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SUMMARY:Andrew Brooke-Taylor (University of Leeds)
DTSTART;VALUE=DATE-TIME:20230207T140000Z
DTEND;VALUE=DATE-TIME:20230207T150000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/1
DESCRIPTION:Title: Co
mplexity of classification problems\nby Andrew Brooke-Taylor (Universi
ty of Leeds) as part of UEA pure maths seminar\n\nLecture held in EFRY 01.
05.\n\nAbstract\nThe notion of "Borel reducibility" gives a framework that
allows us to compare the complexities of different classes of mathematica
l objects. I will give an introduction to this framework\, including how
it has been used to show that a number of proposed classification programm
es in different areas of mathematics were impossible to realise. I'll the
n talk about using the framework to explain why the knot invariants called
"quandles" are often considered to be too hard to work with (joint work w
ith Sheila Miller)\, and finish with a discussion of what happens when the
framework is extended to capture functoriality (joint work with Filippo C
alderoni).\n
LOCATION:https://researchseminars.org/talk/UEAPS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fiona Torzewska (UEA)
DTSTART;VALUE=DATE-TIME:20230217T120000Z
DTEND;VALUE=DATE-TIME:20230217T130000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/2
DESCRIPTION:Title: Cl
assification of charge-conserving loop braid representations\nby Fiona
Torzewska (UEA) as part of UEA pure maths seminar\n\nLecture held in SCI
1.20.\n\nAbstract\nThe loop braid category is the diagonal category made u
p of loop braid groups $LB_n$\, exactly paralleling the relationship betw
een MacLane's braid category and the Artin braid groups. A loop braid repr
esentation is a monoidal functor from the loop braid category $\\mathsf{L}
$ to a suitable target category\, and is $N$-charge-conserving if that tar
get is the category $\\mathrm{Match}^N$ of charge-conserving matrices.\nIn
this talk I will discuss the classification and construction of all such
representations. (These representations fall into varieties indexed by a s
et in bijection with the set of pairs of plane partitions of total degree
$N$.)\n
LOCATION:https://researchseminars.org/talk/UEAPS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamilla Rekvenyi (Imperial)
DTSTART;VALUE=DATE-TIME:20230314T140000Z
DTEND;VALUE=DATE-TIME:20230314T150000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/4
DESCRIPTION:Title: Th
e Orbital Diameter of Primitive Permutation Groups\nby Kamilla Rekveny
i (Imperial) as part of UEA pure maths seminar\n\nLecture held in NEWSCI 0
.06.\n\nAbstract\nLet G be a group acting transitively on a finite set Ω.
Then G acts on ΩxΩ component wise. Define the orbitals to be the orbits
of G on ΩxΩ. The diagonal orbital is the orbital of the form ∆ = {(α
\, α)|α ∈ Ω}. The others are called non-diagonal orbitals. Let Γ be
a non-diagonal orbital. Define an orbital graph to be the non-directed gr
aph with vertex set Ω and edge set (α\,β)∈ Γ with α\,β∈ Ω. If t
he action of G on Ω is primitive\, then all non-diagonal orbital graphs a
re connected. The orbital diameter of a primitive permutation group is the
supremum of the diameters of its non-diagonal orbital graphs.\n\nThere ha
s been a lot of interest in finding bounds on the orbital diameter of prim
itive permutation groups. In my talk I will outline some important backgro
und information and the progress made towards finding explicit bounds on t
he orbital diameter. In particular\, I will discuss some results on the or
bital diameter of the groups of simple diagonal type and their connection
to the covering number of finite simple groups. I will also discuss some r
esults for affine groups\, which provides a nice connection to the represe
ntation theory of quasisimple groups.\n
LOCATION:https://researchseminars.org/talk/UEAPS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Martin (Earlham Institute)
DTSTART;VALUE=DATE-TIME:20230502T130000Z
DTEND;VALUE=DATE-TIME:20230502T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/6
DESCRIPTION:Title: Di
mensions of phylogenetic network varieties\nby Samuel Martin (Earlham
Institute) as part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\
n\nAbstract\nPhylogenetic networks provide a means of describing the evolu
tionary history of taxa that have undergone “horizontal” events\, such
as hybridization or lateral gene transfer. The mutation process of a sing
le site in shared DNA sequence for a set of such taxa can be modelled as a
Markov process on a phylogenetic network\, and the site-pattern probabili
ty distributions from such a model can be viewed as a projective variety.
In this work\, we have given an explicit description of the dimension of t
his variety for a given level-1 phylogenetic network under any group-based
model of evolution. I will give an overview of the model from an algebrai
c perspective and describe our results\, focussing on the toric fiber prod
uct of two ideals\, and finish with some applications to identifiability p
roblems. Joint work with Elizabeth Gross and Robert Krone.\n
LOCATION:https://researchseminars.org/talk/UEAPS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Trias (Imperial)
DTSTART;VALUE=DATE-TIME:20230516T130000Z
DTEND;VALUE=DATE-TIME:20230516T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/7
DESCRIPTION:Title: To
wards a theta correspondence in families for type II dual pairs\nby Ju
stin Trias (Imperial) as part of UEA pure maths seminar\n\nLecture held in
QUEENS 1.03.\n\nAbstract\nThe classical local theta correspondence for p-
adic reductive dual pairs defines a bijection between prescribed subsets o
f irreducible smooth complex representations coming from two groups (H\,H'
)\, forming a dual pair in a symplectic group. Alberto Mínguez extended t
his result for type II dual pairs\, i.e. when (H\,H') is made of general l
inear groups\, to representations with coefficients in an algebraically cl
osed field of characteristic l as long as the characteristic l does not di
vide the pro-orders of H and H'. For coefficients rings like Z[1/p]\, we e
xplain how to build a theory in families for type II dual pairs that is co
mpatible with reduction to residue fields of the base coefficient ring\, w
here central to this approach is the integral Bernstein centre. We transla
te some weaker properties of the classical correspondence\, such as compat
ibility with supercuspidal support\, as a morphism between the integral Be
rnstein centres of H and H' and interpret it for the Weil representation.
In general\, we only know that this morphism is finite though we may expec
t it to be surjective. This would result in a closed immersion between the
associated affine schemes as well as a correspondence between characters
of the Bernstein centre. This is current work with Gil Moss.\n
LOCATION:https://researchseminars.org/talk/UEAPS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Saha (Queen Mary University of London)
DTSTART;VALUE=DATE-TIME:20230523T130000Z
DTEND;VALUE=DATE-TIME:20230523T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/8
DESCRIPTION:Title: Th
e Manin constant\, the modular degree\, and Fourier expansions at cusps\nby Abhishek Saha (Queen Mary University of London) as part of UEA pure
maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nLet f be a normali
zed newform of weight k for $\\Gamma_0(N)$. It is a natural question to tr
y to understand the size (in a $p$-adic sense) of the "denominators" of th
e Fourier expansions of f at a cusp of $X_0(N)$. The problem is easy if N
is square-free but is delicate when N is highly square-full. I will talk a
bout recent joint work with Kȩstutis Česnavičius and Michael Neururer w
here we solve this problem using representation-theoretic techniques. Roug
hly speaking\, we reduce the problem to bounding $p-$adic valuations of lo
cal Whittaker newforms and then use a "basic identity" (a consequence of t
he Jacquet-Langlands local functional equation) to reduce to $p$-adic prop
erties of local epsilon factors of representations of $\\GL_2(\\Q_p)$. \n
\nA key application of our result is to understand the Manin constant c of
an elliptic curve E over the rationals. The integer c scales the differen
tial determined by the normalized newform f associated to E into the pullb
ack of a N\\'{e}ron differential under a minimal modular parametrization.
Manin conjectured that c equals 1 or -1 for optimal parametrizations. We p
rove that c divides the degree of the parametrization under a minor assump
tion at the primes 2 and 3. For this result\, we establish a certain integ
rality property of $\\omega_f$ that follows from the Manin conjecture. We
expect that this integrability property we prove here will be necessary fo
r any further progress towards Manin's conjecture.\n
LOCATION:https://researchseminars.org/talk/UEAPS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanneke Wiersema (Cambridge)
DTSTART;VALUE=DATE-TIME:20230425T130000Z
DTEND;VALUE=DATE-TIME:20230425T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/10
DESCRIPTION:Title: M
odularity in the partial weight one case\nby Hanneke Wiersema (Cambrid
ge) as part of UEA pure maths seminar\n\nLecture held in SCI 3.05.\n\nAbst
ract\nThe strong form of Serre's conjecture states that a two-dimensional
mod p representation of the absolute Galois group of $\\mathbb{Q}$ arises
from a modular form of a specific weight\, level and character. Serre rest
ricted to modular forms of weight at least 2\, but Edixhoven later refined
this conjecture to include weight one modular forms. In this talk we expl
ore analogues of Edixhoven's refinement for Galois representations of tota
lly real fields\, extending recent work of Diamond and Sasaki. In particul
ar\, we show how modularity of partial weight one Hilbert modular forms ca
n be related to modularity of Hilbert modular forms with regular weights\,
and vice versa. We will also discuss the applications of this for p-adic
Hodge theory.\n
LOCATION:https://researchseminars.org/talk/UEAPS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (UEA)
DTSTART;VALUE=DATE-TIME:20230509T130000Z
DTEND;VALUE=DATE-TIME:20230509T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/12
DESCRIPTION:Title: S
copes equivalence for blocks of Ariki-Koike algebras\nby Alice Dell'Ar
ciprete (UEA) as part of UEA pure maths seminar\n\nLecture held in NEWSCI
0.06.\n\nAbstract\nWe consider representations of the Ariki-Koike algebra\
, a $q$-deformation of the group algebra of the complex reflection group $
C_r\\wr\\mathfrak{S}_n$. The representations of this algebra are naturally
indexed by multipartitions of $n$. We examine blocks of the Ariki-Koike a
lgebra\, in an attempt to generalise the combinatorial representation theo
ry of the Iwahori-Hecke algebra. In particular\, we prove a sufficient con
dition such that restriction of modules leads to a natural correspondence
between the multipartitions of $n$ whose Specht modules belong to a block
$B$ and those of $n−\\delta_i(B)$ whose Specht modules belong to the blo
ck $B'$\, obtained from $B$ applying a Scopes' equivalence. This gives us
an equality of decomposition numbers for the corresponding Ariki-Koike alg
ebras.\n
LOCATION:https://researchseminars.org/talk/UEAPS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nutt Tananimit (UEA)
DTSTART;VALUE=DATE-TIME:20230530T130000Z
DTEND;VALUE=DATE-TIME:20230530T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/13
DESCRIPTION:Title: C
onsistent and Inconsistent Generalizations of Martin's Axiom and Weak Squa
re\nby Nutt Tananimit (UEA) as part of UEA pure maths seminar\n\nLectu
re held in SCI 3.05.\n\nAbstract\nWe prove that the forcing axiom $\\texts
f{MA}^{1.5}_{\\aleph_2}(\\text{stratified})$ implies $\\square_{\\omega_1\
, \\omega_1}$. \nUsing this implication\, we show that the forcing axiom $
\\textsf{MM}_{\\aleph_2}(\\aleph_2\\text{-c.c.})$ is inconsistent.\n
LOCATION:https://researchseminars.org/talk/UEAPS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Ardakov (Oxford)
DTSTART;VALUE=DATE-TIME:20230328T130000Z
DTEND;VALUE=DATE-TIME:20230328T140000Z
DTSTAMP;VALUE=DATE-TIME:20230529T050322Z
UID:UEAPS/14
DESCRIPTION:Title: T
he central sheaf of the category of smooth mod-$p$ representations of $SL_
2(\\mathbb{Q}_p)$\nby Konstantin Ardakov (Oxford) as part of UEA pure
maths seminar\n\nLecture held in SCI 3.05.\n\nAbstract\nThis is work in pr
ogress with Peter Schneider. The Bernstein centre of a $p$-adic reductive
group plays a fundamental role in the classical local Langlands correspond
ence. In the mod-p local Langlands program\, the naive analogue of the Ber
nstein centre\, namely the centre of the category $Mod(G)$ of all smooth m
od-$p$ representations\, turns out to be too small: it is for example triv
ial whenever the group in question has trivial centre. Instead\, we consid
er the centres $Z(Mod(G)/\\mathcal{L})$ of the quotient categories $Mod(G)
/\\mathcal{L}$\, as $\\mathcal{L}$ runs over all localizing subcategories
of $Mod(G)$. We show that provided one restricts to the localizing subcate
gories that are $stable$ $under$ $injective$ $envelopes$\, this defines a
sheaf with respect to finite coverings. In the case where $G = SL_2(\\math
bb{Q}_p)$ and $p \\neq 2\,3$\, we use recent results by Ollivier and Schne
ider on the structure of the pro-$p$ Iwahori $Ext$-algebra to construct a
certain projective variety $X$ having the property that every Zariski open
subset $U$ of $X$ gives rise to a stable localizing subcategory $\\mathca
l{L}_U$ of $Mod(G)$. Both connected components of $X$ are certain chains o
f projective lines\, and $X$ and is closely related to the recent work of
Dotto\, Emerton and Gee.\n
LOCATION:https://researchseminars.org/talk/UEAPS/14/
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