type II dual pairs that is compatible
with reduction to residue fields of the base coefficient ring\, where cent
ral to this approach is the integral Bernstein centre. We translate some w
eaker properties of the classical correspondence\, such as compatibility w
ith supercuspidal support\, as a morphism between the integral Bernstein c
entres of H and H' and interpret it for the Weil representation. In genera
l\, we only know that this morphism is finite though we may expect it to b
e surjective. This would result in a closed immersion between the associat
ed affine schemes as well as a correspondence between characters of the Be
rnstein 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:20230523T130000Z
DTEND:20230523T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR sem
inar\n\nLecture held in SCI 3.05.\n\nAbstract\nLet f be a normalized newfo
rm of weight k for $\\Gamma_0(N)$. It is a natural question to try to unde
rstand 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 about rece
nt joint work with Kȩstutis Česnavičius and Michael Neururer where we s
olve this problem using representation-theoretic techniques. Roughly speak
ing\, we reduce the problem to bounding $p-$adic valuations of local Whitt
aker newforms and then use a "basic identity" (a consequence of the Jacque
t-Langlands local functional equation) to reduce to $p$-adic properties of
local epsilon factors of representations of $\\GL_2(\\Q_p)$. \n\nA key a
pplication of our result is to understand the Manin constant c of an ellip
tic curve E over the rationals. The integer c scales the differential dete
rmined by the normalized newform f associated to E into the pullback of a
N\\'{e}ron differential under a minimal modular parametrization. Manin con
jectured that c equals 1 or -1 for optimal parametrizations. We prove that
c divides the degree of the parametrization under a minor assumption at t
he primes 2 and 3. For this result\, we establish a certain integrality pr
operty of $\\omega_f$ that follows from the Manin conjecture. We expect th
at this integrability property we prove here will be necessary for any fur
ther progress towards Manin's conjecture.\n
LOCATION:https://researchseminars.org/talk/UEAPS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (Cambridge)
DTSTART:20230425T130000Z
DTEND:20230425T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/10
DESCRIPTION:Title: M
odularity in the partial weight one case\nby Hanneke Wiersema (Cambrid
ge) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nThe
strong form of Serre's conjecture states that a two-dimensional mod p rep
resentation of the absolute Galois group of $\\mathbb{Q}$ arises from a mo
dular form of a specific weight\, level and character. Serre restricted to
modular forms of weight at least 2\, but Edixhoven later refined this con
jecture to include weight one modular forms. In this talk we explore analo
gues of Edixhoven's refinement for Galois representations of totally real
fields\, extending recent work of Diamond and Sasaki. In particular\, we s
how how modularity of partial weight one Hilbert modular forms can be rela
ted to modularity of Hilbert modular forms with regular weights\, and vice
versa. We will also discuss the applications of this for p-adic Hodge the
ory.\n
LOCATION:https://researchseminars.org/talk/UEAPS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (UEA)
DTSTART:20230509T130000Z
DTEND:20230509T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/12
DESCRIPTION:Title: S
copes equivalence for blocks of Ariki-Koike algebras\nby Alice Dell'Ar
ciprete (UEA) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.06.\n\n
Abstract\nWe consider representations of the Ariki-Koike algebra\, a $q$-d
eformation 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 algebra\,
in an attempt to generalise the combinatorial representation theory of the
Iwahori-Hecke algebra. In particular\, we prove a sufficient condition su
ch that restriction of modules leads to a natural correspondence between t
he multipartitions of $n$ whose Specht modules belong to a block $B$ and t
hose of $n−\\delta_i(B)$ whose Specht modules belong to the block $B'$\,
obtained from $B$ applying a Scopes' equivalence. This gives us an equali
ty of decomposition numbers for the corresponding Ariki-Koike algebras.\n
LOCATION:https://researchseminars.org/talk/UEAPS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nutt Tananimit (UEA)
DTSTART:20230530T130000Z
DTEND:20230530T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLecture held i
n 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://researchseminars.org/talk/UEAPS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Ardakov (Oxford)
DTSTART:20230328T130000Z
DTEND:20230328T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR sem
inar\n\nLecture held in SCI 3.05.\n\nAbstract\nThis is work in progress wi
th Peter Schneider. The Bernstein centre of a $p$-adic reductive group pla
ys a fundamental role in the classical local Langlands correspondence. In
the mod-p local Langlands program\, the naive analogue of the Bernstein ce
ntre\, namely the centre of the category $Mod(G)$ of all smooth mod-$p$ re
presentations\, turns out to be too small: it is for example trivial whene
ver the group in question has trivial centre. Instead\, we consider the ce
ntres $Z(Mod(G)/\\mathcal{L})$ of the quotient categories $Mod(G)/\\mathca
l{L}$\, as $\\mathcal{L}$ runs over all localizing subcategories of $Mod(G
)$. We show that provided one restricts to the localizing subcategories th
at are $stable$ $under$ $injective$ $envelopes$\, this defines a sheaf wit
h 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 Schneider on t
he structure of the pro-$p$ Iwahori $Ext$-algebra to construct a certain p
rojective variety $X$ having the property that every Zariski open subset $
U$ of $X$ gives rise to a stable localizing subcategory $\\mathcal{L}_U$ o
f $Mod(G)$. Both connected components of $X$ are certain chains of project
ive lines\, and $X$ and is closely related to the recent work of Dotto\, E
merton and Gee.\n
LOCATION:https://researchseminars.org/talk/UEAPS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:test
DTSTART:20230801T130000Z
DTEND:20230801T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/15
DESCRIPTION:by test as part of ANTLR seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Jones (The University of Manchester)
DTSTART:20231017T130000Z
DTEND:20231017T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLecture held in SCI 3.0
5.\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\, and discu
ss 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:20231205T140000Z
DTEND:20231205T150000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLecture
held in SCI 3.05.\n\nAbstract\nWe make some observations around different
ially large fields (in characteristic zero). In particular\, we note that
they can be characterised as those differential fields that are existentia
lly closed in the "differential algebraic" Laurent series ring. We also no
te that a field admits a differentially large structure iff it is of infin
ite transcendence degree (over Q). We then turn our attention to the theor
y CODF (closed ordered differential fields). We observe that a real closed
differential field has a prime model extension (in CODF) iff it is alread
y a CODF. This extends a result of Singer showing that CODF has no prime m
odel. We then discuss the question of when a real closed differential fiel
d has a CODF extension inside a differential closure.\nThis is a combinati
on 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:20231003T130000Z
DTEND:20231003T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/18
DESCRIPTION:Title: S
tudying points on varieties via varying families\nby Alex Torzewski (K
ings College London) as part of ANTLR seminar\n\nLecture held in EFRY 01.0
5.\n\nAbstract\nWe show how Lawrence-Venkatesh's method for studying point
s on a variety X can be applied to curves in families. In the process\, we
also outline the original method. The idea is that if there exists a fami
ly over X which varys "a lot"\, then this strongly constrains the existenc
e of points. This is an example of how topology influences arithmetic!\n
LOCATION:https://researchseminars.org/talk/UEAPS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Rockwood (Kings College London)
DTSTART:20231024T130000Z
DTEND:20231024T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/19
DESCRIPTION:Title: F
amilies of branching laws and their arithmetic applications\nby Rob Ro
ckwood (Kings College London) as part of ANTLR seminar\n\nLecture held in
EFRY 01.08.\n\nAbstract\nThe branching laws of certain special pairs of al
gebraic groups $H \\to G$ are related to the $L$-functions of automorphic
representations via the theory of period integrals\, made concrete by the
conjectures of Gan--Gross--Prasad and Ichino--Ikeda. On the algebraic side
\, one can use branching laws for highest weight representations to constr
uct cohomological avatars of automorphic period integrals in the cohomolog
y of Shimura varieties. These classes are related to $p$-adic $L$-function
s and Euler systems\, both of which have applications to important arithme
tic conjectures such as the Bloch--Kato conjectures. I will explain how on
e constructs such avatars and will describe work of myself and Loeffler--Z
erbes 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:20231010T130000Z
DTEND:20231010T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLectu
re held in SCI 3.05.\n\nAbstract\nMotivated by the open word problem for o
ne-relator monoids\, we study decision problems for monoids and groups. I
will present some recent results (joint work with Robert D. Gray & C.-F. N
yberg-Brodda) on submonoid and rational subset membership problems in alg
ebraic structures\, and discuss their implications and connections with th
e word problem. Right-angled Artin groups and trace monoids play a major r
ole 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:20231212T140000Z
DTEND:20231212T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/21
DESCRIPTION:Title: O
n uniquely geodesic graphs and groups\nby Davide Spriano (Oxford Unive
rsity) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\n
Graph with a unique geodesic between any two points are a very natural obj
ect to define\, but they remain a mysterious object. In this talk we will
discuss new results about their classifications\, and show that a group wi
th a uniquely geodesic Cayley graph needs to be virtually free. This is jo
int 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:20231121T140000Z
DTEND:20231121T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/22
DESCRIPTION:Title: F
rom gentle to string algebras: a geometric model\nby Raquel Coelho Sim
oes (Lancaster University) as part of ANTLR seminar\n\n\nAbstract\nGeometr
ic models associated to triangulations of Riemann surfaces arose in the co
ntext of cluster algebras and have since been used as an important tool to
study representation theory of algebras and provide connections with alge
braic geometry and symplectic geometry. \n\nSignificant applications of ge
ometric models include a description of extensions and a classification of
support tau-tilting modules over gentle algebras. Gentle algebras are a p
articular subclass of string algebras\, which are of tame representation t
ype\, 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 surfaces an
d explain how to extend this model to a geometric model of the module cate
gory of any string algebra. This is based on joint work in progress with K
arin Baur.\n
LOCATION:https://researchseminars.org/talk/UEAPS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembélé (KCL)
DTSTART:20240227T140000Z
DTEND:20240227T150000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\
n\nLecture held in TPSC 0.1.\n\nAbstract\nIn this talk\, we describe a par
ametrisation of abelian surfaces with real multiplication by $\\mathbb{Z}[
\\sqrt{2}]$ using Richelot isogenies\, and give some arithmetic applicatio
ns.\n
LOCATION:https://researchseminars.org/talk/UEAPS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Gruber (York)
DTSTART:20240312T140000Z
DTEND:20240312T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/24
DESCRIPTION:Title: C
enters and centralizers in (double) affine Hecke algebras\nby Jonathan
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 objects o
f 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 construction in
the double affine Hecke algebra. This subalgebra contains the center\, an
d it admits a canonical basis akin to the Kazhdan-Lusztig basis of the aff
ine Hecke algebra. I will explain how the canonical basis can be used as a
tool to compute composition multiplicities in Gaitsgory's central sheaves
on affine flag manifolds.\n
LOCATION:https://researchseminars.org/talk/UEAPS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Kurinczuk (Sheffield)
DTSTART:20240319T140000Z
DTEND:20240319T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/25
DESCRIPTION:Title: N
ewforms for cuspidal representations\nby Rob Kurinczuk (Sheffield) as
part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAbstract\nWe will
review the theory of newforms for cuspidal representations of p-adic gener
al linear groups of Jacquet--Piatetski-Shapiro--Shalika\, and Matringe. T
hen compare them with the explicit functions of Paskunas-Stevens for cuspi
dal representations in special cases. This is joint work in progress with
Johannes Girsch.\n
LOCATION:https://researchseminars.org/talk/UEAPS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Prest (Manchester)
DTSTART:20240423T130000Z
DTEND:20240423T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/26
DESCRIPTION:Title: L
inear algebra over general rings\nby Mike Prest (Manchester) as part o
f ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nIn linear alge
bra we meet solution sets to systems of linear equations with coefficients
from a field. Later\, we see that we can replace the field by a more gen
eral ring\, for instance a Weyl algebra where we would be looking at solut
ions of systems of linear partial differential equations. Over general ri
ngs\, however\, such solution sets do not have nice closure properties\; f
or instance they might not be closed under coordinate projections. But\,
if we accept projected systems of equations and their solution sets as bas
ic objects\, then we recover the nice closure properties that one has over
fields and\, over general rings\, find interesting structures sitting wit
hin a rich and extensive theory which ramifies into many aspects of repres
entation theory.\n
LOCATION:https://researchseminars.org/talk/UEAPS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvy Anscombe (Paris)
DTSTART:20240430T130000Z
DTEND:20240430T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/27
DESCRIPTION:Title: U
niformities for Hilbert's Tenth Problem in henselian valued fields\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 asks for
an algorithm to determine correctly whether -- or not -- a given multivari
able polynomial equation with integer coefficients has integer solutions.\
nThe surprising resolution\, by Davis\, Putnam\, Robinson\, and finished b
y Matiyasevich in 1970\, is that there is no such algorithm. In the termin
ology of mathematical logic\, the existential theory of the ring of intege
rs is undecidable. I am interested in the (un?)decidability of the existen
tial theories of a variety of rings and fields\, especially of "large" fie
lds\, for example those fields admitting a non-trivial valuation that sati
sfies "Hensel's Lemma"\, a weak form of completion. In this talk I'll desc
ribe work in this direction (joint with Dittmann\, Fehm\, Jahnke\, and oth
ers\, in various combinations)\, new "uniform" results\, and some links wi
th theories of function fields.\n
LOCATION:https://researchseminars.org/talk/UEAPS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aberdeen Powell (UEA)
DTSTART:20240206T140000Z
DTEND:20240206T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/28
DESCRIPTION:Title: F
robenius reciprocity for fiat 2-categories\nby Aberdeen Powell (UEA) a
s part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nFrobeniu
s reciprocity is a famous property first observed in the setting of group
representations. Representations of 2-categories is a lively and relativel
y young field\, where many classic results of representation theory reappe
ar: the Jordan-Hölder theorem (Mackaay\, Mazorchuk\, Miemietz\, Tubbenhau
er and Zhang\, Finitary birepresentations of fintary bicategories)\, vario
us properties from Morita theory (Mazorchuk and Miemietz\, Morita theory f
or finitary 2-categories)\, etc. In this talk\, we consider Frobenius reci
procity in the context of 2-categories.\n
LOCATION:https://researchseminars.org/talk/UEAPS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curial Gallart Rodriguez (UEA)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/29
DESCRIPTION:Title: C
urrent 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 questi
ons in mathematics can be answered in ZFC by Gödel's incompleteness theor
ems. Numerous concrete examples of mathematical statements have been prove
n to be independent from the ZFC axioms over the years. Many of them being
non-set-theoretic in nature. Most notably\, the Whitehead problem\, the B
orel conjecture\, Kaplansky's conjecture on Banach algebras\, or the Brown
-Douglas-Fillmore problem. Instead of accepting that there are questions t
hat don't have an answer\, the independence phenomenon lead set theorists
to search for axioms beyond ZFC that would give us a clearer picture of th
e set theoretic (and mathematical) universe.\n\nIn this talk I will presen
t the main lineages of axioms that have been considered and their conseque
nces. I will describe their connections and the main methods to study 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:20240507T130000Z
DTEND:20240507T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/30
DESCRIPTION:Title: H
idden dynamical zeta functions\nby Tom Ward as part of ANTLR seminar\n
\nLecture held in SCI 3.05.\n\nAbstract\nI will discuss examples of a phen
omenon first observed (to my knowledge) by Yash Puri. Certain - as it turn
s out\, many - sequences that arise naturally in combinatorics or number t
heory fail to count periodic points (that is\, be the coefficients of a dy
namical zeta function) but succeed after some modest modification. Example
s 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:20240213T140000Z
DTEND:20240213T150000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar
\n\nLecture held in Queen 01.09.\n\nAbstract\nThe authors came across the
problem of finding minimal lottery design numbers j=L(n\,k\,p\,t)\; that i
s\, 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 intersection D\\c
ap B_i with at least t elements. In the context of a lottery\, n represent
s the. number of balls\, k the number of choices of balls on a ticket\, p
the size of a draw.\nFor the UK national lottery\, n=59\, k=p=6 and one ge
ts a (rather meagre) prize as long as t is at least 2.\nUsing the constrai
nt solving library in Prolog\, we calculated j for k=p=6\, t=2 and n all t
he way up to 70. For example L(59\,6\,6\,2)=27. This is the second paper w
here we have aimed to show the value of Prolog and constraint programming
in pure mathematics.\nI’ll give an overview of constraint programming\,
logic programming in Prolog\, and describe how we used these tools to solv
e 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:20240318T140000Z
DTEND:20240318T150000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\nLectur
e held in EFRY01.10.\n\nAbstract\nWhen studying representations of particu
larly unruly\nmathematical structures\, it can often be useful to compose\
nrepresentations of an associated\, simpler structure with an `evaluation'
\nfunctor from the unruly structure to the better behaved one. A\nprevious
ly studied example is the evaluation functor from (the\nidempotented unive
rsal enveloping algebra of) affine type sl(n) to\nfinite type sl(n). In th
is talk I will explain this example in detail. I\nwill then present the ca
tegorification of this evaluation functor\nbetween the corresponding 2-Kac
-Moody algebras for the n=3 case\, and\nalso discuss some of the technique
s used for an inductive construction\nof the evaluation 2-functor for larg
er 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:20240606T100000Z
DTEND:20240606T110000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/34
DESCRIPTION:Title: 3
-Preprojective Algebras of Type D\nby Jordan Haden (UEA) as part of AN
TLR seminar\n\nLecture held in EFry 01.02.\n\nAbstract\nGiven an algebra w
ith finite global dimension\, it is natural to consider two autoequivalenc
es of its bounded derived category: the Serre functor and the shift functo
r. If a power of one is isomorphic to a power of the other\, we say the al
gebra is fractional Calabi-Yau. Closely related are d-representation-finit
e algebras. These are algebras whose module category contains a d-cluster
tilting subcategory\, which is “manageable” even if the algebra has wi
ld representation type. We will explain these concepts\, and how they are
connected\, before presenting an infinite family of algebras which are bot
h 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:20240708T130000Z
DTEND:20240708T140000Z
DTSTAMP:20260421T122040Z
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 ANTLR seminar\n\n\nAbs
tract\nI will talk about several results on Hecke algebras attached to Ber
nstein blocks of reductive p-adic groups\, where we construct a local Lang
lands correspondence for these Bernstein blocks. Our techniques draw inspi
rations from the foundational works of Deligne\, Kazhdan\, Langlands\, Lus
ztig and Shahidi.\n\n\nAs an application\, we prove the Local Langlands Co
njecture for G_2\, which is the first known case in literature of LLC for
exceptional groups. Our correspondence satisfies an expected property on c
uspidal support\, which is compatible with the generalized Springer corres
pondence\, along with a list of characterizing properties including the st
abilization of character sums\, formal degree property etc. In particular\
, we obtain (not necessarily unipotent) "mixed" L-packets containing "F-si
ngular" supercuspidals and non-supercuspidals. I will give explicit exampl
es 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 do
wn certain choices in the construction of the correspondence using stabili
ty of L-packets\; one key input is a homogeneity result due to Waldspurger
and DeBacker. Moreover\, I will mention how to adapt our general strategy
to construct explicit LLC for other reductive groups\, such as GSp_4\, Sp
_4\, etc\, generalizing the depth-zero L-packets of Lust-Stevens. Such exp
licit description of the L-packets has been useful in number-theoretic app
lications\, e.g. modularity lifting questions.\n\nVarious parts of this ta
lk are based on joint works with various collaborators\, and attributions
will be made clear throughout the talk.\n
LOCATION:https://researchseminars.org/talk/UEAPS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashot Minasyan (Southampton)
DTSTART:20241015T130000Z
DTEND:20241015T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/36
DESCRIPTION:Title: G
enerating RAAGs in 1-relator groups\nby Ashot Minasyan (Southampton) a
s 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 the rela
tions that two vertices commute if and only if they are adjacent in $\\Gam
ma$. The monoid with the same presentation is called the trace monoid $T(\
\Gamma)$. RAAGs play a significant role in Geometric Group Theory\, while
Trace monoids have important applications in Computer Science.\n\nThe trac
e 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 subgroup?\n\nT
his 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 a
lso 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 on joint
work with Motiejus Valiunas\, showing that the answer to the latter quest
ion is positive.\n
LOCATION:https://researchseminars.org/talk/UEAPS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım (Leeds)
DTSTART:20241112T140000Z
DTEND:20241112T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/37
DESCRIPTION:Title: S
urface triangulations and friezes\nby Emine Yıldırım (Leeds) as par
t of ANTLR seminar\n\nLecture held in EFRY 01.08.\n\nAbstract\nInterplays
between representation theory of algebras and combinatorics give rise to n
ew 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. Gunawan\, and
G. Todorov.\n
LOCATION:https://researchseminars.org/talk/UEAPS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Williams (Nottingham)
DTSTART:20241001T130000Z
DTEND:20241001T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/38
DESCRIPTION:Title: C
ongruences between eigensystems for GL(n)\nby Chris Williams (Nottingh
am) as part of ANTLR seminar\n\nLecture held in NEWSCI 0.03.\n\nAbstract\n
In this talk\, I will discuss congruences between modular forms\, and -- m
ore generally -- between systems of eigenvalues on GL(n)\, modular forms b
eing the special case $n=2$. In a broad sense\, this seeks to answer the f
ollowing type of question: Let $p$ be prime and $f$ be a modular form of l
evel $\\Gamma_0(M)$ where $p$ divides $M$. For a given integer $m$\, does
there exist another eigenform $g$ congruent to $f$ modulo $p^m$?\n\nFor mo
dular forms\, the answer is yes. Even better\, such congruences can be cap
tured geometrically via 1-dimensional families' of eigenforms (via the eig
encurve'). This geometric object has had profound consequences in Iwasawa
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 D
aniel Barrera and Andy Graham\, where we consider some of the problems in
generalising them to higher dimension. Here the picture becomes more subtl
e -- 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 s
ame automorphic representation.\n
LOCATION:https://researchseminars.org/talk/UEAPS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Warne (UEA)
DTSTART:20241022T130000Z
DTEND:20241022T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/39
DESCRIPTION:Title: F
actorisations of finitely presented special inverse monoids\nby Jonath
an Warne (UEA) as part of ANTLR seminar\n\nLecture held in JSC 2.02.\n\nAb
stract\nInverse monoids are a kind of algebraic object which model partial
bijections in the same way that groups model bijections and semigroups mo
del transformations generally. A special inverse monoid is one defined by
a set of relations of the form $r_i = 1$. We can factorise these $r_i$ int
o component words\, for instance $xyxzxy =1$ may be written $(xy)(xz)(xy)
=1$. In particular\, every special inverse monoid presentation has a uniqu
e factorisation of its relators into minimal invertible pieces.\n\nIn 2001
Ivanov\, Margolis and Meakin produced a paper which included amongst othe
rs two important results. That the special inverse monoid's group of units
is generated by the minimal invertible pieces and that we can decide the
word problem of an E-unitary special inverse monoid by deciding the word a
nd prefix membership problems of its maximal group image. Both allow us to
better understand an inverse monoid by studying corresponding groups.\n\n
In this talk we will use these results to discuss the effects of the minim
al invertible pieces of a special inverse monoid's relators having certain
combinatorial properties on a number of decision problems\, extending res
ults by Dolinka and Gray.\n
LOCATION:https://researchseminars.org/talk/UEAPS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Seminar
DTSTART:20241029T140000Z
DTEND:20241029T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/40
DESCRIPTION:by No Seminar as part of ANTLR seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lassina Dembele (KCL)
DTSTART:20241105T140000Z
DTEND:20241105T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/41
DESCRIPTION:Title: P
arametrising abelian surfaces with RM by $\\mathbb{Z}[\\sqrt{2}]$ using Ri
chelot isogenies\nby Lassina Dembele (KCL) as part of ANTLR seminar\n\
nLecture held in NEWSCI 0.03.\n\nAbstract\nIn this talk\, we describe a pa
rametrisation of abelian surfaces with real multiplication by $\\mathbb{Z}
[\\sqrt{2}]$ using Richelot isogenies\, and give some arithmetic applicati
ons.\n
LOCATION:https://researchseminars.org/talk/UEAPS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Cambridge)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/42
DESCRIPTION:Title: S
teenrod operations via higher Bruhat orders\nby Nicholas Williams (Cam
bridge) as part of ANTLR seminar\n\nLecture held in EFRY 01.08.\n\nAbstrac
t\nThe cohomology of a topological space has a ring structure via the cup
product. The cup product is defined at the level of cochains\, where it is
not commutative\, but it becomes commutative at the cohomology level. At
the cochain level\, the lack of commutativity is resolved homotopically by
an infinite tower of higher products\, known as the Steenrod cup-i produc
ts. This additional structure provides more refined information which can
be used to tell apart non-homotopy-equivalent spaces. Not assuming any bac
kground from algebraic topology\, I will explain recent work with Guillaum
e Laplante-Anfossi\, where we show how conceptual proofs of the key proper
ties of Steenrod's cup-i products can be given using the higher Bruhat ord
ers of Manin and Schechtman.\n
LOCATION:https://researchseminars.org/talk/UEAPS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Levine (UEA)
DTSTART:20241008T130000Z
DTEND:20241008T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/43
DESCRIPTION:Title: E
quations with constraints in virtually abelian groups\nby Alex Levine
(UEA) as part of ANTLR seminar\n\nLecture held in SCI 1.50.\n\nAbstract\nT
he 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 admits a
solution. When considering equations in groups\, one can also add 'constr
aints' to the variables\, such as insisting a specific variable must lie i
n a specific subgroup. We consider the Diophantine problem for virtually a
belian groups\, which has long been considered 'folklore'. We look at add
ing various types of constraints to equations in virtually abelian groups.
\n
LOCATION:https://researchseminars.org/talk/UEAPS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Dmitrieva (UEA)
DTSTART:20241119T140000Z
DTEND:20241119T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/44
DESCRIPTION:Title: G
eneric functions and quasiminimality\nby Anna Dmitrieva (UEA) as part
of ANTLR seminar\n\n\nAbstract\nOne of the well-known accomplishments of m
odel theory is the study of the field of complex numbers. It possesses num
erous nice properties\, including minimality\, i.e. any definable subset i
s finite or cofinite. However\, adding the exponential map to the structur
e makes it possible to define the ring of integers\, preventing minimality
and many other properties. Nevertheless\, there is still hope that the co
mplex exponential field is somewhat well-behaved. For instance\, Zilber’
s quasiminimality conjecture states that the complex exponential field is
quasiminimal\, i.e. every definable subset is countable or co-countable. A
nalogous conjectures were made\, replacing the exponential map with other
analytical functions.\n\nIn this talk we look at the theory of a generic f
unction\, as introduced by Zilber in 2002. As the main result\, we prove t
hat adding an entire generic function to the complex field gives a quasimi
nimal structure\, and\, moreover\, this structure is unique up to an isomo
rphism. Thus we obtain a non-trivial example of an entire function which k
eeps the complex field quasiminimal.\n
LOCATION:https://researchseminars.org/talk/UEAPS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (UEA)
DTSTART:20250225T140000Z
DTEND:20250225T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/45
DESCRIPTION:Title: C
ategorification in Representation Theory\nby Vanessa Miemietz (UEA) as
part of ANTLR seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nI will
explain some of the ideas behind the theory of finitary 2-representations
of finitary 2-categories\, which attempts to categorify the representation
theory of finite dimensional algebras. I will illustrate these on the exa
mple of the categorification of Hecke algebras via Soergel bimodules.\n
LOCATION:https://researchseminars.org/talk/UEAPS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (Royal Holloway)
DTSTART:20250211T140000Z
DTEND:20250211T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/46
DESCRIPTION:Title: M
ultiplicity-free induced characters of symmetric groups\nby Pavel Ture
k (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 characte
r is multiplicity-free if its irreducible constituents appear with multipl
icity one. Wildon in 2009 and independently Godsil and Meagher in 2010 hav
e found all multiplicity-free permutation characters of the symmetric grou
p $S_n$. In this talk\, we focus on a significantly more general problem w
hen the permutation characters are replaced by induced characters of the f
orm $\\rho\\!\\uparrow^{S_n}$ with $\\rho$ irreducible. \n\n
\nDespite the nature of the problem\, I explain\,
combining results from group theory\, representation theory and combinator
ics\, why this problem may be feasible and present a close to full answer.
I also mention some of my (often surprising) results to questions about c
onjugate 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 induced t
o $S_n$.\n
LOCATION:https://researchseminars.org/talk/UEAPS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niccolò Guicciardini (Università di Milano)
DTSTART:20250218T140000Z
DTEND:20250218T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/47
DESCRIPTION:Title: T
he status of mathematics in sixteenth-century Europe\nby Niccolò Guic
ciardini (Università di Milano) as part of ANTLR seminar\n\nLecture held
in LT4.\n\nAbstract\nAt the dawn of the so-called scientific revolution\,
the mathematical sciences acquired a new status as the key to understandin
g the structure of reality in a way that contradicted Aristotelian physics
and cosmology. This new role for mathematics did not come without controv
ersy. In this talk I will explore some of these debates\, placing them in
philosophical\, scientific and sociological contexts. I will begin with Co
pernicus’s statements in the Preface to De revolutionibus (1543) conc
erning the role of mathematics in revealing the harmony of the planetary s
ystem and end with Galileo’s statement in the Assayer (1623) that the Bo
ok of Nature is written in mathematical characters and his statement at th
e end of the first Day of the Dialogo sui due massimi sistemi del mondo (1
632) that mathematics provides man with knowledge as certain as that avai
lable to God. As we shall see these statements\, which characterise the sc
ientific revolution\, were controversial.\n
LOCATION:https://researchseminars.org/talk/UEAPS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiuhua Luo (Nantong University)
DTSTART:20250204T140000Z
DTEND:20250204T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/48
DESCRIPTION:Title: T
he structure of separated monomorphism category and its applications\n
by Xiuhua Luo (Nantong University) as part of ANTLR seminar\n\nLecture hel
d in Queens 01.09.\n\nAbstract\nInitiated by G. Birkhoff\, there is a long
history of studying (separated) monomorphism category. It was generalized
to finite acyclic (bounded) quiver representations over a finite-dimensio
nal algebra around ten year ago. It turns out that this category is relate
d with many mathematical branches\, such as singularity theory\, preprojec
tive algebra\, and plays an important role in relative homological algebra
.\n\nIn this talk\, firstly\, the properties of the separated monomorphism
category are given in a more general setup. Secondly\, I will explain the
relation between separated monomorphism category and Gorenstein-projectiv
e modules. Finally\, the construction of this category will be described.\
n
LOCATION:https://researchseminars.org/talk/UEAPS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Bays (University of Oxford)
DTSTART:20250311T140000Z
DTEND:20250311T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/49
DESCRIPTION:Title: A
n asymmetric version of Elekes-Szabó via group actions\nby Martin Bay
s (University of Oxford) as part of ANTLR seminar\n\nLecture held in EFRY
01.05.\n\nAbstract\nElekes and Rónyai showed that a bivariate real polyno
mial f(x\,y)\nexpands\, meaning $|f(A\,A)| \\geq c|A|^{1+\\eta}$ for all f
inite A\, unless\nf can be written as the composition of addition or multi
plication with\nunivariate polynomials. The proof can be seen as going via
the group\nconfiguration theorem of model theory. I will talk about recen
t work\nwith Tingxiang Zou\, in which we consider a more general setup whe
re\nwe can apply a homogeneous space version of this group configuration\n
theorem\, and yet still subsequently reduce to an abelian group. We\ndeduc
e asymmetric expansion $|f(A\,B)| \\geq c|A|^{1+\\eta}$ even when B is\nal
lowed to be drastically smaller than A. Moreover\, we obtain a similar\nre
sult when y is allowed to be a tuple. Allowing x to also be a tuple\nintro
duces new phenomena\, and if time permits I may mention some partial\nresu
lts in this case.\n
LOCATION:https://researchseminars.org/talk/UEAPS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorna Gregory (UEA)
DTSTART:20250318T140000Z
DTEND:20250318T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/50
DESCRIPTION:Title: R
epresentation Type\, Decidability and Pseudofinite-dimensional Modules ove
r Finite-dimensional Algebras\nby Lorna Gregory (UEA) as part of ANTLR
seminar\n\nLecture held in EFRY 01.05.\n\nAbstract\nThe representation ty
pe of a finite-dimensional k-algebra is an algebraic measure of how hard i
t is to classify its finite-dimensional indecomposable modules. Intuitivel
y\, a finite-dimensional k-algebra is of tame representation type if we ca
n classify its finite-dimensional modules and wild representation type if
its module category contains a copy of the category of finite-dimensional
modules of all other finite-dimensional k-algebras. An archetypical (altho
ugh not finite-dimensional) tame algebra is k[x]. The structure theorem fo
r finitely generated modules over a PID describes its finite-dimensional m
odules. Drozd’s famous dichotomy theorem states that all finite-dimensio
nal algebras are either wild or tame.\n\n\nThe (theory of) a class of modu
les is said to be decidable if there is an algorithm which given a sentenc
e in the language of modules (a sentence is a particular kind of statement
about modules) answers whether it is true in all modules in that class. A
long-standing conjecture of Mike Prest claims that the (theory of) the cl
ass of all modules over a finite-dimensional algebra is decidable theory i
f and only if it is of tame representation type. The reverse direction of
this conjecture is often hard to prove even in particular examples. One di
fficulty is that the conjecture talks about all modules rather than just f
inite-dimensional ones. In this talk I will present work in progress aroun
d and in support of a new conjecture\, inspired by Prest’s conjecture\,
which claims that the (theory of) the class of finite-dimensional modules
over a finite-dimensional algebra is decidable if and only if it is of tam
e representation type.\n
LOCATION:https://researchseminars.org/talk/UEAPS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Angdinata (UCL)
DTSTART:20250325T140000Z
DTEND:20250325T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/51
DESCRIPTION:Title: T
eaching a computer algebraic number theory\nby David Angdinata (UCL) a
s part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nFor most
of recorded human history\, mathematics has been done with good-old pen a
nd paper. With the advent of modern computers\, lightning-fast calculation
s and large-scale datasets have granted us unprecedented advances in mathe
matics\, both in pure and applied forms. On the other hand\, they have mer
ely been algorithmic tools for us to compute with\, while lacking the capa
city 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 fo
rmalising fundamental constructions in an interactive theorem prover calle
d Lean.\n
LOCATION:https://researchseminars.org/talk/UEAPS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vlad Vankov (Bristol)
DTSTART:20250429T130000Z
DTEND:20250429T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/52
DESCRIPTION:Title: C
ohomology\, groups and negatively curved geometry\nby Vlad Vankov (Bri
stol) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nO
ver the last thirty years\, hyperbolic and relatively hyperbolic groups ha
ve found characterisations in terms of homological algebra in various form
s\, for example through bounded cohomology and bounded-valued cohomology.
To link the algebra and the geometry\, locally finite spaces are usually u
sed. This can pose issues when dealing with other generalisations of hyper
bolicity\, such as acylindrically hyperbolic groups. To address this\, in
joint work with Francesco Milizia\, Nansen Petrosyan and Alessandro Sisto\
, we study a cohomology theory that detects hyperbolicity for general metr
ic spaces. As a consequence\, we are able to provide a characterisation of
hyperbolically embedded subgroups in terms of homological algebra.\n
LOCATION:https://researchseminars.org/talk/UEAPS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caner Nazaroglu
DTSTART:20250508T120000Z
DTEND:20250508T130000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/53
DESCRIPTION:Title: S
tatistics for random representations of Lie algebras\nby Caner Nazarog
lu as part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAbstract\nHo
w does a typical finite-dimensional representation of a complex Lie algebr
a look like? In this talk\, we address this question for the infinite fami
ly $\\mathfrak{sl}_{r+1}(\\mathbb{C})$ with $r \\geq 2$. Specifically\, we
derive the asymptotic statistical properties of a representation sampled
uniformly from all representations with a given large dimension. This natu
rally extends similar studies on integer partitions with methods inspired
from statistical mechanics. The multivariable generalization we consider c
ontains some new features compared to integer partitions\, which have been
studied from a large range of points of view from combinatorics to modula
rity. In the talk\, we will review those aspects familiar from integer par
titions\, describe the physics inspired approach to the problem\, and fina
lly detail our results for the general case. This is joint work with Walte
r Bridges and Kathrin Bringmann.\n
LOCATION:https://researchseminars.org/talk/UEAPS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rose Berry (UEA)
DTSTART:20250512T130000Z
DTEND:20250512T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/54
DESCRIPTION:Title: T
he Derived l-modular Unipotent Block of p-adic GLn\nby Rose Berry (UEA
) as part of ANTLR seminar\n\nLecture held in LT3.\n\nAbstract\nComplex re
presentations of p-adic groups are in many ways well-understood. The categ
ory has Bernstein's decomposition into blocks\, and for many groups each b
lock is known to be equivalent to modules over a Hecke Algebra. In particu
lar\, the unipotent block (the block containing the trivial representation
) of GLn is equivalent to the modules over an extended affine hecke algebr
a of type A. Over \\bar{Fl} the situation is more complicated in the gener
al case: the Bernstein block decomposition can fail (eg for SP8)\, and the
re is no longer in general an equivalence with the Hecke algebra. However\
, some groups\, such as GLn and its inner forms\, still have a Bernstein d
ecomposition. Furthermore\, Vigernas showed that the unipotent block of GL
n contains a subcategory that is equivalent to modules over a mild extensi
on of the Hecke Algebra\, the Schur Algebra\, and this subcategory generat
es the principal block under extensions. Building on this work\, we show t
hat the derived category of the principal block of GLn is triangulated-equ
ivalent to the perfect complexes over a dg-enriched Schur algebra. We prov
e this by combining general finiteness results about Schur algebras with t
he well-known structure of the l-modular unipotent blocks of GLn over fini
te fields.\n
LOCATION:https://researchseminars.org/talk/UEAPS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Vaz (Université catholique de Louvain)
DTSTART:20250508T150000Z
DTEND:20250508T160000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/55
DESCRIPTION:Title: A
tour on quantum topology and categorification\nby Pedro Vaz (Universi
té catholique de Louvain) as part of ANTLR seminar\n\nLecture held in EFR
Y 01.10.\n\nAbstract\nQuantum topology is a generic term used to designate
algebraic-topological constructions that are\, in some broad sense\, clos
e to the Jones polynomial and its variants.\nIn this talk\, I will give an
overview of topological quantum invariants and their categorification\, f
rom their historical origins with the Jones polynomial to modern developme
nts. I will introduce the main concepts and present several examples\, hig
hlighting their multidisciplinary impact within contemporary mathematics.\
n
LOCATION:https://researchseminars.org/talk/UEAPS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Mackaay (Universidade do Algarve)
DTSTART:20250506T100000Z
DTEND:20250506T110000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/56
DESCRIPTION:Title: P
arabolic induction and restriction play an important role in the (finite-d
imensional) representation theory\nby Marco Mackaay (Universidade do A
lgarve) as part of ANTLR seminar\n\nLecture held in SCI 3.05.\n\nAbstract\
nParabolic induction and restriction play an important role in the (finite
-dimensional) representation theory \nof extended affine type A Hecke alge
bras\, so it is natural to look for a categorical analog in the birepresen
tation \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 wi
ll sketch such an analog for a maximal parabolic.\n
LOCATION:https://researchseminars.org/talk/UEAPS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Luo
DTSTART:20250930T130000Z
DTEND:20250930T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/57
DESCRIPTION:Title: O
n the Local Converse Theorem for Depth 1/N Supercuspidal Representations o
f $\\mathrm{GL}(2N\, F)$\nby David Luo as part of ANTLR seminar\n\n\nA
bstract\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 supercu
spidal representations\, i.e. those supercuspidals of minimal positive dep
th. Via explicit computations of twisted gamma factors\, we show that midd
le supercuspidal representations may be uniquely determined through twisti
ng by quasi-characters of $F^{\\times}$ and simple supercuspidal represent
ations of $\\GL(N\, F)$. Furthermore\, we give a conjecture which refines
the local converse theorem for general supercuspidal representations of $\
\GL(n\, F)$.\n
LOCATION:https://researchseminars.org/talk/UEAPS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Kamsma
DTSTART:20251009T130000Z
DTEND:20251009T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/58
DESCRIPTION:Title: C
ofibrant generation of pure monomorphisms in presheaf categories\nby M
ark Kamsma as part of ANTLR seminar\n\n\nAbstract\nThe title of this talk\
, and its main result\, are purely category-theoretic. However\, we use mo
del-theoretic methods to obtain the result. For a fixed monoid $S$\, there
is an algebraic question whether or not pure monomorphisms between sets w
ith an $S$-action are cofibrantly generated. In (positive) model theory\,
we sometimes call pure monomorphisms immersions: those homomorphisms that
reflect solutions to systems of equations. An earlier result by Lieberman\
, Vasey and Rosický established an equivalence between the existence of a
stable independence relation on a category and cofibrant generation of a
certain class of morphisms. We use this equivalence\, as well as ideas of
Mustafin\, to characterise for which monoids $S$ the class of pure monomor
phisms 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 thr
ough in the greater generality of presheaf categories\, hence the title\,
and main result\, of the talk.\n\nThis is joint work with Sean Cox\, Jonat
han Feigert\, Marcos Mazari-Armida and Jiří Rosický.\n
LOCATION:https://researchseminars.org/talk/UEAPS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Keyes (KCL)
DTSTART:20251014T130000Z
DTEND:20251014T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/59
DESCRIPTION:Title: T
owards Artin’s conjecture on $p$-adic forms in low degree\nby Chris
Keyes (KCL) as part of ANTLR seminar\n\n\nAbstract\nArtin conjectured 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 zero\; eq
uivalently\, the field $\\mathbb{Q}_p$ is $C_2$. This conjecture is false\
, with the first counterexample in degree 4 over $\\mathbb{Q}_2$ discovere
d by Terjanian. However\, all known counterexamples have composite degree\
, begging the question: does Artin's conjecture hold if we restrict to pri
me degrees $d$? We have evidence in degrees 2 and 3 due to results of Hass
e and Lewis\, respectively\, and the celebrated Ax--Kochen theorem establi
shes an asymptotic version of Artin's conjecture when $p$ is large relativ
e to $d$. In recent joint work with Lea Beneish\, we establish Artin's con
jecture in degree 5 when $p > 5$ and in degree 7 when $p > 679$. In this t
alk\, we will explore the ideas and techniques spanning nearly a century b
ehind these results\, from the Lang--Weil theorem to effective Bertini the
orems and parallel computing.\n
LOCATION:https://researchseminars.org/talk/UEAPS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Fournier-Facio
DTSTART:20251021T130000Z
DTEND:20251021T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/60
DESCRIPTION:Title: F
irst-order theory of torsion-free Tarski monsters\nby Francesco Fourni
er-Facio as part of ANTLR seminar\n\n\nAbstract\nA torsion-free Tarski mon
ster is a non-abelian group all of whose proper nontrivial subgroups are i
nfinite cyclic. I will present joint work with Remi Coulon and Turbo Ho\,
where we construct torsion-free Tarski monsters with controlled first-orde
r theory\, something which is usually only done for groups with hyperbolic
features. No preliminary knowledge of any of these words will be assumed.
\n
LOCATION:https://researchseminars.org/talk/UEAPS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Camina
DTSTART:20251104T140000Z
DTEND:20251104T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/61
DESCRIPTION:Title: C
osets of normal subgroups: what can they tell us about the group\nby A
lan Camina as part of ANTLR seminar\n\nLecture held in C. HALL 01.08.\n\nA
bstract\nIn this talk we discuss how information about the non-trivial cos
ets of a normal subgroup can influence the structure of a finite group.\n
\nHere is one example:\n\nLet $G$ be a finite group with a normal subgroup
$N$. 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 prime $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://researchseminars.org/talk/UEAPS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Philipp Wächter
DTSTART:20251111T140000Z
DTEND:20251111T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/62
DESCRIPTION:Title: E
quations in Wreath Products of Abelian Groups\nby Jan Philipp Wächter
as part of ANTLR seminar\n\nLecture held in NEWSCI 0.08.\n\nAbstract\nSol
ving equations is among the most classical and fundamental questions in\nM
athematics. Typically\, equations are solved over fields of numbers such a
s\nthe rational\, real or complex numbers. Solving equations over the ring
of\nintegers (Hilbert’s 10th problem) is famously known to be undecidab
le. If\,\ninstead of considering the two operations of addition and multip
lication of a\nring\, we restrict ourselves to a single one\, we very natu
rally arrive at the\nDiophantine problem over a group: given a system of/a
single equation(s)\ncontaining variables and constants (from the group)\,
can we decide whether we\nmay substitute the variables with some group el
ements such that the equation\nholds? In many groups this problem is gener
ally undecidable. However\, we can\nrestrict the question further and cons
ider only quadratic equations (where\nevery variable appears at most twice
\, counting positive and negative\ninstances).\nIn the talk\, we will disc
uss (ongoing) joint work with Ruiwen Dong and Leon\nPernak to solve quadra
tic equations in (restricted) wreath products of abelian\ngroups. The talk
will contain a short introduction on equations over groups\,\nthe lamplig
hter group and its generalization to wreath products of abelian\ngroups. T
hen we will look at the case of nonorientable equations over these\ngroups
.\n
LOCATION:https://researchseminars.org/talk/UEAPS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Mantova (University of Leeds)
DTSTART:20251118T140000Z
DTEND:20251118T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/63
DESCRIPTION:Title: C
omposition of transseries\, monotonicity\, and analyticity\nby Vincenz
o Mantova (University of Leeds) as part of ANTLR seminar\n\nLecture held i
n Queens 1.03.\n\nAbstract\nTransseries generalise power series by includi
ng exponential and logarithmic terms\, if not more\, and can be interprete
d as germs of a non-standard Hardy field by composition (for instance\, on
surreal numbers). I'll discuss a few results that must 'obviously' be tru
e\, yet their proofs are not obvious: that composition is monotonic in bot
h arguments\, once claimed but not proved by Edgar for LE-series\, that it
satisfies a suitable Taylor theorem and that in fact composition is 'anal
ytic with large radius of convergence' (joint with V. Bagayoko)\, somethin
g which appeared before in various special forms\, but not in full general
ity. I'll show how monotonicity and Taylor can be used to prove some fairl
y general normalisation results for hyperbolic transseries (joint with D.
Peran\, J.-P. Rolin\, T. Servi).\n
LOCATION:https://researchseminars.org/talk/UEAPS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie Roth (University of East Anglia)
DTSTART:20251125T140000Z
DTEND:20251125T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/64
DESCRIPTION:Title: O
n the unitriangularity of decomposition matrices of finite groups of Lie t
ype of exceptional type\nby Marie Roth (University of East Anglia) as
part of ANTLR seminar\n\nLecture held in SCI 0.31.\n\nAbstract\nDecomposit
ion matrices encode the link between ordinary and modular representations
of finite groups.\nIn 2020\, Brunat--Dudas--Taylor showed that the decompo
sition matrix of the unipotent $\\ell$-blocks of a finite group $G$ of Lie
type in good characteristic has unitriangular shape\, answering a conject
ure of Geck. Their theorem holds under some conditions on the prime $\\ell
$\, in particular when $\\ell$ is good. In this talk\, we will discuss how
to extend this result\, firstly to $\\ell$ bad (for any $G$ simple adjoin
t) and then to other blocks\, namely the isolated blocks (for $G$ simple a
djoint of type $G_2$\, $F_4$\, and $E_6$). This work was part of my PhD th
esis under the supervision of Gunter Malle and Olivier Dudas.\n
LOCATION:https://researchseminars.org/talk/UEAPS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gemma Crowe
DTSTART:20260217T140000Z
DTEND:20260217T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/65
DESCRIPTION:Title: T
he conjugacy problem in twisted right-angled Artin groups\nby Gemma Cr
owe as part of ANTLR seminar\n\n\nAbstract\nThere exists a vast literature
around the idea of constructing groups (and monoids) via some corresponde
nce with finite simple graphs. One well-known example is right-angled Arti
n groups (RAAGs)\, where edges in our graph correspond precisely to commut
ing generators in our group. \nIn this talk\, we will discuss an adaptatio
n of this group\, known as twisted RAAGs (T-RAAGs)\, where we introduce th
e option of ‘Klein-bottle’ relations\, which correspond to directed ed
ges of our graph. We will then survey some results about these groups (inc
luding many open questions!) and show T-RAAGs have decidable conjugacy pro
blem. This is based on joint work with Islam Foniqi.\n
LOCATION:https://researchseminars.org/talk/UEAPS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Norris (Queen Mary University of London)
DTSTART:20251209T140000Z
DTEND:20251209T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/66
DESCRIPTION:Title: O
n $p$-ordinary mod $p$ local Langlands correspondences.\nby Miriam Nor
ris (Queen Mary University of London) as part of ANTLR seminar\n\nLecture
held in NEWSCI 0.04.\n\nAbstract\nTo a suitably “nice” automorphic rep
resentation\, we can attach a $p$-adic representation of the absolute Galo
is group of a number field. We call a Galois representation arising in thi
s way automorphic. One of the goals of the Langlands programme is to class
ify the image of automorphic Galois representations within the set of all
Galois representations\, thereby establishing a correspondence.\n\nWhen $n
=2$ and the number field is $\\mathbb{Q}$\, such a correspondence has been
constructed by combining mod $p$ and $p$-adic correspondences with local
–global compatibility results. In particular\, the $p$-adic corresponden
ce is a representation of $GL_2(\\mathbb{Q}_p)$\, associated to a local Ga
lois representation\, which appears in the cohomology of the modular curve
.\n\nIn work of Breuil and Herzig\, a candidate for a more general corresp
ondence for $p$-ordinary local Galois representations was constructed. In
this talk I will discuss joint work with Shu Sasaki in which we construct
a framework that should generalise Breuil and Herzig's construction\, in p
articular allowing for the non-generic case.\n
LOCATION:https://researchseminars.org/talk/UEAPS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Islam Foniqi (University of East Anglia)
DTSTART:20251202T140000Z
DTEND:20251202T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/67
DESCRIPTION:Title: D
roms’ theorems for twisted right-angled Artin groups.\nby Islam Foni
qi (University of East Anglia) as part of ANTLR seminar\n\nLecture held in
LT 4.\n\nAbstract\nRight-angled Artin groups (RAAGs) form an important li
nk between combinatorics and group theory\, since the structure of the gro
up is determined by its defining graph. Twisted right-angled Artin groups
(T-RAAGs) generalize this idea by adding directed edges\, which allow us t
o encode both commutation and certain “twisted’’ relations. In this
talk\, based on joint work with Simone Blumer and Claudio Quadrelli\, we e
xplain how Droms’ classical theorems for RAAGs extend to this broader se
tting. We determine exactly which T-RAAGs have the property that all finit
ely generated subgroups are again T-RAAGs\, give a graph-theoretic criteri
on for coherence\, and solve the isomorphism problem for an important subc
lass.\n
LOCATION:https://researchseminars.org/talk/UEAPS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katie Reilly (UEA)
DTSTART:20260203T140000Z
DTEND:20260203T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/68
DESCRIPTION:Title: O
ne-Relator Inverse Monoids with Decidable Word Problem Are Algorithmically
Unclassifiable\nby Katie Reilly (UEA) as part of ANTLR seminar\n\nLec
ture held in EFRY 01.10.\n\nAbstract\nA classical result from Combinatoria
l Group Theory\, the Adian-Rabin Theorem\, states that there does not exis
t an algorithm which takes a finitely presented group G and decides whethe
r G possesses a given Markov property. An example of such a property is ha
ving decidable word problem. Consequently\, there is no algorithm that tak
es a finitely presented group and decides whether the group has decidable
word problem. On the other hand\, Magnus proved in the 1930s that every on
e-relator group has decidable word problem\, so in the one-relator case su
ch an algorithm (trivially) does exist.\n\nIn contrast\, in 2019\, Gray pr
oved that there exists a one-relator inverse monoid with undecidable word
problem. One key question arising from that work is whether it might be po
ssible to classify the one-relator inverse monoids with decidable word pro
blem. Related to this one can ask whether there is an algorithm that takes
a one-relator inverse monoid as input and decides whether or not that one
-relator inverse monoid has decidable word problem.\n\nIn this talk\, I wi
ll show that there does not exist an algorithm which takes a one-relator i
nverse monoid M as input and decides whether M has decidable word problem.
In other words\, the one-relator inverse monoids with decidable word prob
lem are algorithmically unclassifiable.\n
LOCATION:https://researchseminars.org/talk/UEAPS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Kirby (UEA)
DTSTART:20260210T140000Z
DTEND:20260210T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/69
DESCRIPTION:Title: G
alois groups\, differential equations\, and special functions\nby Jona
than Kirby (UEA) as part of ANTLR seminar\n\nLecture held in NewSci 0.05.\
n\nAbstract\nI will outline a path through Galois groups\, differential Ga
lois groups\, and transcendence of functions to some new applications to o
ld functions\, including the non-integrability in finite terms of Lambert
’s W function\, algebraic independence of solutions of Kepler’s equati
on of 1607\, and exponential-algebraic independence of Bessel functions. A
ll these terms will be explained so no prior knowledge is required!\n\n \n
\nThis is joint work with Rémi Jaoui\n
LOCATION:https://researchseminars.org/talk/UEAPS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Broomhead (Plymouth)
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/70
DESCRIPTION:Title: C
onvex geometry for fans of triangulated categories\nby Nathan Broomhea
d (Plymouth) as part of ANTLR seminar\n\nLecture held in EFRY 01.02.\n\nAb
stract\nFans and other convex-geometric objects have recently appeared in
homological algebra in several related contexts. For example\, as g-fans i
n the silting theory of finite-dimensional algebras and as scattering diag
rams in Bridgeland stability theory. I will discuss joint work with David
Pauksztello\, David Ploog and Jon Woolf on a general construction which we
hope will provide a natural and unifying framework.\n\nStarting with a tr
iangulated category D and a finite rank quotient lattice L of its Grothend
ieck group\, we show that each heart H in D determines a closed convex `he
art cone' in the dual vector space V=Hom(L\,R). The heart cones of H and a
ll its forward tilts form a `heart fan' in V. If H is `algebraic'\, i.e. i
s a length category with finitely many simple objects\, then the heart con
e is simplicial and the heart fan is complete.\n
LOCATION:https://researchseminars.org/talk/UEAPS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Nichols (UEA)
DTSTART:20260303T140000Z
DTEND:20260303T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/71
DESCRIPTION:Title: F
ree Shelves: Connecting Representations of Braid Groups and Forcing over M
odels with Reinhardt Embeddings\nby Eric Nichols (UEA) as part of ANTL
R seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nSet Theory often seems
very disconnected from other pure math topics like Algebra and Representa
tion Theory. However\, if we look closer we can often find deep connection
s between these fields. In this talk we explore the connection between I3
embeddings\, representations of Braid Groups\, and set theoretic forcing b
y searching for examples of a free Shelf (or Left Distributive Magma). Hig
hlighting how shelves arise out of I3 embeddings and out of algebra\, show
ing that I3 embeddings provide examples of free shelves\, and the necessit
y of these free shelves for forcing over models with Reinhardt embeddings.
\n\nThis talk will not go into formal detail on the involved set theory\,
instead focusing on pictorial motivations and general concepts. As a resul
t this talk should be accessible to all!\n
LOCATION:https://researchseminars.org/talk/UEAPS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny Roberts (KCL)
DTSTART:20260310T140000Z
DTEND:20260310T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/72
DESCRIPTION:Title: N
ewform Eisenstein congruences of local origin\nby Jenny Roberts (KCL)
as part of ANTLR seminar\n\nLecture held in QUEENS 01.09.\n\nAbstract\nThe
theory of Eisenstein congruences dates back to Ramanujan’s surprising d
iscovery that the Fourier coefficients of the discriminant function are co
ngruent 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}. Eisenstei
n congruences were later used by Ribet in his proof of the converse to Her
brand's theorem. In this talk\, I will first discuss the steps Ribet used
in his proof and then compare these steps to work in my thesis on congruen
ces between Eisenstein series and newforms of weight k > 2\, squarefree le
vel and non-trivial character.\n
LOCATION:https://researchseminars.org/talk/UEAPS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcus Tressl (The University of Manchester)
DTSTART:20260317T140000Z
DTEND:20260317T150000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/73
DESCRIPTION:Title: E
very join-semilattice with smallest element is isomorphic to the semilatti
ce of compact open sets of some space.\nby Marcus Tressl (The Universi
ty of Manchester) as part of ANTLR seminar\n\nLecture held in EFRY 1.01.\n
\nAbstract\nThe assertion belongs to the representation theory of partiall
y ordered sets\, to Non-Hausdorff topology and to domain theory\, but is
(co-)motivated by algebraic questions about the analysis of structures th
at can be seen as global sections of a sheaf (like a ring or like a genera
lized product). I will first explain my interest in the statement of the t
itle and then construct the asserted space in a functorial way.\n
LOCATION:https://researchseminars.org/talk/UEAPS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Parente
DTSTART:20260223T160000Z
DTEND:20260223T170000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/74
DESCRIPTION:by Francesco Parente as part of ANTLR seminar\n\nAbstract: TBA
\n
LOCATION:https://researchseminars.org/talk/UEAPS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Solomon (Institut de Mathematiques de Jussieu\, Paris)
DTSTART:20260421T130000Z
DTEND:20260421T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/75
DESCRIPTION:Title: H
eisenberg SICs\, Stark Units and Weil Representations\nby David Solomo
n (Institut de Mathematiques de Jussieu\, Paris) as part of ANTLR seminar\
n\n\nAbstract\nSICs\, also known as equiangular tight frames\, are configu
rations of d² equiangular lines in ℂᵈ whose applications in signal pr
ocessing and quantum physics have been known and studied for more than 30
years. More recently\, numerical investigations of so-called Heisenberg SI
Cs (which have an action of 𝓗(ℤ/dℤ) via its Schrödinger representa
tion) have revealed surprising\, heuristic connections with conjectural 'S
tark units' and hence with Hilbert's 12th Problem over real-quadratic fiel
ds.\n\nJust as intriguingly\, the action of Galois on these units seems to
be connected to the action of SL₂(ℤ/dℤ) on the set of Heisenberg SI
Cs via its d-dimensional Weil representation as a subgroup of the automorp
hism group of 𝓗(ℤ/dℤ).\n\nIn my talk\, I will first give an overvie
w of recent SIC-related research\, as well as the Stark Conjectures (which
date from the 1970s but are still largely unproven). I will explain the e
xperimental evidence connecting SICs with Stark-Units over the field ℚ(
√(d − 1)(d + 3)). On a more specialised note and as time permits\, I w
ill outline my recent work on the lifted Weil representation in the case d
= pⁿ and possible connections to a p-adic theory of SICs.\n
LOCATION:https://researchseminars.org/talk/UEAPS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Kirby (University of East Anglia)
DTSTART:20260428T130000Z
DTEND:20260428T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/76
DESCRIPTION:Title: G
alois groups\, differential equations\, and special functions\nby Jona
than Kirby (University of East Anglia) as part of ANTLR seminar\n\n\nAbstr
act\nI will outline a path through Galois groups\, differential Galois gro
ups\, and transcendence of functions to some new applications to old funct
ions\, including the non-integrability in finite terms of Lambert's W func
tion\, algebraic independence of solutions of Kepler's equation of 1607\,
and exponential-algebraic independence of Bessel functions. All these term
s will be explained so no prior knowledge is required!\n\nThis is joint wo
rk with Rémi Jaoui.\n
LOCATION:https://researchseminars.org/talk/UEAPS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Mackaay (Universidade do Algarve)
DTSTART:20260505T130000Z
DTEND:20260505T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/77
DESCRIPTION:by Marco Mackaay (Universidade do Algarve) as part of ANTLR se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Beard (Carnegie Mellon)
DTSTART:20260601T130000Z
DTEND:20260601T140000Z
DTSTAMP:20260421T122040Z
UID:UEAPS/78
DESCRIPTION:by Jeremy Beard (Carnegie Mellon) as part of ANTLR seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/UEAPS/78/
END:VEVENT
END:VCALENDAR