BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Carlo Pagano (University of Glasgow) DTSTART:20201014T150000Z DTEND:20201014T160000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/1 DESCRIPTION:Title: Recent developments on the 2-infinity parts of class groups and related problems\nby Carlo Pagano (University of Glasgow) as part of A lgebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nIn this talk I w ill review some of the recent progress on the Cohen--Lenstra--Gerth conjec tures and related problems.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Wahei Hara (University of Glasgow) DTSTART:20201021T150000Z DTEND:20201021T160000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/2 DESCRIPTION:Title: On derived equivalence for a 7-dimensional flop associated to G_ 2 Grassmannians\nby Wahei Hara (University of Glasgow) as part of Alge bra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nWe discuss a 7-dime nsional flop that comes from the geometry of G_2 homogeneous varieties. We construct tilting bundles on both sides of the flop\, and show derived eq uivalence for the flop using those tilting bundles.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Cameron (University of St. Andrews) DTSTART:20201028T160000Z DTEND:20201028T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/3 DESCRIPTION:Title: The geometry of diagonal groups\nby Peter Cameron (Universit y of St. Andrews) as part of Algebra and Number Theory Seminar\, Glasgow\n \n\nAbstract\nDiagonal groups form one of the classes of groups in the cel ebrated O'Nan--Scott theorem which underpins the application of finite sim ple 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 ne cessarily simple or even finite. We construct and characterise a geometric object whose automorphism group is the diagonal group if the dimension is at least 3. In dimension 2 these objects are equivalent to Latin squares and exist in great profusion\, but in higher dimension the group emerges n aturally from the combinatorial axioms. The work links group theory\, comb inatorics and statistics.\n\n(joint work with Rosemary Bailey\, Cheryl Pra eger and Csaba Schneider)\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Khrystyna Serhiyenko (University of Kentucky) DTSTART:20201104T160000Z DTEND:20201104T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/4 DESCRIPTION:Title: Geometric model for syzygies over certain 2-Calabi-Yau tilted al gebras\nby Khrystyna Serhiyenko (University of Kentucky) as part of Al gebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nA module is said to be a syzygy if it is a submodule of a projective. In the case of 2-Cal abi-Yau (2-CY) tilted algebras the non-projective syzygies form a triangul ated 3-CY category. In this setting\, the category of syzygies is equival ent to the category of Cohen-Macauley modules and also the singularity cat egory of the algebra. We find a geometric model for this category for a p articular type of 2-CY tilted algebras given by quivers with relations. M ore precisely\, we construct a decorated polygon with a checkerboard patte rn whose 2-diagonals correspond to syzygies. Moreover\, other aspects of the syzygy category such as morphisms\, extensions\, Auslander-Reiten tri angles\, and the shift also have a geometric interpretation in this polygo n. This is joint work with Ralf Schiffler.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gareth Tracey (Oxford University) DTSTART:20201111T160000Z DTEND:20201111T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/5 DESCRIPTION:Title: On the expected number of random primes required to generate a G alois group\nby Gareth Tracey (Oxford University) as part of Algebra a nd Number Theory Seminar\, Glasgow\n\n\nAbstract\nGiven a finite group $X$ \, a classical approach to proving that $X$ is the Galois group of a Galoi s extension $K/\\mathbb{Q}$ can be described roughly as follows: (1) prove that $\\Gal(K/\\mathbb{Q})$ is contained in $X$ by using known properties of the extension (for example\, the Galois group of an irreducible polyno mial $f(x)\\in\\mathbb{Z}[x]$ of degree $n$ embeds into the symmetric grou p $\\Sym(n)$)\; (2) try to prove that $X = \\Gal(K/\\mathbb{Q})$ by comput ing the Frobenius automorphisms modulo successive primes\, which gives con jugacy classes in $\\Gal(K/\\mathbb{Q})$\, and hence in $X$. If these conj ugacy classes can only occur in the case $\\Gal(K/\\mathbb{Q})=X$\, then w e are done.\n\nAlthough better algorithms exist in practice\, this approac h 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 rapidly de veloping area of finite group theory.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ross Paterson (University of Glasgow) DTSTART:20201118T160000Z DTEND:20201118T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/6 DESCRIPTION:Title: 2-Selmer Groups of Twists after Quadratic Extension\nby Ross Paterson (University of Glasgow) as part of Algebra and Number Theory Sem inar\, Glasgow\n\n\nAbstract\nAs E varies in a natural family of elliptic 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\, Swinnerton- 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 of such curves over K\, then the size is no longer the only interesting structure at hand\; in fact the 2-Selmer group over K has a natural action of the Ga lois group of K. It is then natural to ask the more refined question: what are the statistical properties of this Galois module?\n\nI will report on joint work with Adam Morgan\, in which we consider this question in the c ase that K is a quadratic field and E varies over quadratic twists of a fi xed curve\, and give some interesting corollaries for the Mordell-Weil gro ups as a result.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxime Fairon (University of Glasgow) DTSTART:20201125T160000Z DTEND:20201125T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/7 DESCRIPTION:Title: Double (quasi-)Poisson algebras and their morphisms\nby Maxi me Fairon (University of Glasgow) as part of Algebra and Number Theory Sem inar\, Glasgow\n\n\nAbstract\nThe talk will begin with a review of the not ion of double (quasi-)Poisson algebras\, which were introduced by Van den Bergh as noncommutative analogues of (quasi-)Poisson algebras. I will then explain how their morphisms can be used to understand morphisms of associ ated Poisson varieties. As an application\, I will describe how the double (quasi-)Poisson algebra associated to an arbitrary quiver by Van den Berg h does not depend on the orientation of the quiver\, up to isomorphism. We will see that this produces many Poisson isomorphisms between (multiplica tive) quiver varieties. This is partly based on arXiv:2008.01409.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Man-Wai\, Mandy\, Cheung (Harvard University) DTSTART:20201202T160000Z DTEND:20201202T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/8 DESCRIPTION:Title: Tropical disks counting\, stability conditions in symplectic geo metry and quiver representations\nby Man-Wai\, Mandy\, Cheung (Harvard University) as part of Algebra and Number Theory Seminar\, Glasgow\n\n\nA bstract\nBridgeland developed stability scattering diagrams relating scatt ering diagrams with quiver representations. Scattering diagrams were devel oped as a machinery in mirror symmetry. Together with Travis Mandel\, we a ssociate tropical disks counting with quiver representations by using the stability scattering diagrams.\nNext\, together with Yu-Wei Fan and Yu-She n Lin\, we look at the stable objects for the A2 quiver. It is known 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 corres ponded the special Lagrangian with the stable objects in the derived categ ory of coherent sheaves.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Arthur Soulié (University of Glasgow) DTSTART:20201209T160000Z DTEND:20201209T170000Z DTSTAMP:20260422T230717Z 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 Theory Semi nar\, Glasgow\n\n\nAbstract\nMany families of groups\, such as braid group s\, have a representation theory of wild type\, in the sense that there is no known classification schema to organize the representations. However\, using actions on the homology groups of the coverings of some associated spaces\, there are systematic procedures to construct linear representatio ns for such families of groups\, which help to understand their representa tion theory.\nI will present a unified functorial construction of homologi cal representations for these families of groups. This general method is p articularly suitable to generate new families of representations of motion groups such as braid groups on surfaces or loop braid groups. For instanc e\, this construction provides the family of Lawrence-Bigelow representati ons for braid groups. We will also discuss irreducibility results for the obtained representations. Finally\, general notions of polynomiality on fu nctors are a useful tool to classify these representations and allow to pr ove some twisted homological stability results: polynomiality results can be proved for some of the homological representations\, in particular the Lawrence-Bigelow representations.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Wilsch (IST Austria) DTSTART:20201216T160000Z DTEND:20201216T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/10 DESCRIPTION:Title: Equidistribution and freeness on Grassmanians\nby Florian W ilsch (IST Austria) as part of Algebra and Number Theory Seminar\, Glasgow \n\n\nAbstract\nWe associate a tangent lattice to a primitive integer latt ice and study its typical shape. This is motivated by Peyre’s program on the freeness of rational points on Fano varieties: A primitive integer la ttice can be regarded a point on a Grassmanian\, and the shape of its tang ent lattice determines this point’s freeness.\nThe reason behind this in terest in freeness is Manin’s conjecture about the number of rational po ints of bounded height on Fano varieties: This number might be dominated b y “bad” points on subvarieties\, or more generally\, a thin set of “ bad“ points that has to be excluded in the count. Peyre proposed to excl ude points of low freeness\, so that points of high freeness should confor m to the asymptotic formula proposed by Manin’s conjecture and its varia nts. Our analysis verifies this for Grassmanians by proving that there are relatively few points of low freeness.\nThis is joint work with Tim Brown ing and Tal Horesh.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Dinakar Muthiah (University of Glasgow) DTSTART:20210224T160000Z DTEND:20210224T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/11 DESCRIPTION:Title: Affine Lusztig-Kato formula\nby Dinakar Muthiah (University of Glasgow) as part of Algebra and Number Theory Seminar\, Glasgow\n\n\nA bstract\nThe Lusztig-Kato formula is an important precursor to the geometr ic Satake correspondence. Recent constructions point to geometric Satake f or affine and general Kac-Moody groups. This leads to a conjectural Luszti g-Kato formula. I will review this and discuss work in progress with H. Na kajima\, which implies the formula in affine type A.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Fanelli (University of Bordeaux) DTSTART:20210217T160000Z DTEND:20210217T170000Z DTSTAMP:20260422T230717Z 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 Theory Semi nar\, Glasgow\n\n\nAbstract\nIn this talk\, I will discuss some pathologie s for the generic fibre of del Pezzo fibrations in characteristic p>0\, m otivated by the recent developments of the MMP in positive characteristic . The recent joint work with Stefan Schröer applies to deduce information on the structure of 3-dimensional Mori fibre spaces and answers an old qu estion by János Kollár.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Bartel (University of Glasgow) DTSTART:20210324T160000Z DTEND:20210324T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/13 DESCRIPTION:Title: Statistics for ray class groups of number fields\nby Alex B artel (University of Glasgow) as part of Algebra and Number Theory Seminar \, Glasgow\n\n\nAbstract\nThe Cohen--Lenstra heuristics are a probabilisti c model for\nclass groups of quadratic number fields. I will report on joi nt work\nwith Carlo Pagano\, in which we generalise these heuristics to ra y class\ngroups. A central role in our heuristics is played by so-called A rakelov\nray class groups. Apart from demonstrating their utility for our\ nimmediate purpose\, I will advertise their beauty by re-interpreting a\nc lassical construction that attaches closed geodesics on the quotient of\nt he hyperbolic upper half plane by SL(2\,Z) to (narrow) ideal classes of\nr eal quadratic fields. Only minimal number theoretic background will be\nas sumed.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Koymans (Max Planck Institute for Mathematics) DTSTART:20210120T160000Z DTEND:20210120T170000Z DTSTAMP:20260422T230717Z 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 Number Theo ry Seminar\, Glasgow\n\n\nAbstract\nArithmetic statistics concerns the stu dy of arithmetic objects in families\, and has recently attracted substant ial attention. In this talk we will give an overview of the so-called $n = p$ case and discuss the most important results in this area. Parts of thi s talk are joint work with Stephanie Chan\, Djordjo Milovic and Carlo Paga no.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ken Brown (University of Glasgow) DTSTART:20210317T160000Z DTEND:20210317T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/15 DESCRIPTION:Title: Connected Hopf algebras\nby Ken Brown (University of Glasgo w) as part of Algebra and Number Theory Seminar\, Glasgow\n\n\nAbstract\nI will give a survey of some results on infinite dimensional connected Hopf algebras obtained by myself and others over the last decade. I will aim t o make it comprehensible by those with no previous knowledge of Hopf algeb ras.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel El-Baz (TU Graz) DTSTART:20210203T160000Z DTEND:20210203T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/16 DESCRIPTION:Title: Local statistics: dynamics\, number theory and universality \nby Daniel El-Baz (TU Graz) as part of Algebra and Number Theory Seminar\ , Glasgow\n\n\nAbstract\nLocal statistics are a way to go beyond equidistr ibution in measuring the 'randomness' of a sequence. Those sequences can c ome from a wide range of sources --- from quantum mechanics to number theo ry --- but there appear to be few laws governing their local statistics.\n \nWe will explore those universality phenomena and discuss the methods tha t go into proving some of those results\, using ergodic theory and analyti c number theory.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Rome (University of Michigan) DTSTART:20210210T160000Z DTEND:20210210T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/17 DESCRIPTION:Title: Counting Quadratic Points on Surfaces\nby Nick Rome (Univer sity of Michigan) as part of Algebra and Number Theory Seminar\, Glasgow\n \n\nAbstract\nWe will discuss Manin's conjecture on rational points of bou nded height on algebraic varieties. In particular\, we will show how the r ecent counterexamples of Le Rudulier can be extended by counting quadratic points on certain del Pezzo surfaces.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Chlouveraki (Laboratoire de Mathématiques de Versailles) DTSTART:20210310T160000Z DTEND:20210310T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/18 DESCRIPTION:Title: On the reality of complex reflection groups (and their associat ed Hecke algebras)\nby Maria Chlouveraki (Laboratoire de Mathématique s de Versailles) as part of Algebra and Number Theory Seminar\, Glasgow\n\ n\nAbstract\nIwahori-Hecke algebras associated to Weyl groups appear natur ally as endomorphism algebras in the representation theory of finite reduc tive groups. Weyl groups are real reflection groups\, which in turn are pa rticular cases of complex reflection groups. Hecke algebras associated to complex reflection groups were introduced by Broué\, Malle and Rouquier 2 0 years ago\, but many of the properties of real Hecke algebras were simpl y conjectured in the complex case. In this talk\, we are going to discuss the most fundamental of these conjectures\, their state of art and our con tributions to it.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Joni Teräväinen (University of Oxford) DTSTART:20210303T160000Z DTEND:20210303T170000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/19 DESCRIPTION:Title: On the Liouville function at polynomial arguments\nby Joni Teräväinen (University of Oxford) as part of Algebra and Number Theory S eminar\, Glasgow\n\n\nAbstract\nLet $\\lambda$ be the Liouville function a nd $P(x)$ any polynomial that is not a square. An open problem formulated by Chowla and others asks to show that the sequence $\\lambda(P(n))$ chang es sign infinitely often. We present a solution to this problem for new cl asses of polynomials $P$\, including any product of linear factors or any product of quadratic factors of a certain type. The proofs also establish some nontrivial cancellation in Chowla and Elliott type correlation averag es.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Kalck DTSTART:20210602T150000Z DTEND:20210602T160000Z DTSTAMP:20260422T230717Z UID:algebra_14_134725/20 DESCRIPTION:Title: A surface and a threefold with equivalent singularity categorie s\nby Martin Kalck as part of Algebra and Number Theory Seminar\, Glas gow\n\n\nAbstract\nWe start with an introduction to singularity categories and equivalences between them.\n In particular\, we recall known results about singular equivalences between commutative rings\, whic h go back\n to Knörrer\, Yang\, Kawamata and a joint work w ith Karmazyn. Then we explain a new singular equivalence\n b etween an affine surface and an affine threefold. This seems to be the fir st (non-trivial) example of a singular equivalence involving\n rings of even and odd Krull dimension.\n LOCATION:https://researchseminars.org/talk/algebra_14_134725/20/ END:VEVENT END:VCALENDAR