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:20260422T225656Z UID:WiSe/1 DESCRIPTION:Title: Wha t is the Honey Comb Model?\nby Seamus Albion (University of Queensland ) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/1/ END:VEVENT BEGIN:VEVENT SUMMARY:GyeongHyeon Nam (University of Queensland) DTSTART:20201016T010000Z DTEND:20201016T030000Z DTSTAMP:20260422T225656Z UID:WiSe/2 DESCRIPTION:Title: Wha t is the Birch and Swinnerton-Dyer Conjecture?\nby GyeongHyeon Nam (Un iversity of Queensland) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Colman (University of Melbourne) DTSTART:20201023T010000Z DTEND:20201023T030000Z DTSTAMP:20260422T225656Z UID:WiSe/3 DESCRIPTION:Title: Wha t is Hodge theory?\nby Owen Colman (University of Melbourne) as part o f What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Linyuan Liu (IAS) DTSTART:20201030T010000Z DTEND:20201030T030000Z DTSTAMP:20260422T225656Z UID:WiSe/4 DESCRIPTION:Title: Wha t is mixed Hodge theory?\nby Linyuan Liu (IAS) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Joe Baine (University of Sydney) DTSTART:20201113T010000Z DTEND:20201113T030000Z DTSTAMP:20260422T225656Z UID:WiSe/6 DESCRIPTION:Title: Wha t is a Soergel bimodule?\nby Joe Baine (University of Sydney) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Cailan Li (Columbia University) DTSTART:20201120T030000Z DTEND:20201120T050000Z DTSTAMP:20260422T225656Z UID:WiSe/7 DESCRIPTION:Title: Wha t is categorification?\nby Cailan Li (Columbia University) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Lynch (University of Tübingen) DTSTART:20201127T050000Z DTEND:20201127T070000Z DTSTAMP:20260422T225656Z UID:WiSe/8 DESCRIPTION:Title: Wha t is Thurston Geometrization?\nby Stephen Lynch (University of Tübing en) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhaoting Wei (Texas A&M University-Commerce) DTSTART:20201204T010000Z DTEND:20201204T030000Z DTSTAMP:20260422T225656Z UID:WiSe/9 DESCRIPTION:Title: Wha t is the Kobayashi-Hitchin correspondence?\nby Zhaoting Wei (Texas A&M University-Commerce) as part of What is ...? Seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/WiSe/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohin Berichon (University of Queensland) DTSTART:20210305T000000Z DTEND:20210305T020000Z DTSTAMP:20260422T225656Z UID:WiSe/10 DESCRIPTION:Title: Wh at is the exotic structure on R^4?\nby Rohin Berichon (University of Q ueensland) as part of What is ...? Seminar\n\n\nAbstract\nA classical ques tion in differential topology asks how many distinct differentiable struct ures exist on a certain topological manifold. Remarkably\, there is a uniq ue differentiable structure on Euclidean spaces of dimensions not equal to 4\, but uncountably many on Euclidean 4-space. In this presentation\, we discuss the multiple constructions for exotic structures on 4 dimensional Euclidean space\, and how to produce an uncountable family of these exotic structures.\n LOCATION:https://researchseminars.org/talk/WiSe/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Gammage (Harvard University) DTSTART:20210311T000000Z DTEND:20210311T020000Z DTSTAMP:20260422T225656Z UID:WiSe/11 DESCRIPTION:Title: Wh at is Mirror Symmetry?\nby Benjamin Gammage (Harvard University) as pa rt of What is ...? Seminar\n\n\nAbstract\nMirror symmetry predicts that a Kähler manifold X (near a certain scaling limit) admits a dual space X^ s o that symplectic invariants of X are equal to algebraic invariants of X^. We will begin by reviewing the Fukaya category of Lagrangian submanifolds of X\, focusing on the case when X is a Stein manifold\, and then describ e the homological mirror symmetry conjecture that the Fukaya category of X is equal to the category of coherent sheaves on X^. If time permits\, we will explain how to prove this conjecture.\n LOCATION:https://researchseminars.org/talk/WiSe/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Stokes (University College London) DTSTART:20210318T230000Z DTEND:20210319T010000Z DTSTAMP:20260422T225656Z UID:WiSe/12 DESCRIPTION:Title: Wh at is an integrable difference equation?\nby Alexander Stokes (Univers ity College London) as part of What is ...? Seminar\n\n\nAbstract\nAn inte resting feature of the field of integrable systems in general is that ther e is no single definition (applicable to all contexts) of what integrabili ty is\, but “you know it when you see it”\, so much work in this area relates to defining or describing integrability in different classes of sy stems. \nThis is especially so in the theory of discrete integrable system s\, and in this talk we will present some novel definitions of certain cla sses of integrable difference equations\, emphasising how they are formula ted in parallel with the classical differential case. \nA particularly bea utiful feature of the discrete case is that integrability can be described in terms of a wide range of concepts\, varying from analytic measures of entropy to the geometry of complex algebraic surfaces associated with affi ne Weyl groups.\nWe will see definitions of integrability for lattice equa tions\, for second-order equations defining birational mappings of the pla ne\, and a particularly beautiful way of defining discrete analogues of th e Painlevé differential equations.\n LOCATION:https://researchseminars.org/talk/WiSe/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Weekes (University of British Columbia) DTSTART:20210401T000000Z DTEND:20210401T020000Z DTSTAMP:20260422T225656Z UID:WiSe/13 DESCRIPTION:Title: Wh at is a Coulomb branch?\nby Alex Weekes (University of British Columbi a) as part of What is ...? Seminar\n\n\nAbstract\nAs hinted at in their na me\, Coulomb branches come from physics: they are spaces which physicists associate to certain quantum field theories. But it so happens that many s paces of mathematical interest arise as Coulomb branches\, which are espec ially important in representation theory and in the study of integrable sy stems.\nAs with many constructions in quantum field theory\, a precise mat hematical definition of Coulomb branches was difficult to achieve. Fortuna tely for us this was accomplished in recent work of Braverman\, Finkelberg 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 Cou lomb branches\, making stops along the way to see some of the interesting spaces that arise.\n LOCATION:https://researchseminars.org/talk/WiSe/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Romanov (University of Sydney) DTSTART:20210415T000000Z DTEND:20210415T020000Z DTSTAMP:20260422T225656Z UID:WiSe/14 DESCRIPTION:Title: Wh at is a Hecke algebra?\nby Anna Romanov (University of Sydney) as part of What is ...? Seminar\n\n\nAbstract\nIf you hang around representation theory circles\, you have probably heard a definition of a Hecke algebra. (For example\, if you attended Anna Puskas’s WiSe talk last June.) If yo u hang around representation theory circles a lot\, you have probably hear d several definitions of a Hecke algebra. If you are like me\, you may hav e found this confusing. In this talk\, we will explore a few definitions o f Hecke algebras. I will try to explain why they arise naturally in the re presentation theory of groups\, and how the different definitions are rela ted. We’ll also take a detour into Gelfand pairs\, and explain how these fit into the story.\n LOCATION:https://researchseminars.org/talk/WiSe/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Whitehead (Swarthmore College) DTSTART:20210422T000000Z DTEND:20210422T020000Z DTSTAMP:20260422T225656Z UID:WiSe/15 DESCRIPTION:Title: Wh at is an Apollonian Packing?\nby Ian Whitehead (Swarthmore College) as part of What is ...? Seminar\n\n\nAbstract\nFix four mutually tangent cir cles in the plane. Fill in the spaces between these circles with additiona l tangent circles. By repeating this process ad infinitum\, on smaller and smaller scales\, we obtain an Apollonian circle packing. In this talk I w ill sketch a proof of Descartes' theorem on circle configurations\, and in troduce a group which acts on packings in two different ways\, with a subt le duality between them. If time allows\, I will also talk about my own re cent work relating packings to Kac-Moody root systems. This connection is via a four-variable generating function for curvatures that appear in an A pollonian packing\, which is essentially a character for a rank 4 indefini te Kac-Moody root system. I will discuss its domain of convergence\, the T its cone of the root system\, which inherits the rich geometry of Apolloni an packings.\n LOCATION:https://researchseminars.org/talk/WiSe/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Heller (Gottfried Wilhelm Leibniz Universität Hannover) DTSTART:20210429T050000Z DTEND:20210429T070000Z DTSTAMP:20260422T225656Z UID:WiSe/16 DESCRIPTION:Title: Wh at is a hyperkähler manifold?\nby Sebastian Heller (Gottfried Wilhelm Leibniz Universität Hannover) as part of What is ...? Seminar\n\n\nAbstr act\nA hyperkähler structure is a geometric structure which occurs natura lly in different fields such as algebraic geometry\, theoretical physics a nd Riemannian geometry.\nFor differential geometers\, a hyperkähler manif old is a Riemannian manifold with three anti-\ncommuting\, parallel and or thogonal complex structures. The most prominent examples –\nCalabi-Yau m anifolds – play an important role in string theory.\n\nAfter discussing the definition and first properties of hyperkähler manifolds\, we will ex plain some examples in detail. These examples are either constructed as hy perkähler quotients by adapting the symplectic reduction method to the K ähler forms or as the space of real holomorphic sections of the associate d twistor spaces. If time permits\, we will end the talk by referring to c urrent research results.\n LOCATION:https://researchseminars.org/talk/WiSe/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Thompson (Monash University) DTSTART:20210506T010000Z DTEND:20210506T030000Z DTSTAMP:20260422T225656Z UID:WiSe/17 DESCRIPTION:Title: Wh at is a hyperbolic knot?\nby Emily Thompson (Monash University) as par t of What is ...? Seminar\n\n\nAbstract\nOne of the major advances in mode rn knot theory is the result of William Thurston that classifies all knots as one of three types: a torus knot\, a satellite knot\, or a hyperbolic knot. When a knot is hyperbolic\, we can apply tools and results from hype rbolic geometry to study it. But what is a hyperbolic knot?!\n\nIn the fir st half of this talk we will discuss some general knot theory\, the upper half space model of hyperbolic space\, and what makes a knot hyperbolic. I n the second half we will carefully step through the decomposition of the figure-8 knot complement into two ideal tetrahedra and use this decomposit ion to prove that the figure-8 knot is hyperbolic.\n LOCATION:https://researchseminars.org/talk/WiSe/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Steven Rayan (University of Saskatchewan) DTSTART:20210513T000000Z DTEND:20210513T020000Z DTSTAMP:20260422T225656Z UID:WiSe/18 DESCRIPTION:Title: Wh at is a hyperpolygon?\nby Steven Rayan (University of Saskatchewan) as part of What is ...? Seminar\n\n\nAbstract\nHyperpolygons are geometric o bjects originating in representation theory and\, in particular\, act as a bridge between a number of important geometric and representation-theoret ic moduli spaces. Given this role\, hyperpolygons interact naturally with a number of other notions that have been presented in this series\, inclu ding Higgs bundles\, character varieties\, hyperkähler geometry\, nonabel ian Hodge theory\, integrable systems\, mirror symmetry\, and Coulomb bran ches\, to name a few. In the first part of the talk\, we will review the construction of a Nakajima quiver variety\, of which hyperpolygon space i s a particular instance. In the second half of the talk\, we will focus on the connections that hyperpolygons have with the various other notions from this series\, which include a number of recent\, interesting results. \n LOCATION:https://researchseminars.org/talk/WiSe/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pengfei Huang (Universität Heidelberg) DTSTART:20210521T060000Z DTEND:20210521T080000Z DTSTAMP:20260422T225656Z UID:WiSe/19 DESCRIPTION:Title: Wh at is nonabelian Hodge theory?\nby Pengfei Huang (Universität Heidelb erg) as part of What is ...? Seminar\n\n\nAbstract\nNonabelian Hodge theor y can be thought as nonabelian analogue of (abelian) Hodge theory by repla cing the abelian (coefficient) groups into nonabelian (coefficient) groups . This is mainly due to the celebrated work of Donaldson\, Corlette\, Hitc hin\, and Simpson\, which gives us a correspondence between local systems and Higgs bundles. More precisely\, the nonabelian Hodge theory gives an e quivalence between the category of reductive representations of the fundam ental group\, the category of semisimple flat bundles\, and the category o f polystable Higgs bundles with vanishing rational Chern classes\, through pluri-harmonic metrics. Moreover\, such an equivalence of categories is f unctorial\, and preserves tensor products\, direct sums\, and duals. In mo duli viewpoint\, this theory indicates that\, the moduli space of irreduci ble representations (called character variety\, or Betti moduli space)\, as a smooth affine variety\, is complex analytic isomorphic to the moduli space of irreducible flat bundles (called de Rham moduli space)\, which is a smooth Stein manifold (in the sense of analytic topology)\, and is real analytic isomorphic to the moduli space of stable Higgs bundles (called D olbeault moduli space)\, which is a smooth quasi-projective variety. All o f these objects can be generalized to a family of flat λ-connections para metrized by λ ∈ C\, a notion introduced by Deligne\, further studied by Simpson\, and Mochizuki. \n\nIn this talk\, I will begin with a quick rev iew of (abelian) Hodge theory as the motivation of this theory. Then I wil l introduce this theory precisely from an analytic viewpoint by introducin g the work of Donaldson\, Corlette\, Hitchin\, Simpson\, and Mochizuki on the existence of pluri-harmonic metrics. Then I will talk about this theor y from the moduli viewpoint. A good reference of this theory is a survey p aper by S. Rayan and A. Garcı́a-Raboso ( “Introduction to nonabelian H odge theory: flat connections\, Higgs bundles\, and complex variations of Hodge structure\, Fields Inst. Monogr. 34 (2015)\, 131-171.”)\, you can also take the first chapter of my thesis as a reference.\n LOCATION:https://researchseminars.org/talk/WiSe/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Weekes (University of Saskatchewan) DTSTART:20210827T000000Z DTEND:20210827T020000Z DTSTAMP:20260422T225656Z UID:WiSe/20 DESCRIPTION:Title: Wh at is the Affine Grassmanian?\nby Alex Weekes (University of Saskatche wan) as part of What is ...? Seminar\n\n\nAbstract\nAffine Grassmannians a re infinite-dimensional spaces which play an important role in geometric r epresentation theory. One part of the richness of these spaces is that th ey can defined in several seemingly distinct ways: via loop groups\, via a moduli space of principal bundles\, via Kac-Moody groups\, or via lattice s. In this talk we'll overview the definition of the affine Grassmannian\ , with some motivation from number theory\, and discuss a few examples whi ch relate back to (possibly) more familiar spaces like the nilpotent cone. Finally\, if time permits\, we'll touch on more advanced topics such as the geometric Satake equivalence.\n LOCATION:https://researchseminars.org/talk/WiSe/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Spong (The University of Queensland) DTSTART:20210910T010000Z DTEND:20210910T030000Z DTSTAMP:20260422T225656Z UID:WiSe/21 DESCRIPTION:Title: Wh at is equivariant elliptic cohomology?\nby Matthew Spong (The Universi ty of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nElliptic cohomology was introduced in the late 1980s following Witten's results abo ut the index theory of families of differential operators on free loop spa ces. In a certain sense it is an approximation to the K-theory of the free loop space. The first equivariant version of the theory was constructed i n 1994 by Grojnowski\, who made comments about its mysterious relationship to the representation theory of loop groups. In this talk\, we outline a construction of equivariant elliptic cohomology whose main ingredient is t he loop group equivariant K-theory of the free loop space. The constructio n is based on a recent construction of Kitchloo.\n LOCATION:https://researchseminars.org/talk/WiSe/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Nurcombe (The University of Queensland) DTSTART:20211022T010000Z DTEND:20211022T030000Z DTSTAMP:20260422T225656Z UID:WiSe/22 DESCRIPTION:Title: Wh at is Kazhdan-Lusztig Theory?\nby Madeline Nurcombe (The University of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nIn 1979\, Kazh dan and Lusztig introduced a new basis for the Hecke algebra of a Coxeter group\, related to the standard basis by polynomial coefficients. These po lynomials relate diverse areas in Lie Theory\, such as Verma modules of se misimple Lie algebras\, Schubert varieties in algebraic geometry\, and pri mitive ideals of enveloping algebras\, leading to a new topic called Kazhd an-Lusztig theory. In this talk\, I will focus on the Kazhdan-Lusztig basi s in the simpler case of the Hecke algebra of the symmetric group\, giving some necessary background information on the symmetric group\, Bruhat ord er and Hecke algebra. I will then relate this to the more general case of the Hecke algebra of a Coxeter group.\n LOCATION:https://researchseminars.org/talk/WiSe/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Maryam Khaqan (University of Stockholm) DTSTART:20211011T080000Z DTEND:20211011T100000Z DTSTAMP:20260422T225656Z UID:WiSe/23 DESCRIPTION:Title: Wh at is moonshine?\nby Maryam Khaqan (University of Stockholm) as part o f What is ...? Seminar\n\n\nAbstract\nMoonshine began as a series of numer ical coincidences connecting finite groups to modular forms but has since evolved into a rich theory that sheds light on the underlying algebraic st ructures that these coincidences reflect. In this talk\, I will give a bri ef history of moonshine\, describe some of the existing examples of the ph enomenon in the literature\, and discuss how my work fits into the story.\ n LOCATION:https://researchseminars.org/talk/WiSe/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Spong (The University of Queensland) DTSTART:20210924T010000Z DTEND:20210924T030000Z DTSTAMP:20260422T225656Z UID:WiSe/24 DESCRIPTION:Title: Wh at is (non-equivariant) elliptic cohomology?\nby Matthew Spong (The Un iversity of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nIn this talk we will begin with a sketch of what elliptic cohomology is reall y about. Thus we will introduce the concept of a genus\, which is an invar iant of manifolds which are equipped with extra structure\, and from there we will define an elliptic genus. We then aim to briefly describe the rol e of elliptic genera in elliptic cohomology\, and to sketch the relationsh ip to index theory on free loop spaces. If time permits\, we will finally describe a version of elliptic cohomology which was constructed in terms o f the K-theory of free loop spaces by Kitchloo and Morava.\n LOCATION:https://researchseminars.org/talk/WiSe/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeline Nurcombe (The University of Queensland) DTSTART:20211105T010000Z DTEND:20211105T030000Z DTSTAMP:20260422T225656Z UID:WiSe/25 DESCRIPTION:Title: Wh at is Kazhdan-Lusztig Theory? - Part II\nby Madeline Nurcombe (The Uni versity of Queensland) as part of What is ...? Seminar\n\n\nAbstract\nThis is Part II of the talk started on 22 October. \n\nIn 1979\, Kazhdan and L usztig introduced a new basis for the Hecke algebra of a Coxeter group\, r elated to the standard basis by polynomial coefficients. These polynomials relate diverse areas in Lie Theory\, such as Verma modules of semisimple Lie algebras\, Schubert varieties in algebraic geometry\, and primitive id eals of enveloping algebras\, leading to a new topic called Kazhdan-Luszti g 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 some nec essary background information on the symmetric group\, Bruhat order and He cke algebra. I will then relate this to the more general case of the Hecke algebra of a Coxeter group.\n LOCATION:https://researchseminars.org/talk/WiSe/25/ END:VEVENT END:VCALENDAR