BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Carlo Pagano (University of Glasgow)
DTSTART:20201014T150000Z
DTEND:20201014T160000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/1
DESCRIPTION:Title: Recent developments on the 2-infinity parts of class grou
ps and related problems\nby Carlo Pagano (University of Glasgow) as pa
rt of Algebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nIn this t
alk I will review some of the recent progress on the Cohen--Lenstra--Gerth
conjectures and related problems.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (University of Glasgow)
DTSTART:20201021T150000Z
DTEND:20201021T160000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/2
DESCRIPTION:Title: On derived equivalence for a 7-dimensional flop associate
d to G_2 Grassmannians\nby Wahei Hara (University of Glasgow) as part
of Algebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nWe discuss a
7-dimensional flop that comes from the geometry of G_2 homogeneous variet
ies. We construct tilting bundles on both sides of the flop\, and show der
ived equivalence for the flop using those tilting bundles.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Cameron (University of St. Andrews)
DTSTART:20201028T160000Z
DTEND:20201028T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/3
DESCRIPTION:Title: The geometry of diagonal groups\nby Peter Cameron (Un
iversity of St. Andrews) as part of Algebra and Number Theory Seminar\, Gl
asgow\n\n\nAbstract\nDiagonal groups form one of the classes of groups in
the celebrated O'Nan--Scott theorem which underpins the application of fin
ite simple groups to permutation group theory. But they form a much wider
class. A diagonal group is built from a dimension and an arbitrary group\,
not necessarily simple or even finite. We construct and characterise a ge
ometric object whose automorphism group is the diagonal group if the dimen
sion is at least 3. In dimension 2 these objects are equivalent to Latin s
quares and exist in great profusion\, but in higher dimension the group em
erges naturally from the combinatorial axioms. The work links group theory
\, combinatorics and statistics.\n\n(joint work with Rosemary Bailey\, Che
ryl Praeger and Csaba Schneider)\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khrystyna Serhiyenko (University of Kentucky)
DTSTART:20201104T160000Z
DTEND:20201104T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/4
DESCRIPTION:Title: Geometric model for syzygies over certain 2-Calabi-Yau ti
lted algebras\nby Khrystyna Serhiyenko (University of Kentucky) as par
t of Algebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nA module i
s said to be a syzygy if it is a submodule of a projective. In the case o
f 2-Calabi-Yau (2-CY) tilted algebras the non-projective syzygies form a t
riangulated 3-CY category. In this setting\, the category of syzygies is
equivalent to the category of Cohen-Macauley modules and also the singular
ity category of the algebra. We find a geometric model for this category
for a particular type of 2-CY tilted algebras given by quivers with relati
ons. More precisely\, we construct a decorated polygon with a checkerboar
d pattern whose 2-diagonals correspond to syzygies. Moreover\, other asp
ects of the syzygy category such as morphisms\, extensions\, Auslander-Rei
ten triangles\, and the shift also have a geometric interpretation in this
polygon. This is joint work with Ralf Schiffler.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Tracey (Oxford University)
DTSTART:20201111T160000Z
DTEND:20201111T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/5
DESCRIPTION:Title: On the expected number of random primes required to gener
ate a Galois group\nby Gareth Tracey (Oxford University) as part of Al
gebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nGiven a finite gr
oup $X$\, a classical approach to proving that $X$ is the Galois group of
a Galois extension $K/\\mathbb{Q}$ can be described roughly as follows: (1
) prove that $\\Gal(K/\\mathbb{Q})$ is contained in $X$ by using known pro
perties of the extension (for example\, the Galois group of an irreducible
polynomial $f(x)\\in\\mathbb{Z}[x]$ of degree $n$ embeds into the symmetr
ic group $\\Sym(n)$)\; (2) try to prove that $X = \\Gal(K/\\mathbb{Q})$ by
computing the Frobenius automorphisms modulo successive primes\, which gi
ves conjugacy classes in $\\Gal(K/\\mathbb{Q})$\, and hence in $X$. If the
se conjugacy classes can only occur in the case $\\Gal(K/\\mathbb{Q})=X$\,
then we are done.\n\nAlthough better algorithms exist in practice\, this
approach has led to some recent breakthroughs in the problem of finding a
Galois extension of number fields with a given Galois group. In this talk
we will describe some of these new results\, and the link to a new and rap
idly developing area of finite group theory.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Paterson (University of Glasgow)
DTSTART:20201118T160000Z
DTEND:20201118T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/6
DESCRIPTION:Title: 2-Selmer Groups of Twists after Quadratic Extension\n
by Ross Paterson (University of Glasgow) as part of Algebra and Number The
ory Seminar\, Glasgow\n\n\nAbstract\nAs E varies in a natural family of el
liptic curves over the rational numbers\, the average size of the 2-Selmer
group of E has been well studied\, e.g. in the work of Heath-Brown\, Swin
nerton-Dyer\, Kane\, Poonen--Rains\, Bhargava--Shankar and many others. If
we fix a Galois number field K\, and look instead at the 2-Selmer group o
f such curves over K\, then the size is no longer the only interesting str
ucture at hand\; in fact the 2-Selmer group over K has a natural action of
the Galois group of K. It is then natural to ask the more refined questio
n: what are the statistical properties of this Galois module?\n\nI will re
port on joint work with Adam Morgan\, in which we consider this question i
n the case that K is a quadratic field and E varies over quadratic twists
of a fixed curve\, and give some interesting corollaries for the Mordell-W
eil groups as a result.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fairon (University of Glasgow)
DTSTART:20201125T160000Z
DTEND:20201125T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/7
DESCRIPTION:Title: Double (quasi-)Poisson algebras and their morphisms\n
by Maxime Fairon (University of Glasgow) as part of Algebra and Number The
ory Seminar\, Glasgow\n\n\nAbstract\nThe talk will begin with a review of
the notion of double (quasi-)Poisson algebras\, which were introduced by V
an den Bergh as noncommutative analogues of (quasi-)Poisson algebras. I wi
ll then explain how their morphisms can be used to understand morphisms of
associated Poisson varieties. As an application\, I will describe how the
double (quasi-)Poisson algebra associated to an arbitrary quiver by Van d
en Bergh does not depend on the orientation of the quiver\, up to isomorph
ism. We will see that this produces many Poisson isomorphisms between (mul
tiplicative) quiver varieties. This is partly based on arXiv:2008.01409.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Man-Wai\, Mandy\, Cheung (Harvard University)
DTSTART:20201202T160000Z
DTEND:20201202T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/8
DESCRIPTION:Title: Tropical disks counting\, stability conditions in symplec
tic geometry and quiver representations\nby Man-Wai\, Mandy\, Cheung (
Harvard University) as part of Algebra and Number Theory Seminar\, Glasgow
\n\n\nAbstract\nBridgeland developed stability scattering diagrams relatin
g scattering diagrams with quiver representations. Scattering diagrams wer
e developed as a machinery in mirror symmetry. Together with Travis Mandel
\, we associate tropical disks counting with quiver representations by usi
ng the stability scattering diagrams.\nNext\, together with Yu-Wei Fan and
Yu-Shen Lin\, we look at the stable objects for the A2 quiver. It is know
n that the derived Fukaya-Seidel category of the rational elliptic surface
is the derived category of the A2 quiver. We made use of the relation and
corresponded the special Lagrangian with the stable objects in the derive
d category of coherent sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Soulié (University of Glasgow)
DTSTART:20201209T160000Z
DTEND:20201209T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/9
DESCRIPTION:Title: Homological representations of families of groups\nby
Arthur Soulié (University of Glasgow) as part of Algebra and Number Theo
ry Seminar\, Glasgow\n\n\nAbstract\nMany families of groups\, such as brai
d groups\, have a representation theory of wild type\, in the sense that t
here is no known classification schema to organize the representations. Ho
wever\, using actions on the homology groups of the coverings of some asso
ciated spaces\, there are systematic procedures to construct linear repres
entations for such families of groups\, which help to understand their rep
resentation theory.\nI will present a unified functorial construction of h
omological representations for these families of groups. This general meth
od is particularly suitable to generate new families of representations of
motion groups such as braid groups on surfaces or loop braid groups. For
instance\, this construction provides the family of Lawrence-Bigelow repre
sentations for braid groups. We will also discuss irreducibility results f
or the obtained representations. Finally\, general notions of polynomialit
y on functors are a useful tool to classify these representations and allo
w to prove some twisted homological stability results: polynomiality resul
ts can be proved for some of the homological representations\, in particul
ar the Lawrence-Bigelow representations.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Wilsch (IST Austria)
DTSTART:20201216T160000Z
DTEND:20201216T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/10
DESCRIPTION:Title: Equidistribution and freeness on Grassmanians\nby Fl
orian Wilsch (IST Austria) as part of Algebra and Number Theory Seminar\,
Glasgow\n\n\nAbstract\nWe associate a tangent lattice to a primitive integ
er lattice and study its typical shape. This is motivated by Peyre’s pro
gram on the freeness of rational points on Fano varieties: A primitive int
eger lattice can be regarded a point on a Grassmanian\, and the shape of i
ts tangent lattice determines this point’s freeness.\nThe reason behind
this interest in freeness is Manin’s conjecture about the number of rati
onal points of bounded height on Fano varieties: This number might be domi
nated by “bad” points on subvarieties\, or more generally\, a thin set
of “bad“ points that has to be excluded in the count. Peyre proposed
to exclude points of low freeness\, so that points of high freeness should
conform to the asymptotic formula proposed by Manin’s conjecture and it
s variants. Our analysis verifies this for Grassmanians by proving that th
ere are relatively few points of low freeness.\nThis is joint work with Ti
m Browning and Tal Horesh.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dinakar Muthiah (University of Glasgow)
DTSTART:20210224T160000Z
DTEND:20210224T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/11
DESCRIPTION:Title: Affine Lusztig-Kato formula\nby Dinakar Muthiah (Uni
versity of Glasgow) as part of Algebra and Number Theory Seminar\, Glasgow
\n\n\nAbstract\nThe Lusztig-Kato formula is an important precursor to the
geometric Satake correspondence. Recent constructions point to geometric S
atake for affine and general Kac-Moody groups. This leads to a conjectural
Lusztig-Kato formula. I will review this and discuss work in progress wit
h H. Nakajima\, which implies the formula in affine type A.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Fanelli (University of Bordeaux)
DTSTART:20210217T160000Z
DTEND:20210217T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/12
DESCRIPTION:Title: Del Pezzo fibrations in positive characteristic\nby
Andrea Fanelli (University of Bordeaux) as part of Algebra and Number Theo
ry Seminar\, Glasgow\n\n\nAbstract\nIn this talk\, I will discuss some pat
hologies for the generic fibre of del Pezzo fibrations in characteristic
p>0\, motivated by the recent developments of the MMP in positive charact
eristic. The recent joint work with Stefan Schröer applies to deduce info
rmation on the structure of 3-dimensional Mori fibre spaces and answers an
old question by János Kollár.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Bartel (University of Glasgow)
DTSTART:20210324T160000Z
DTEND:20210324T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/13
DESCRIPTION:Title: Statistics for ray class groups of number fields\nby
Alex Bartel (University of Glasgow) as part of Algebra and Number Theory
Seminar\, Glasgow\n\n\nAbstract\nThe Cohen--Lenstra heuristics are a proba
bilistic model for\nclass groups of quadratic number fields. I will report
on joint work\nwith Carlo Pagano\, in which we generalise these heuristic
s to ray class\ngroups. A central role in our heuristics is played by so-c
alled Arakelov\nray class groups. Apart from demonstrating their utility f
or our\nimmediate purpose\, I will advertise their beauty by re-interpreti
ng a\nclassical construction that attaches closed geodesics on the quotien
t of\nthe hyperbolic upper half plane by SL(2\,Z) to (narrow) ideal classe
s of\nreal quadratic fields. Only minimal number theoretic background will
be\nassumed.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Koymans (Max Planck Institute for Mathematics)
DTSTART:20210120T160000Z
DTEND:20210120T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/14
DESCRIPTION:Title: Arithmetic statistics in the $n = p$ case\nby Peter
Koymans (Max Planck Institute for Mathematics) as part of Algebra and Numb
er Theory Seminar\, Glasgow\n\n\nAbstract\nArithmetic statistics concerns
the study of arithmetic objects in families\, and has recently attracted s
ubstantial attention. In this talk we will give an overview of the so-call
ed $n = p$ case and discuss the most important results in this area. Parts
of this talk are joint work with Stephanie Chan\, Djordjo Milovic and Car
lo Pagano.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Brown (University of Glasgow)
DTSTART:20210317T160000Z
DTEND:20210317T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/15
DESCRIPTION:Title: Connected Hopf algebras\nby Ken Brown (University of
Glasgow) as part of Algebra and Number Theory Seminar\, Glasgow\n\n\nAbst
ract\nI will give a survey of some results on infinite dimensional connect
ed Hopf algebras obtained by myself and others over the last decade. I wil
l aim to make it comprehensible by those with no previous knowledge of Hop
f algebras.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel El-Baz (TU Graz)
DTSTART:20210203T160000Z
DTEND:20210203T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/16
DESCRIPTION:Title: Local statistics: dynamics\, number theory and universal
ity\nby Daniel El-Baz (TU Graz) as part of Algebra and Number Theory S
eminar\, Glasgow\n\n\nAbstract\nLocal statistics are a way to go beyond eq
uidistribution in measuring the 'randomness' of a sequence. Those sequence
s can come from a wide range of sources --- from quantum mechanics to numb
er theory --- but there appear to be few laws governing their local statis
tics.\n\nWe will explore those universality phenomena and discuss the meth
ods that go into proving some of those results\, using ergodic theory and
analytic number theory.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Rome (University of Michigan)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/17
DESCRIPTION:Title: Counting Quadratic Points on Surfaces\nby Nick Rome
(University of Michigan) as part of Algebra and Number Theory Seminar\, Gl
asgow\n\n\nAbstract\nWe will discuss Manin's conjecture on rational points
of bounded height on algebraic varieties. In particular\, we will show ho
w the recent counterexamples of Le Rudulier can be extended by counting qu
adratic points on certain del Pezzo surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Chlouveraki (Laboratoire de Mathématiques de Versailles)
DTSTART:20210310T160000Z
DTEND:20210310T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/18
DESCRIPTION:Title: On the reality of complex reflection groups (and their a
ssociated Hecke algebras)\nby Maria Chlouveraki (Laboratoire de Mathé
matiques de Versailles) as part of Algebra and Number Theory Seminar\, Gla
sgow\n\n\nAbstract\nIwahori-Hecke algebras associated to Weyl groups appea
r naturally as endomorphism algebras in the representation theory of finit
e reductive groups. Weyl groups are real reflection groups\, which in turn
are particular cases of complex reflection groups. Hecke algebras associa
ted to complex reflection groups were introduced by Broué\, Malle and Rou
quier 20 years ago\, but many of the properties of real Hecke algebras wer
e simply conjectured in the complex case. In this talk\, we are going to d
iscuss the most fundamental of these conjectures\, their state of art and
our contributions to it.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teräväinen (University of Oxford)
DTSTART:20210303T160000Z
DTEND:20210303T170000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/19
DESCRIPTION:Title: On the Liouville function at polynomial arguments\nb
y Joni Teräväinen (University of Oxford) as part of Algebra and Number T
heory Seminar\, Glasgow\n\n\nAbstract\nLet $\\lambda$ be the Liouville fun
ction and $P(x)$ any polynomial that is not a square. An open problem form
ulated by Chowla and others asks to show that the sequence $\\lambda(P(n))
$ changes sign infinitely often. We present a solution to this problem for
new classes of polynomials $P$\, including any product of linear factors
or any product of quadratic factors of a certain type. The proofs also est
ablish some nontrivial cancellation in Chowla and Elliott type correlation
averages.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck
DTSTART:20210602T150000Z
DTEND:20210602T160000Z
DTSTAMP:20260404T111446Z
UID:algebra_14_134725/20
DESCRIPTION:Title: A surface and a threefold with equivalent singularity ca
tegories\nby Martin Kalck as part of Algebra and Number Theory Seminar
\, Glasgow\n\n\nAbstract\nWe start with an introduction to singularity cat
egories and equivalences between them.\n In particular\, we
recall known results about singular equivalences between commutative rings
\, which go back\n to Knörrer\, Yang\, Kawamata and a joint
work with Karmazyn. Then we explain a new singular equivalence\n
between an affine surface and an affine threefold. This seems to be
the first (non-trivial) example of a singular equivalence involving\n
rings of even and odd Krull dimension.\n
LOCATION:https://stable.researchseminars.org/talk/algebra_14_134725/20/
END:VEVENT
END:VCALENDAR