BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Monica Nevins (University of Ottawa) DTSTART:20210225T230000Z DTEND:20210226T003000Z DTSTAMP:20260412T170811Z UID:SAGO/1 DESCRIPTION:Title: Cha racters and types: the personality of a representation of a p-adic group\, revealed by branching to its compact open subgroups\nby Monica Nevins (University of Ottawa) as part of Algebra Seminar (presented by SMRI)\n\n \nAbstract\nMonica Nevins (University of Ottawa)\n\nFriday 26th February\n \n10:00am - 11:30am (AEDT)\n\n(Other time zones: Thur 11:00pm GMT / Fri 12 :00am CET / Thur 3:00pm PST / Thur 6:00pm EST / Fri 7:00am CST (China))\n\ nOnline via Zoom\n\nAbstract: The theory of complex representations of p-a dic groups can feel very technical and unwelcoming\, but its central role in the conjectural local Langlands correspondence has pushed us to pursue its understanding. In this talk\, I will aim to share the spirit of\, and open questions in\, the representation theory of G\, through the lens of r estricting these representations to maximal compact open subgroups. Our po int of departure: the Bruhat-Tits building of G\, a 50-year-old combinator ial and geometric object that continues to reveal secrets about the struct ure and representation theory of G today.\n\nRegister here: https://uni-sy dney.zoom.us/meeting/register/tZUrd--uqj0iHNcugXMnXTmSQfZVh08zruaN\n LOCATION:https://researchseminars.org/talk/SAGO/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Shun-Jen Cheng (Institute of Mathematics\, Academia Sinica) DTSTART:20210506T053000Z DTEND:20210506T070000Z DTSTAMP:20260412T170811Z UID:SAGO/2 DESCRIPTION:Title: ‘ Representation theory of exceptional Lie superalgebras\nby Shun-Jen Ch eng (Institute of Mathematics\, Academia Sinica) as part of Algebra Semina r (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SAGO/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Magdalena Boos (Ruhr-University Bochum) DTSTART:20210617T053000Z DTEND:20210617T070000Z DTSTAMP:20260412T170811Z UID:SAGO/3 DESCRIPTION:Title: Adv ertising symmetric quivers and their representations\nby Magdalena Boo s (Ruhr-University Bochum) as part of Algebra Seminar (presented by SMRI)\ n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SAGO/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Gus Lonergan (A Priori Investment Management LLC) DTSTART:20210623T230000Z DTEND:20210624T003000Z DTSTAMP:20260412T170811Z UID:SAGO/4 DESCRIPTION:Title: 'Ge ometric Satake over KU'\nby Gus Lonergan (A Priori Investment Manageme nt LLC) as part of Algebra Seminar (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SAGO/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulrich Thiel (University of Kaiserslautern) DTSTART:20210708T053000Z DTEND:20210708T070000Z DTSTAMP:20260412T170811Z UID:SAGO/5 DESCRIPTION:Title: Tow ards the classification of symplectic linear quotient singularities admitt ing a symplectic resolution\nby Ulrich Thiel (University of Kaiserslau tern) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstract\nAbstra ct: Over the past two decades\, there has been much progress on the classi fication of symplectic linear quotient singularities V/G admitting a sympl ectic (equivalently\, crepant) resolution of singularities. The classifica tion is almost complete but there is an infinite series of groups in dimen sion 4 - the symplectically primitive but complex imprimitive groups - and 10 exceptional groups up to dimension 10\, for which it is still open. Re cently\, we have proven that for all but possibly 39 cases in the remainin g infinite series there is no symplectic resolution. We have thereby reduc ed the classification problem to finitely many open cases. We do not expec t any of the remaining cases to admit a symplectic resolution. This is joi nt work with Gwyn Bellamy and Johannes Schmitt.\n LOCATION:https://researchseminars.org/talk/SAGO/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shrawan Kumar (University of North Carolina) DTSTART:20210723T010000Z DTEND:20210723T023000Z DTSTAMP:20260412T170811Z UID:SAGO/6 DESCRIPTION:Title: Roo t components for tensor product of affine Kac-Moody Lie algebra modules\nby Shrawan Kumar (University of North Carolina) as part of Algebra Semi nar (presented by SMRI)\n\n\nAbstract\nThis is a joint work with Samuel Je ralds. Let gg be an affine Kac-Moody Lie algebra and let λ\, µ be two do minant integral weights for g. We prove that under some mild restriction\, for any positive root β\, V(λ) ⊗ V(µ) contains V(λ + µ - β) as a component\, where V(λ) denotes the integrable highest weight (irreducible ) g-module with highest weight λ. This extends the corresponding result b y Kumar from the case of finite dimensional semisimple Lie algebras to the affine Kac-Moody Lie algebras. One crucial ingredient in the proof is the action of Virasoro algebra via the Goddard-Kent-Olive construction on the tensor product V(λ) ⊗ V(µ). Then\, we prove the corresponding geometr ic results including the higher cohomology vanishing on the G-Schubert var ieties in the product partial flag variety G/P × G/P with coefficients in certain sheaves coming from the ideal sheaves of G-sub Schubert varieties . This allows us to prove the surjectivity of the Gaussian map.\n LOCATION:https://researchseminars.org/talk/SAGO/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuhua He (Chinese University of Hong Kong) DTSTART:20210805T053000Z DTEND:20210805T070000Z DTSTAMP:20260412T170811Z UID:SAGO/7 DESCRIPTION:Title: Tit s groups of Iwahori-Weyl groups and presentations of Hecke algebras\nb y Xuhua He (Chinese University of Hong Kong) as part of Algebra Seminar (p resented by SMRI)\n\n\nAbstract\nLet G(ℂ) be a complex reductive group a nd W be its Weyl group. In 1966\, Tits introduced a certain subgroup of G( ℂ)\, which is an extension of W by an elementary abelian 𝟸-group. Thi s group is called the Tits group and provides a nice lifting of W. In thi s talk\, I will discuss a generalization of the notion of the Tits group 𝒯 to a reductive p-adic group G. Such 𝒯\, if exists\, gives a nice l ifting of the Iwahori-Weyl group of G. I will show that the Tits group exi sts when the reductive group splits over an unramified extension of the p- adic field and will provide an example in the ramified case that such a Ti ts group does not exist. Finally\, as an application\, we will provide a n ice presentation of the Hecke algebra of the p-adic group G with In-level structure. Based on the recent joint work with Ganapathy (arXiv:2107.0176 8).\n LOCATION:https://researchseminars.org/talk/SAGO/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lauren K. Williams (Harvard University) DTSTART:20210819T000000Z DTEND:20210819T010000Z DTSTAMP:20260412T170811Z UID:SAGO/8 DESCRIPTION:Title: Sch ubert polynomials\, the inhomogeneous TASEP\, and evil-avoiding permutatio ns\nby Lauren K. Williams (Harvard University) as part of Algebra Semi nar (presented by SMRI)\n\n\nAbstract\nThe totally asymmetric simple exclu sion process (TASEP) was introduced around 1970 as a model for translation in protein synthesis and traffic flow. It has interesting physical proper ties (e.g. boundary-induced phase transitions) and also beautiful mathemat ical properties. The inhomogeneous TASEP is a Markov chain of weighted par ticles hopping on a ring\, in which the probability that two particles int erchange depends on the weight of those particles. If each particle has a distinct weight\, then we can think of this as a Markov chain on permutati ons. In many cases\, the steady state probabilities can be expressed in te rms of Schubert polynomials. Based on joint work with Donghyun Kim.\n LOCATION:https://researchseminars.org/talk/SAGO/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hankyung Ko (Uppsala University) DTSTART:20210826T053000Z DTEND:20210826T070000Z DTSTAMP:20260412T170811Z UID:SAGO/9 DESCRIPTION:Title: A s ingular Coxeter presentation\nby Hankyung Ko (Uppsala University) as p art of Algebra Seminar (presented by SMRI)\n\n\nAbstract\nSMRI Algebra and Geometry Online\n’A singular Coxeter presentation’\nHankyung Ko (Upps ala University)\n\nThursday\, Aug 26\n3:30pm-5:30pm (AEST)\nRegister: \nht tps://uni-sydney.zoom.us/meeting/register/tZYqcO2uqDkpE9DpzrQ6bJCXU2M0pdUM Xo-k \n\nAbstract: A Coxeter system is a presentation of a group by genera tors and a specific \nform of relations\, namely the braid relations and t he reflection relations. The \nCoxeter presentation leads to\, among other s\, a similar presentation of the \n(Iwahori-)Hecke algebras and the Kazhd an-Lusztig theory\, which provides combinatorial \nanswers to major proble ms in Lie theoretic representation theory and geometry. \nExtending such a pplications to the `singular land’ requires the singular version of \nth e Hecke algebra. Underlying combinatorics of the singular Hecke algebra/ca tegory \ncomes from the parabolic double cosets and is the first step in u nderstanding the \nsingular Hecke category. In this talk\, I will present a Coxeter theory of the \nparabolic double cosets developed in a joint wor k with Ben Elias. In particular\, I \nwill explain a generalization of the reduced expressions and describe the braid and \nnon-braid relations.\n\n Biography: Hangyung Ko is a postdoc researcher at Matematiska institutione n\, Uppsala \nUniversity\, working on Lie theoretic representation theory. She is mainly interested \nin representation theory of algebraic groups i n positive characteristic\, category O\, \nhigher(categorical) representat ion theory\, and related topics like Coxeter groups \nand their Hecke alge bras\, Soergel bimodules\, quantum groups\, R-matrices and \nK-matrices\, polynomial functors and functor cohomology\, category theory and \nhomolog ical algebra.\n\nNote: These seminars will be recorded\, including partici pant questions (participants \nonly when asking questions)\, and uploaded to the SMRI YouTube Channel \nhttps://www.youtube.com/c/SydneyMathematical ResearchInstituteSMRI \n\nOther upcoming SMRI events can be found here: \n https://mathematical-research-institute.sydney.edu.au/news-events/\n LOCATION:https://researchseminars.org/talk/SAGO/9/ END:VEVENT BEGIN:VEVENT SUMMARY:John Greenlees (University of Warwick) DTSTART:20210916T060000Z DTEND:20210916T073000Z DTSTAMP:20260412T170811Z UID:SAGO/10 DESCRIPTION:Title: Th e singularity category of C^*(BG) for a finite group G\nby John Greenl ees (University of Warwick) as part of Algebra Seminar (presented by SMRI) \n\n\nAbstract\nAbstract: The cohomology ring H^*(BG) (with coefficients i n a field k of characteristic p) is a very special graded commutative ring \, but this comes out much more clearly if one uses the cochains C^*(BG)\ , which can be viewed as a commutative ring up to homotopy. For example C ^*(BG) is always Gorenstein (whilst this is not quite true for H^*(BG)). \ n\nThis leads one to study C^*(BG) as if it was a commutative local Noethe rian ring\, though of course one has to use homotopy invariant methods. Th e ring C^*(BG) is regular if and only if G is p-nilpotent and so it is nat ural to look for ways of deciding where C^*(BG) lies on the spectrum betwe en regular and Gorenstein rings. For a commutative Noetherian ring\, one c onsiders the singularity category D_{sg}(R) (the quotient of finite comple xes of finitely generated modules by finitely generated projectives). This is trivial if and only if R is regular\, so is the appropriate tool. The talk will describe how to define this for C^*(BG)\, show it has good basic properties and describe the singularity category in the simplest case it is not trivial (when G has a cyclic Sylow p-subgroup).\n LOCATION:https://researchseminars.org/talk/SAGO/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Giles Gardam (University of Münster) DTSTART:20211005T050000Z DTEND:20211005T063000Z DTSTAMP:20260412T170811Z UID:SAGO/11 DESCRIPTION:Title: So lving semidecidable problems in group theory\nby Giles Gardam (Univers ity of Münster) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstr act\nGroup theory is littered with undecidable problems. A classic example is the word problem: there are groups for which there exists no algorithm that can decide if a product of generators represents the trivial element or not. Many problems (the word problem included) are at least semidecida ble\, meaning that there is a correct algorithm guaranteed to terminate if the answer is "yes"\, but with no guarantee on how long one has to wait. I will discuss strategies to try and tackle various semidecidable problems computationally with the key example being the discovery of a counterexam ple to the Kaplansky unit conjecture.\n\nBiography: Giles Gardam is a rese arch associate at the University of Münster working in geometric group th eory. He studied mathematics and computer science at the University of Syd ney\, receiving his Bachelor's degree in 2012\, and completed his doctorat e at Oxford in 2017. He was then a postdoc at the Technion before starting at Münster in 2019.\n LOCATION:https://researchseminars.org/talk/SAGO/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Kamnitzer (University of Toronto) DTSTART:20211020T230000Z DTEND:20211021T003000Z DTSTAMP:20260412T170811Z UID:SAGO/12 DESCRIPTION:Title: Sy mplectic duality and (generalized) affine Grassmannian slices\nby Joel Kamnitzer (University of Toronto) as part of Algebra Seminar (presented b y SMRI)\n\n\nAbstract\nUnder the geometric Satake equivalence\, slices in the affine Grassmannian give\na geometric incarnation of dominant weight s paces in representations of reductive\ngroups. These affine Grassmannian slices are quantized by algebras known as truncated\nshifted Yangians. Fr om this perspective\, we expect to categorify these weight spaces\nusing c ategory O for these truncated shifted Yangians. \n\nThe slices in the aff ine Grassmannian and truncated shifted Yangians can also be defined\nas sp ecial cases of the Coulomb branch construction of Braverman-Finkelberg-Nak ajima.\nFrom this perspective\, we find many insights. First\, we can gen eralize affine\nGrassmannian slices to the case of non-dominant weights an d arbitrary symmetric\nKac-Moody Lie algebras. Second\, we establish a li nk with modules for KLRW algebras.\nFinally\, we defined a categorical g-a ction on the categories O\, using Hamiltonian\nreduction.\n LOCATION:https://researchseminars.org/talk/SAGO/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Morava (Johns Hopkins University) DTSTART:20211110T230000Z DTEND:20211111T003000Z DTSTAMP:20260412T170811Z UID:SAGO/13 DESCRIPTION:Title: On the group completion of the Burau representation\nby Jack Morava (Joh ns Hopkins University) as part of Algebra Seminar (presented by SMRI)\n\n\ nAbstract\nOn fundamental groups\, the discriminant \\prod_{i \\neq k} (z_ i - z_k) \\in \\C^\\times of a finite collection of points of the plane de fines the abelianization homomorphism sending a braid to its number of ove rcrossings less undercrossings or writhe. In terms of diffeomorphisms of t he punctured plane\, it defines a kind of `invertible topological quantum field theory' associated to the Burau representation\, and in the classica l physics of point particles the real part of its logarithmic derivative i s the potential energy of a collection of Coulomb charges\, while its imag inary part is essentially the Nambu-Goto area of a loop of string in the t hree-sphere. \n \nIts higher homotopy theory defines a very interesting a double-loop map \n\\Z \\times \\Omega^2 S^3 \\to \\Pic(S^0)\nto the cate gory of lines over the stable homotopy ring-spectrum\, related to Hopkins and Mahowald's exotic (E_2) multiplication on classical integral homology\ , perhaps related to the `anyons' of nonclassical physics.\n\n(based on jo int work with D Rolfsen)\n LOCATION:https://researchseminars.org/talk/SAGO/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Shane Kelly (Tokyo Institute of Technology) DTSTART:20211202T040000Z DTEND:20211202T053000Z DTSTAMP:20260412T170811Z UID:SAGO/14 DESCRIPTION:Title: Bl owup formulas for nilpotent sensitive cohomology theories\nby Shane Ke lly (Tokyo Institute of Technology) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstract\nThis is joint work in progress with Shuji Saito. M any cohomology theories of interest (l-adic cohomology\, de Rham cohomolog y\, motivic cohomology\, K-theory...) have long exact sequences associated to blowups. Such a property can be neatly encoded in a Grothendieck topol ogy such as the cdh-topology or the h-topology. These topologies appeared in Voevodsky's proof of the Bloch-Kato conjecture\, and more recently in B eilinson's simple proof of Fontaine's CdR conjecture\, and in Bhatt and Sc holze's work on projectivity of the affine Grassmanian.\n\nA feature of th ese topologies which often turns out to be a bug is that the associated sh eaves cannot see nilpotents. In this talk I will discuss a modification wh ich can see nilpotents\, and which still has long exact sequences for many blowups.\n LOCATION:https://researchseminars.org/talk/SAGO/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Sang-hyun Kim (Korea Institute for Advanced Study) DTSTART:20220302T020000Z DTEND:20220302T033000Z DTSTAMP:20260412T170811Z UID:SAGO/15 DESCRIPTION:Title: Op timal regularity of mapping class group actions on the circle\nby Sang -hyun Kim (Korea Institute for Advanced Study) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstract\nWe prove that for each finite index sub group H of the mapping class group of a \nclosed hyperbolic surface\, and for each real number r>1 there does not exist a faithful \nC^r-action (in Hoelder’s sense) of H on a circle. For this\, we partially determine the \noptimal regularity of faithful actions by right-angled Artin groups on a circle. (Joint \nwith Thomas Koberda and Cristobal Rivas).\n LOCATION:https://researchseminars.org/talk/SAGO/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Vazirani (University of California\, Davis)) DTSTART:20220414T000000Z DTEND:20220414T013000Z DTSTAMP:20260412T170811Z UID:SAGO/16 DESCRIPTION:Title: Fr om representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra\nby Monica Vazirani (Universit y of California\, Davis)) as part of Algebra Seminar (presented by SMRI)\n \nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/SAGO/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Donovan (Tsinghua University) DTSTART:20220923T020000Z DTEND:20220923T030000Z DTSTAMP:20260412T170811Z UID:SAGO/17 DESCRIPTION:Title: Ho mological comparison of resolution and smoothing\nby Will Donovan (Tsi nghua University) as part of Algebra Seminar (presented by SMRI)\n\nLectur e held in Carslaw 173.\n\nAbstract\nAbstract: A singular space often comes equipped with (1) a resolution\, given by a morphism from a smooth space\ , and (2) a smoothing\, namely a deformation with smooth generic fibre. I will discuss work in progress on how these may be related homologically\, starting with the threefold ordinary double point as a key example.\n LOCATION:https://researchseminars.org/talk/SAGO/17/ END:VEVENT END:VCALENDAR