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:20260404T094547Z UID:SAGO/1 DESCRIPTION:Title: Characters 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 SM RI)\n\n\nAbstract\nMonica Nevins (University of Ottawa)\n\nFriday 26th Feb ruary\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 (Chi na))\n\nOnline via Zoom\n\nAbstract: The theory of complex representations of p-adic groups can feel very technical and unwelcoming\, but its centra l 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 le ns of restricting these representations to maximal compact open subgroups. Our point of departure: the Bruhat-Tits building of G\, a 50-year-old com binatorial and geometric object that continues to reveal secrets about the structure and representation theory of G today.\n\nRegister here: https:/ /uni-sydney.zoom.us/meeting/register/tZUrd--uqj0iHNcugXMnXTmSQfZVh08zruaN\ n LOCATION:https://stable.researchseminars.org/talk/SAGO/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Shun-Jen Cheng (Institute of Mathematics\, Academia Sinica) DTSTART:20210506T053000Z DTEND:20210506T070000Z DTSTAMP:20260404T094547Z UID:SAGO/2 DESCRIPTION:Title: ‘Representation theory of exceptional Lie superalgebras\nby Shun -Jen Cheng (Institute of Mathematics\, Academia Sinica) as part of Algebra Seminar (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SAGO/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Magdalena Boos (Ruhr-University Bochum) DTSTART:20210617T053000Z DTEND:20210617T070000Z DTSTAMP:20260404T094547Z UID:SAGO/3 DESCRIPTION:Title: Advertising symmetric quivers and their representations\nby Magdal ena Boos (Ruhr-University Bochum) as part of Algebra Seminar (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SAGO/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Gus Lonergan (A Priori Investment Management LLC) DTSTART:20210623T230000Z DTEND:20210624T003000Z DTSTAMP:20260404T094547Z UID:SAGO/4 DESCRIPTION:Title: 'Geometric Satake over KU'\nby Gus Lonergan (A Priori Investment M anagement LLC) as part of Algebra Seminar (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SAGO/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulrich Thiel (University of Kaiserslautern) DTSTART:20210708T053000Z DTEND:20210708T070000Z DTSTAMP:20260404T094547Z UID:SAGO/5 DESCRIPTION:Title: Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution\nby Ulrich Thiel (University of Kai serslautern) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstract\ nAbstract: Over the past two decades\, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently\, crepant) resolution of singularities. The cla ssification is almost complete but there is an infinite series of groups i n dimension 4 - the symplectically primitive but complex imprimitive group s - and 10 exceptional groups up to dimension 10\, for which it is still o pen. Recently\, we have proven that for all but possibly 39 cases in the r emaining infinite series there is no symplectic resolution. We have thereb y reduced the classification problem to finitely many open cases. We do no t expect any of the remaining cases to admit a symplectic resolution. This is joint work with Gwyn Bellamy and Johannes Schmitt.\n LOCATION:https://stable.researchseminars.org/talk/SAGO/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shrawan Kumar (University of North Carolina) DTSTART:20210723T010000Z DTEND:20210723T023000Z DTSTAMP:20260404T094547Z UID:SAGO/6 DESCRIPTION:Title: Root components for tensor product of affine Kac-Moody Lie algebra mod ules\nby Shrawan Kumar (University of North Carolina) as part of Algeb ra Seminar (presented by SMRI)\n\n\nAbstract\nThis is a joint work with Sa muel Jeralds. Let gg be an affine Kac-Moody Lie algebra and let λ\, µ be two dominant integral weights for g. We prove that under some mild restri ction\, 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 (irre ducible) g-module with highest weight λ. This extends the corresponding r esult by 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 geometric results including the higher cohomology vanishing on the G-Schub ert varieties in the product partial flag variety G/P × G/P with coeffici ents in certain sheaves coming from the ideal sheaves of G-sub Schubert va rieties. This allows us to prove the surjectivity of the Gaussian map.\n LOCATION:https://stable.researchseminars.org/talk/SAGO/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuhua He (Chinese University of Hong Kong) DTSTART:20210805T053000Z DTEND:20210805T070000Z DTSTAMP:20260404T094547Z UID:SAGO/7 DESCRIPTION:Title: Tits groups of Iwahori-Weyl groups and presentations of Hecke algebras \nby Xuhua He (Chinese University of Hong Kong) as part of Algebra Sem inar (presented by SMRI)\n\n\nAbstract\nLet G(ℂ) be a complex reductive group and W be its Weyl group. In 1966\, Tits introduced a certain subgrou p of G(ℂ)\, which is an extension of W by an elementary abelian 𝟸-gro up. This group is called the Tits group and provides a nice lifting of W. In this 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 lifting of the Iwahori-Weyl group of G. I will show that the Tits gro up exists when the reductive group splits over an unramified extension of the p-adic field and will provide an example in the ramified case that suc h a Tits group does not exist. Finally\, as an application\, we will provi de a nice presentation of the Hecke algebra of the p-adic group G with In- level structure. Based on the recent joint work with Ganapathy (arXiv:210 7.01768).\n LOCATION:https://stable.researchseminars.org/talk/SAGO/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Lauren K. Williams (Harvard University) DTSTART:20210819T000000Z DTEND:20210819T010000Z DTSTAMP:20260404T094547Z UID:SAGO/8 DESCRIPTION:Title: Schubert polynomials\, the inhomogeneous TASEP\, and evil-avoiding per mutations\nby Lauren K. Williams (Harvard University) as part of Algeb ra Seminar (presented by SMRI)\n\n\nAbstract\nThe totally asymmetric simpl e exclusion process (TASEP) was introduced around 1970 as a model for tran slation in protein synthesis and traffic flow. It has interesting physical properties (e.g. boundary-induced phase transitions) and also beautiful m athematical properties. The inhomogeneous TASEP is a Markov chain of weigh ted particles hopping on a ring\, in which the probability that two partic les interchange 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 pe rmutations. In many cases\, the steady state probabilities can be expresse d in terms of Schubert polynomials. Based on joint work with Donghyun Kim. \n LOCATION:https://stable.researchseminars.org/talk/SAGO/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hankyung Ko (Uppsala University) DTSTART:20210826T053000Z DTEND:20210826T070000Z DTSTAMP:20260404T094547Z UID:SAGO/9 DESCRIPTION:Title: A singular Coxeter presentation\nby Hankyung Ko (Uppsala Universit y) as part of Algebra Seminar (presented by SMRI)\n\n\nAbstract\nSMRI Alge bra and Geometry Online\n’A singular Coxeter presentation’\nHankyung K o (Uppsala University)\n\nThursday\, Aug 26\n3:30pm-5:30pm (AEST)\nRegiste r: \nhttps://uni-sydney.zoom.us/meeting/register/tZYqcO2uqDkpE9DpzrQ6bJCXU 2M0pdUMXo-k \n\nAbstract: A Coxeter system is a presentation of a group by generators and a specific \nform of relations\, namely the braid relation s and the reflection relations. The \nCoxeter presentation leads to\, amon g others\, a similar presentation of the \n(Iwahori-)Hecke algebras and th e Kazhdan-Lusztig theory\, which provides combinatorial \nanswers to major problems in Lie theoretic representation theory and geometry. \nExtending such applications to the `singular land’ requires the singular version of \nthe Hecke algebra. Underlying combinatorics of the singular Hecke alg ebra/category \ncomes from the parabolic double cosets and is the first st ep in understanding the \nsingular Hecke category. In this talk\, I will p resent a Coxeter theory of the \nparabolic double cosets developed in a jo int work with Ben Elias. In particular\, I \nwill explain a generalization of the reduced expressions and describe the braid and \nnon-braid relatio ns.\n\nBiography: Hangyung Ko is a postdoc researcher at Matematiska insti tutionen\, Uppsala \nUniversity\, working on Lie theoretic representation theory. She is mainly interested \nin representation theory of algebraic g roups in positive characteristic\, category O\, \nhigher(categorical) repr esentation theory\, and related topics like Coxeter groups \nand their Hec ke algebras\, Soergel bimodules\, quantum groups\, R-matrices and \nK-matr ices\, polynomial functors and functor cohomology\, category theory and \n homological algebra.\n\nNote: These seminars will be recorded\, including participant questions (participants \nonly when asking questions)\, and up loaded to the SMRI YouTube Channel \nhttps://www.youtube.com/c/SydneyMathe maticalResearchInstituteSMRI \n\nOther upcoming SMRI events can be found h ere: \nhttps://mathematical-research-institute.sydney.edu.au/news-events/\ n LOCATION:https://stable.researchseminars.org/talk/SAGO/9/ END:VEVENT BEGIN:VEVENT SUMMARY:John Greenlees (University of Warwick) DTSTART:20210916T060000Z DTEND:20210916T073000Z DTSTAMP:20260404T094547Z UID:SAGO/10 DESCRIPTION:Title: The singularity category of C^*(BG) for a finite group G\nby John Greenlees (University of Warwick) as part of Algebra Seminar (presented b y SMRI)\n\n\nAbstract\nAbstract: The cohomology ring H^*(BG) (with coeffic ients in a field k of characteristic p) is a very special graded commutati ve 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 ex ample 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 Noetherian ring\, though of course one has to use homotopy invariant meth ods. The ring C^*(BG) is regular if and only if G is p-nilpotent and so it is natural to look for ways of deciding where C^*(BG) lies on the spectru m between regular and Gorenstein rings. For a commutative Noetherian ring\ , one considers the singularity category D_{sg}(R) (the quotient of finite complexes of finitely generated modules by finitely generated projectives ). This is trivial if and only if R is regular\, so is the appropriate too l. The talk will describe how to define this for C^*(BG)\, show it has goo d basic properties and describe the singularity category in the simplest c ase it is not trivial (when G has a cyclic Sylow p-subgroup).\n LOCATION:https://stable.researchseminars.org/talk/SAGO/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Giles Gardam (University of Münster) DTSTART:20211005T050000Z DTEND:20211005T063000Z DTSTAMP:20260404T094547Z UID:SAGO/11 DESCRIPTION:Title: Solving semidecidable problems in group theory\nby Giles Gardam ( University of Münster) as part of Algebra Seminar (presented by SMRI)\n\n \nAbstract\nGroup theory is littered with undecidable problems. A classic example is the word problem: there are groups for which there exists no al gorithm that can decide if a product of generators represents the trivial element or not. Many problems (the word problem included) are at least sem idecidable\, meaning that there is a correct algorithm guaranteed to termi nate 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 p roblems computationally with the key example being the discovery of a coun terexample to the Kaplansky unit conjecture.\n\nBiography: Giles Gardam is a research associate at the University of Münster working in geometric g roup theory. He studied mathematics and computer science at the University of Sydney\, receiving his Bachelor's degree in 2012\, and completed his d octorate at Oxford in 2017. He was then a postdoc at the Technion before s tarting at Münster in 2019.\n LOCATION:https://stable.researchseminars.org/talk/SAGO/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Kamnitzer (University of Toronto) DTSTART:20211020T230000Z DTEND:20211021T003000Z DTSTAMP:20260404T094547Z UID:SAGO/12 DESCRIPTION:Title: Symplectic duality and (generalized) affine Grassmannian slices\n by Joel Kamnitzer (University of Toronto) as part of Algebra Seminar (pres ented by SMRI)\n\n\nAbstract\nUnder the geometric Satake equivalence\, sli ces in the affine Grassmannian give\na geometric incarnation of dominant w eight spaces in representations of reductive\ngroups. These affine Grassm annian slices are quantized by algebras known as truncated\nshifted Yangia ns. From this perspective\, we expect to categorify these weight spaces\n using category O for these truncated shifted Yangians. \n\nThe slices in the affine Grassmannian and truncated shifted Yangians can also be defined \nas special cases of the Coulomb branch construction of Braverman-Finkelb erg-Nakajima.\nFrom this perspective\, we find many insights. First\, we can generalize affine\nGrassmannian slices to the case of non-dominant wei ghts and arbitrary symmetric\nKac-Moody Lie algebras. Second\, we establi sh a link with modules for KLRW algebras.\nFinally\, we defined a categori cal g-action on the categories O\, using Hamiltonian\nreduction.\n LOCATION:https://stable.researchseminars.org/talk/SAGO/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Jack Morava (Johns Hopkins University) DTSTART:20211110T230000Z DTEND:20211111T003000Z DTSTAMP:20260404T094547Z UID:SAGO/13 DESCRIPTION:Title: On the group completion of the Burau representation\nby Jack Mora va (Johns Hopkins University) as part of Algebra Seminar (presented by SMR I)\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 p lane defines the abelianization homomorphism sending a braid to its number of overcrossings less undercrossings or writhe. In terms of diffeomorphis ms of the punctured plane\, it defines a kind of `invertible topological q uantum field theory' associated to the Burau representation\, and in the c lassical physics of point particles the real part of its logarithmic deriv ative is the potential energy of a collection of Coulomb charges\, while i ts imaginary part is essentially the Nambu-Goto area of a loop of string i n the three-sphere. \n \nIts higher homotopy theory defines a very interes ting a double-loop map \n\\Z \\times \\Omega^2 S^3 \\to \\Pic(S^0)\nto t he category of lines over the stable homotopy ring-spectrum\, related to H opkins and Mahowald's exotic (E_2) multiplication on classical integral ho mology\, perhaps related to the `anyons' of nonclassical physics.\n\n(base d on joint work with D Rolfsen)\n LOCATION:https://stable.researchseminars.org/talk/SAGO/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Shane Kelly (Tokyo Institute of Technology) DTSTART:20211202T040000Z DTEND:20211202T053000Z DTSTAMP:20260404T094547Z UID:SAGO/14 DESCRIPTION:Title: Blowup formulas for nilpotent sensitive cohomology theories\nby S hane Kelly (Tokyo Institute of Technology) as part of Algebra Seminar (pre sented by SMRI)\n\n\nAbstract\nThis is joint work in progress with Shuji S aito. Many cohomology theories of interest (l-adic cohomology\, de Rham co homology\, motivic cohomology\, K-theory...) have long exact sequences ass ociated to blowups. Such a property can be neatly encoded in a Grothendiec k topology such as the cdh-topology or the h-topology. These topologies ap peared in Voevodsky's proof of the Bloch-Kato conjecture\, and more recent ly in Beilinson's simple proof of Fontaine's CdR conjecture\, and in Bhatt and Scholze's work on projectivity of the affine Grassmanian.\n\nA featur e of these topologies which often turns out to be a bug is that the associ ated sheaves cannot see nilpotents. In this talk I will discuss a modifica tion which can see nilpotents\, and which still has long exact sequences f or many blowups.\n LOCATION:https://stable.researchseminars.org/talk/SAGO/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Sang-hyun Kim (Korea Institute for Advanced Study) DTSTART:20220302T020000Z DTEND:20220302T033000Z DTSTAMP:20260404T094547Z UID:SAGO/15 DESCRIPTION:Title: Optimal regularity of mapping class group actions on the circle\n by Sang-hyun Kim (Korea Institute for Advanced Study) as part of Algebra S eminar (presented by SMRI)\n\n\nAbstract\nWe prove that for each finite in dex subgroup 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-acti on (in Hoelder’s sense) of H on a circle. For this\, we partially determ ine the \noptimal regularity of faithful actions by right-angled Artin gro ups on a circle. (Joint \nwith Thomas Koberda and Cristobal Rivas).\n LOCATION:https://stable.researchseminars.org/talk/SAGO/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Monica Vazirani (University of California\, Davis)) DTSTART:20220414T000000Z DTEND:20220414T013000Z DTSTAMP:20260404T094547Z UID:SAGO/16 DESCRIPTION:Title: From representations of the rational Cherednik algebra to parabolic H ilbert schemes via the Dunkl-Opdam subalgebra\nby Monica Vazirani (Un iversity of California\, Davis)) as part of Algebra Seminar (presented by SMRI)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/SAGO/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Donovan (Tsinghua University) DTSTART:20220923T020000Z DTEND:20220923T030000Z DTSTAMP:20260404T094547Z UID:SAGO/17 DESCRIPTION:Title: Homological comparison of resolution and smoothing\nby Will Donov an (Tsinghua University) as part of Algebra Seminar (presented by SMRI)\n\ nLecture held in Carslaw 173.\n\nAbstract\nAbstract: A singular space ofte n comes equipped with (1) a resolution\, given by a morphism from a smooth space\, and (2) a smoothing\, namely a deformation with smooth generic fi bre. I will discuss work in progress on how these may be related homologic ally\, starting with the threefold ordinary double point as a key example. \n LOCATION:https://stable.researchseminars.org/talk/SAGO/17/ END:VEVENT END:VCALENDAR