BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Seamus Albion (University of Queensland) DTSTART:20201009T010000Z DTEND:20201009T030000Z DTSTAMP:20260404T110957Z UID:WiSe/1 DESCRIPTION:Title: What is the Honey Comb Model?\nby Seamus Albion (University of Que ensland) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/1/ END:VEVENT BEGIN:VEVENT SUMMARY:GyeongHyeon Nam (University of Queensland) DTSTART:20201016T010000Z DTEND:20201016T030000Z DTSTAMP:20260404T110957Z UID:WiSe/2 DESCRIPTION:Title: What is the Birch and Swinnerton-Dyer Conjecture?\nby GyeongHyeon Nam (University of Queensland) as part of What is ...? Seminar\n\nAbstract : TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Colman (University of Melbourne) DTSTART:20201023T010000Z DTEND:20201023T030000Z DTSTAMP:20260404T110957Z UID:WiSe/3 DESCRIPTION:Title: What is Hodge theory?\nby Owen Colman (University of Melbourne) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Linyuan Liu (IAS) DTSTART:20201030T010000Z DTEND:20201030T030000Z DTSTAMP:20260404T110957Z UID:WiSe/4 DESCRIPTION:Title: What is mixed Hodge theory?\nby Linyuan Liu (IAS) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Baine (University of Sydney) DTSTART:20201113T010000Z DTEND:20201113T030000Z DTSTAMP:20260404T110957Z UID:WiSe/6 DESCRIPTION:Title: What is a Soergel bimodule?\nby Joe Baine (University of Sydney) a s part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Cailan Li (Columbia University) DTSTART:20201120T030000Z DTEND:20201120T050000Z DTSTAMP:20260404T110957Z UID:WiSe/7 DESCRIPTION:Title: What is categorification?\nby Cailan Li (Columbia University) as p art of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Lynch (University of Tübingen) DTSTART:20201127T050000Z DTEND:20201127T070000Z DTSTAMP:20260404T110957Z UID:WiSe/8 DESCRIPTION:Title: What is Thurston Geometrization?\nby Stephen Lynch (University of Tübingen) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhaoting Wei (Texas A&M University-Commerce) DTSTART:20201204T010000Z DTEND:20201204T030000Z DTSTAMP:20260404T110957Z UID:WiSe/9 DESCRIPTION:Title: What is the Kobayashi-Hitchin correspondence?\nby Zhaoting Wei (Te xas A&M University-Commerce) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/WiSe/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohin Berichon (University of Queensland) DTSTART:20210305T000000Z DTEND:20210305T020000Z DTSTAMP:20260404T110957Z UID:WiSe/10 DESCRIPTION:Title: What is the exotic structure on R^4?\nby Rohin Berichon (Universi ty of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nA classic al question in differential topology asks how many distinct differentiable structures exist on a certain topological manifold. Remarkably\, there is a unique differentiable structure on Euclidean spaces of dimensions not e qual to 4\, but uncountably many on Euclidean 4-space. In this presentatio n\, we discuss the multiple constructions for exotic structures on 4 dimen sional Euclidean space\, and how to produce an uncountable family of these exotic structures.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Gammage (Harvard University) DTSTART:20210311T000000Z DTEND:20210311T020000Z DTSTAMP:20260404T110957Z UID:WiSe/11 DESCRIPTION:Title: What is Mirror Symmetry?\nby Benjamin Gammage (Harvard University ) as part of What is ...? Seminar\n\n\nAbstract\nMirror symmetry predicts that a Kähler manifold X (near a certain scaling limit) admits a dual spa ce X^ so that symplectic invariants of X are equal to algebraic invariants of X^. We will begin by reviewing the Fukaya category of Lagrangian subma nifolds of X\, focusing on the case when X is a Stein manifold\, and then describe the homological mirror symmetry conjecture that the Fukaya catego ry of X is equal to the category of coherent sheaves on X^. If time permit s\, we will explain how to prove this conjecture.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Stokes (University College London) DTSTART:20210318T230000Z DTEND:20210319T010000Z DTSTAMP:20260404T110957Z UID:WiSe/12 DESCRIPTION:Title: What is an integrable difference equation?\nby Alexander Stokes ( University College London) as part of What is ...? Seminar\n\n\nAbstract\n An interesting feature of the field of integrable systems in general is th at there is no single definition (applicable to all contexts) of what inte grability is\, but “you know it when you see it”\, so much work in thi s area relates to defining or describing integrability in different classe s of systems. \nThis is especially so in the theory of discrete integrable systems\, and in this talk we will present some novel definitions of cert ain classes of integrable difference equations\, emphasising how they are formulated in parallel with the classical differential case. \nA particula rly beautiful feature of the discrete case is that integrability can be de scribed in terms of a wide range of concepts\, varying from analytic measu res of entropy to the geometry of complex algebraic surfaces associated wi th affine Weyl groups.\nWe will see definitions of integrability for latti ce equations\, for second-order equations defining birational mappings of the plane\, and a particularly beautiful way of defining discrete analogue s of the Painlevé differential equations.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Weekes (University of British Columbia) DTSTART:20210401T000000Z DTEND:20210401T020000Z DTSTAMP:20260404T110957Z UID:WiSe/13 DESCRIPTION:Title: What is a Coulomb branch?\nby Alex Weekes (University of British Columbia) as part of What is ...? Seminar\n\n\nAbstract\nAs hinted at in t heir name\, Coulomb branches come from physics: they are spaces which phys icists associate to certain quantum field theories. But it so happens that many spaces of mathematical interest arise as Coulomb branches\, which ar e especially important in representation theory and in the study of integr able systems.\nAs with many constructions in quantum field theory\, a prec ise mathematical definition of Coulomb branches was difficult to achieve. Fortunately for us this was accomplished in recent work of Braverman\, Fin kelberg and Nakajima (BFN)\, who provide a rigorous definition in a large family of cases.\nIn this talk we will take a look at the BFN construction of Coulomb branches\, making stops along the way to see some of the inter esting spaces that arise.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Romanov (University of Sydney) DTSTART:20210415T000000Z DTEND:20210415T020000Z DTSTAMP:20260404T110957Z UID:WiSe/14 DESCRIPTION:Title: What is a Hecke algebra?\nby Anna Romanov (University of Sydney) as part of What is ...? Seminar\n\n\nAbstract\nIf you hang around represen tation theory circles\, you have probably heard a definition of a Hecke al gebra. (For example\, if you attended Anna Puskas’s WiSe talk last June. ) If you hang around representation theory circles a lot\, you have probab ly heard several definitions of a Hecke algebra. If you are like me\, you may have found this confusing. In this talk\, we will explore a few defini tions of Hecke algebras. I will try to explain why they arise naturally in the representation theory of groups\, and how the different definitions a re related. We’ll also take a detour into Gelfand pairs\, and explain ho w these fit into the story.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Whitehead (Swarthmore College) DTSTART:20210422T000000Z DTEND:20210422T020000Z DTSTAMP:20260404T110957Z UID:WiSe/15 DESCRIPTION:Title: What is an Apollonian Packing?\nby Ian Whitehead (Swarthmore Coll ege) as part of What is ...? Seminar\n\n\nAbstract\nFix four mutually tang ent circles in the plane. Fill in the spaces between these circles with ad ditional tangent circles. By repeating this process ad infinitum\, on smal ler and smaller scales\, we obtain an Apollonian circle packing. In this t alk I will sketch a proof of Descartes' theorem on circle configurations\, and introduce a group which acts on packings in two different ways\, with a subtle duality between them. If time allows\, I will also talk about my own recent work relating packings to Kac-Moody root systems. This connect ion is via a four-variable generating function for curvatures that appear in an Apollonian packing\, which is essentially a character for a rank 4 i ndefinite Kac-Moody root system. I will discuss its domain of convergence\ , the Tits cone of the root system\, which inherits the rich geometry of A pollonian packings.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Heller (Gottfried Wilhelm Leibniz Universität Hannover) DTSTART:20210429T050000Z DTEND:20210429T070000Z DTSTAMP:20260404T110957Z UID:WiSe/16 DESCRIPTION:Title: What is a hyperkähler manifold?\nby Sebastian Heller (Gottfried Wilhelm Leibniz Universität Hannover) as part of What is ...? Seminar\n\n \nAbstract\nA hyperkähler structure is a geometric structure which occurs naturally in different fields such as algebraic geometry\, theoretical ph ysics and Riemannian geometry.\nFor differential geometers\, a hyperkähle r manifold is a Riemannian manifold with three anti-\ncommuting\, parallel and orthogonal complex structures. The most prominent examples –\nCalab i-Yau manifolds – play an important role in string theory.\n\nAfter disc ussing the definition and first properties of hyperkähler manifolds\, we will explain some examples in detail. These examples are either constructe d as hyperkähler quotients by adapting the symplectic reduction method to the Kähler forms or as the space of real holomorphic sections of the ass ociated twistor spaces. If time permits\, we will end the talk by referrin g to current research results.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Thompson (Monash University) DTSTART:20210506T010000Z DTEND:20210506T030000Z DTSTAMP:20260404T110957Z UID:WiSe/17 DESCRIPTION:Title: What is a hyperbolic knot?\nby Emily Thompson (Monash University) as part of What is ...? Seminar\n\n\nAbstract\nOne of the major advances in modern knot theory is the result of William Thurston that classifies al l knots as one of three types: a torus knot\, a satellite knot\, or a hype rbolic knot. When a knot is hyperbolic\, we can apply tools and results fr om hyperbolic geometry to study it. But what is a hyperbolic knot?!\n\nIn the first half of this talk we will discuss some general knot theory\, the upper half space model of hyperbolic space\, and what makes a knot hyperb olic. In the second half we will carefully step through the decomposition of the figure-8 knot complement into two ideal tetrahedra and use this dec omposition to prove that the figure-8 knot is hyperbolic.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchewan) DTSTART:20210513T000000Z DTEND:20210513T020000Z DTSTAMP:20260404T110957Z UID:WiSe/18 DESCRIPTION:Title: What is a hyperpolygon?\nby Steven Rayan (University of Saskatche wan) as part of What is ...? Seminar\n\n\nAbstract\nHyperpolygons are geom etric objects originating in representation theory and\, in particular\, a ct as a bridge between a number of important geometric and representation- theoretic moduli spaces. Given this role\, hyperpolygons interact natural ly with a number of other notions that have been presented in this series\ , including Higgs bundles\, character varieties\, hyperkähler geometry\, nonabelian Hodge theory\, integrable systems\, mirror symmetry\, and Coulo mb branches\, to name a few. In the first part of the talk\, we will rev iew the construction of a Nakajima quiver variety\, of which hyperpolygon space is a particular instance. In the second half of the talk\, we will focus on the connections that hyperpolygons have with the various other n otions from this series\, which include a number of recent\, interesting r esults.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pengfei Huang (Universität Heidelberg) DTSTART:20210521T060000Z DTEND:20210521T080000Z DTSTAMP:20260404T110957Z UID:WiSe/19 DESCRIPTION:Title: What is nonabelian Hodge theory?\nby Pengfei Huang (Universität Heidelberg) as part of What is ...? Seminar\n\n\nAbstract\nNonabelian Hodg e theory can be thought as nonabelian analogue of (abelian) Hodge theory b y replacing the abelian (coefficient) groups into nonabelian (coefficient) groups. This is mainly due to the celebrated work of Donaldson\, Corlette \, Hitchin\, and Simpson\, which gives us a correspondence between local s ystems and Higgs bundles. More precisely\, the nonabelian Hodge theory giv es an equivalence between the category of reductive representations of the fundamental group\, the category of semisimple flat bundles\, and the cat egory of polystable Higgs bundles with vanishing rational Chern classes\, through pluri-harmonic metrics. Moreover\, such an equivalence of categori es is functorial\, and preserves tensor products\, direct sums\, and duals . In moduli viewpoint\, this theory indicates that\, the moduli space of i rreducible representations (called character variety\, or Betti moduli sp ace)\, as a smooth affine variety\, is complex analytic isomorphic to the moduli space of irreducible flat bundles (called de Rham moduli space)\, w hich is a smooth Stein manifold (in the sense of analytic topology)\, and is real analytic isomorphic to the moduli space of stable Higgs bundles (c alled Dolbeault moduli space)\, which is a smooth quasi-projective variety . All of these objects can be generalized to a family of flat λ-connectio ns parametrized by λ ∈ C\, a notion introduced by Deligne\, further stu died by Simpson\, and Mochizuki. \n\nIn this talk\, I will begin with a qu ick review of (abelian) Hodge theory as the motivation of this theory. The n I will introduce this theory precisely from an analytic viewpoint by int roducing the work of Donaldson\, Corlette\, Hitchin\, Simpson\, and Mochiz uki on the existence of pluri-harmonic metrics. Then I will talk about thi s theory from the moduli viewpoint. A good reference of this theory is a s urvey paper by S. Rayan and A. Garcı́a-Raboso ( “Introduction to nonab elian Hodge theory: flat connections\, Higgs bundles\, and complex variati ons of Hodge structure\, Fields Inst. Monogr. 34 (2015)\, 131-171.”)\, y ou can also take the first chapter of my thesis as a reference.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Weekes (University of Saskatchewan) DTSTART:20210827T000000Z DTEND:20210827T020000Z DTSTAMP:20260404T110957Z UID:WiSe/20 DESCRIPTION:Title: What is the Affine Grassmanian?\nby Alex Weekes (University of Sa skatchewan) as part of What is ...? Seminar\n\n\nAbstract\nAffine Grassman nians are infinite-dimensional spaces which play an important role in geom etric representation theory. One part of the richness of these spaces is that they can defined in several seemingly distinct ways: via loop groups\ , via a moduli space of principal bundles\, via Kac-Moody groups\, or via lattices. In this talk we'll overview the definition of the affine Grassm annian\, with some motivation from number theory\, and discuss a few examp les which relate back to (possibly) more familiar spaces like the nilpoten t cone. Finally\, if time permits\, we'll touch on more advanced topics s uch as the geometric Satake equivalence.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Spong (The University of Queensland) DTSTART:20210910T010000Z DTEND:20210910T030000Z DTSTAMP:20260404T110957Z UID:WiSe/21 DESCRIPTION:Title: What is equivariant elliptic cohomology?\nby Matthew Spong (The U niversity of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nEl liptic cohomology was introduced in the late 1980s following Witten's resu lts about the index theory of families of differential operators on free l oop spaces. In a certain sense it is an approximation to the K-theory of t he free loop space. The first equivariant version of the theory was constr ucted in 1994 by Grojnowski\, who made comments about its mysterious relat ionship to the representation theory of loop groups. In this talk\, we out line a construction of equivariant elliptic cohomology whose main ingredie nt is the loop group equivariant K-theory of the free loop space. The cons truction is based on a recent construction of Kitchloo.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Nurcombe (The University of Queensland) DTSTART:20211022T010000Z DTEND:20211022T030000Z DTSTAMP:20260404T110957Z UID:WiSe/22 DESCRIPTION:Title: What is Kazhdan-Lusztig Theory?\nby Madeline Nurcombe (The Univer sity of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nIn 1979 \, Kazhdan and Lusztig introduced a new basis for the Hecke algebra of a C oxeter group\, related to the standard basis by polynomial coefficients. T hese polynomials relate diverse areas in Lie Theory\, such as Verma module s of semisimple Lie algebras\, Schubert varieties in algebraic geometry\, and primitive ideals of enveloping algebras\, leading to a new topic calle d Kazhdan-Lusztig theory. In this talk\, I will focus on the Kazhdan-Luszt ig basis in the simpler case of the Hecke algebra of the symmetric group\, giving some necessary background information on the symmetric group\, Bru hat order and Hecke algebra. I will then relate this to the more general c ase of the Hecke algebra of a Coxeter group.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Maryam Khaqan (University of Stockholm) DTSTART:20211011T080000Z DTEND:20211011T100000Z DTSTAMP:20260404T110957Z UID:WiSe/23 DESCRIPTION:Title: What is moonshine?\nby Maryam Khaqan (University of Stockholm) as part of What is ...? Seminar\n\n\nAbstract\nMoonshine began as a series o f numerical coincidences connecting finite groups to modular forms but has since evolved into a rich theory that sheds light on the underlying algeb raic structures that these coincidences reflect. In this talk\, I will giv e a brief history of moonshine\, describe some of the existing examples of the phenomenon in the literature\, and discuss how my work fits into the story.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Spong (The University of Queensland) DTSTART:20210924T010000Z DTEND:20210924T030000Z DTSTAMP:20260404T110957Z UID:WiSe/24 DESCRIPTION:Title: What is (non-equivariant) elliptic cohomology?\nby Matthew Spong (The University of Queensland) as part of What is ...? Seminar\n\n\nAbstra ct\nIn this talk we will begin with a sketch of what elliptic cohomology i s really about. Thus we will introduce the concept of a genus\, which is a n invariant of manifolds which are equipped with extra structure\, and fro m there we will define an elliptic genus. We then aim to briefly describe the role of elliptic genera in elliptic cohomology\, and to sketch the rel ationship to index theory on free loop spaces. If time permits\, we will f inally describe a version of elliptic cohomology which was constructed in terms of the K-theory of free loop spaces by Kitchloo and Morava.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Nurcombe (The University of Queensland) DTSTART:20211105T010000Z DTEND:20211105T030000Z DTSTAMP:20260404T110957Z UID:WiSe/25 DESCRIPTION:Title: What is Kazhdan-Lusztig Theory? - Part II\nby Madeline Nurcombe ( The University of Queensland) as part of What is ...? Seminar\n\n\nAbstrac t\nThis is Part II of the talk started on 22 October. \n\nIn 1979\, Kazhda n and Lusztig introduced a new basis for the Hecke algebra of a Coxeter gr oup\, related to the standard basis by polynomial coefficients. These poly nomials relate diverse areas in Lie Theory\, such as Verma modules of semi simple Lie algebras\, Schubert varieties in algebraic geometry\, and primi tive ideals of enveloping algebras\, leading to a new topic called Kazhdan -Lusztig theory. In this talk\, I will focus on the Kazhdan-Lusztig basis in the simpler case of the Hecke algebra of the symmetric group\, giving s ome necessary background information on the symmetric group\, Bruhat order and Hecke algebra. I will then relate this to the more general case of th e Hecke algebra of a Coxeter group.\n LOCATION:https://stable.researchseminars.org/talk/WiSe/25/ END:VEVENT END:VCALENDAR