BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joseph Bernstein (Tel Aviv University) DTSTART:20210425T153000Z DTEND:20210425T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/1 DESCRIPTION:Title: Remark on rigidity in Lie theory (joint with Ed Shpiz)< /a>\nby Joseph Bernstein (Tel Aviv University) as part of Springfest in ho nor of Vera Serganova\n\n\nAbstract\nLet g be a finite dimensional Lie alg ebra over a field k of characteristic 0\,\ni.e. it is a pair (L\, b) of a vector space L and a bracket operation b. \n\n A proof of the PBW theorem is usually based on a construction of a representation p of the\nLie alge bra g by derivations of the algebra F=F(L) of formal functions on the spa ce L\,\nthat lifts to a faithful representation of the universal envelopin g algebra U(g).\n\n It turns out that one can choose such representation in a canonical way.\nI will discuss how one can describe this canonical re presentation.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Finkelberg (National Research University Higher School of Economics) DTSTART:20210426T153000Z DTEND:20210426T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/2 DESCRIPTION:Title: Gaiotto conjecture on quantum geometric Satake for quan tum supergroups\nby Michael Finkelberg (National Research University H igher School of Economics) as part of Springfest in honor of Vera Serganov a\n\n\nAbstract\nThis is a joint work with Roman Travkin and Alexander Bra verman. D.Gaiotto conjectured that the category of finite dimensional repr esentations of U_q(gl(N-1|N)) is equivalent to the category of q-monodromi c GL(N-1\,C[[t]])-equivariant perverse sheaves on the determinant line bun dle on the affine Grassmannian of GL(N). I will explain an approach to thi s via the category of factorizable sheaves.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Kac (MIT) DTSTART:20210426T181500Z DTEND:20210426T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/3 DESCRIPTION:Title: Cyclic elements and applications\nby Victor Kac (MI T) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nBasic r esults on cyclic elements in simple Lie algebras will be explained\, along with some applications\, including normal forms of nilpotent elements and integrability of classical affine W-algebras.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Coulembier (University of Sydney) DTSTART:20210427T080000Z DTEND:20210427T090000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/4 DESCRIPTION:Title: Beyond abelian envelopes\nby Kevin Coulembier (Univ ersity of Sydney) as part of Springfest in honor of Vera Serganova\n\n\nAb stract\nWe will give a short overview of the motivation for and main examp les of abelian envelopes of rigid monoidal categories. Then we will introd uce a theory which generalises abelian envelopes and is applicable to any rigid monoidal category.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Iryna Kashuba (University of Sao Paulo) DTSTART:20210427T170000Z DTEND:20210427T180000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/5 DESCRIPTION:Title: Representation type of Jordan algebras and superalgebra s\nby Iryna Kashuba (University of Sao Paulo) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nWe will review recent and classica l results on the representations of finite dimensional Jordan algebras and superalgebras. We will weigh the pros against the cons of using the Tits- Kantor-Koecher construction for this problem.\n\nJoint with Representation Theory and Mathematical Physics Seminar\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Volodymyr Mazorchuk (Uppsala University) DTSTART:20210428T153000Z DTEND:20210428T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/6 DESCRIPTION:Title: Simple modules for Lie algebras and superalgebras\n by Volodymyr Mazorchuk (Uppsala University) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nIn this talk I will try to survey the st ate of the art for the problem of classification of simple modules for com plex Lie algebras and superalgebras. The main emphasis will be on some rec ent techniques and results on how to reduce the Lie superalgebra problem t o the Lie algebra problem.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Pevtsova (University of Washington) DTSTART:20210428T181500Z DTEND:20210428T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/7 DESCRIPTION:Title: Support and tensor product property for integrable Hopf algebras\nby Julia Pevtsova (University of Washington) as part of Spr ingfest in honor of Vera Serganova\n\n\nAbstract\nI’ll describe the hype rsurface approach to the theory of support varieties for finite dimensiona l Hopf algebras. The idea comes from commutative algebra going back to the work of Eisenbud\, Avramov-Buchweitz and Avramov-Iyengar. It has been rec ently implemented in two different non-commutative contexts: finite superg roup schemes in a joint project with D. Benson\, S. Iyengar and H. Krause and non-braided settings such as small quantum borels in a joint project w ith C. Negron.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Thorsten Heidersdorf (University of Bonn) DTSTART:20210429T153000Z DTEND:20210429T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/8 DESCRIPTION:Title: Character formulas and the DS functor\nby Thorsten Heidersdorf (University of Bonn) as part of Springfest in honor of Vera Se rganova\n\n\nAbstract\nI will report on joint work with Maria Gorelik on o btaining good character formulas for irreducible representations of Lie su peralgebras in terms of Euler characters. We prove a formula relating the Euler characters to Kac-Wakimoto terms and determine the image of super ve rsions of the Euler characters under the functor ds induced by the Duflo-S erganova functor DS on the supercharacter ring.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jon Brundan (University of Oregon) DTSTART:20210429T181500Z DTEND:20210429T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/9 DESCRIPTION:Title: Okounkov-Vershik approach to representations of the par tition category\nby Jon Brundan (University of Oregon) as part of Spri ngfest in honor of Vera Serganova\n\n\nAbstract\nI will report on joint wo rk with Max Vargas revisiting the representation theory of the partition c ategory. Our approach is similar in spirit to the Okounkov-Vershik approac h to representation theory of symmetric groups\, with the Jucys-Murphy ele ments replaced by Enyang-Jucys-Murphy elements. Our techniques recover all of the results of Comes and Ostrik from their work on the Deligne categor y Rep(S_t)\, and we can do a little bit more besides.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Yasmine Fittouhi and Anthony Joseph (Weizmann Institute of Science ) DTSTART:20210503T153000Z DTEND:20210503T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/10 DESCRIPTION:Title: Components of the nilfibre in type $A$ for Parabolic A ction\nby Yasmine Fittouhi and Anthony Joseph (Weizmann Institute of S cience) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nLe t $G$ be a simple algebraic group\, $P$ a parabolic subgroup and $\\mathfr ak m$ the nilradical of its Lie algebra $\\mathfrak p$. A theorem of Richa rdson says that $P$ has a dense orbit in $\\mathfrak m$.\n\nAs a consequen ce the invariant algebra $\\mathbb C[\\mathfrak m]^{P'}$ is polynomial. Th us one may ask if this action admits a Weierstrass section\, that is to sa y a linear subvariety $e+V$ of $\\mathfrak m$ such that restriction of inv ariants defines an isomorphism onto $\\mathbb C[e+V]$.\nIn type $A$\, a pr oposal for the generators was given by Benlolo and Sanderson and verified by Joseph and Melnikov. \n\nIn previous work this was used to construct a Weierstrass section (in type $A$) but by heavy combinatorics. \nThe nilfi bre $\\mathscr N$ (for this action) is the zero set in $\\mathfrak m$ of $ \\mathbb C[\\mathfrak m]^{P'}_+$. It is generally not irreducible. \nFro m the computed Weierstrass section we obtained a ``canonical'' component o f $\\mathscr N$ and show it to be a ``B saturation set''.\nHere it is sugg ested that the remaining components take a similar form and in turn lead t o further non-equivalent Weierstrass sections.\nHopefully this will be a t emplate for constructing Weierstrass sections in general type. \nPrelimina ry computations are reported.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Etingof (MIT) DTSTART:20210503T181500Z DTEND:20210503T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/11 DESCRIPTION:Title: New examples of incompressible symmetric tensor catego ries in positive characteristic\nby Pavel Etingof (MIT) as part of Spr ingfest in honor of Vera Serganova\n\n\nAbstract\nI'll describe generaliza tions ${\\rm Ver}_{p^n}$\, ${\\rm Ver}_{p^n}^+$ of the incompressible abel ian symmetric tensor categories defined in my joint work with D. Benson (a rXiv:1807.05549) for $p=2$ and by Gelfand-Kazhdan and Georgiev-Mathieu in 1990s for $n=1$. Namely\, ${\\rm Ver}_{p^n}$ is the abelian envelope of th e quotient of the category of tilting modules for $SL_2(\\bf k)$ by the $n $-th Steinberg module\, and ${\\rm Ver}_{p^n}^+$ is its subcategory genera ted by $PGL_2(\\bf k)$-modules. The categories ${\\rm Ver}_{p^n}$ are redu ctions to characteristic $p$ of Verlinde braided tensor categories in char acteristic zero\, which explains the notation. I will try to describe the structure of these categories in detail\, and in particular explain that t hey categorify the real cyclotomic rings $\\mathbb{Z}[2\\cos(2\\pi/p^n)]$\ , and that ${\\rm Ver}_{p^n}$ embeds into ${\\rm Ver}_{p^{n+1}}$. We conje cture that every symmetric tensor category of moderate growth over $\\bf k $ admits a fiber functor to the union ${\\rm Ver}_{p^\\infty}$ of the nest ed sequence ${\\rm Ver}_{p}\\subset {\\rm Ver}_{p^2}\\subset\\cdots$. This would provide a positive characteristic analog of Deligne's theorem in ch aracteristic zero and a generalization of the result of arXiv:1503.01492\, which shows that this conjecture holds for fusion categories (in which ca se the fiber functor lands in ${\\rm Ver}_p$). This is joint work with D. Benson and V. Ostrik.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Penkov (Jacobs University Bremen) DTSTART:20210504T153000Z DTEND:20210504T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/12 DESCRIPTION:Title: Bounded weight modules at infinity\nby Ivan Penkov (Jacobs University Bremen) as part of Springfest in honor of Vera Sergano va\n\n\nAbstract\nIn this talk\, I present a recent classification of sim ple bounded weight modules for the Lie algebras $sl(\\infty)$\, $o(\\infty )$\, $sp(\\infty)$ (joint work with D. Grantcharov\, exploiting an unpubli shed idea of I. Dimitrov) and will discuss their primitive ideals (bounded primitive ideals). I will also present some results from a current joint work with D. Grantcharov and V. Serganova on the category of simple bounde d weight modules for the Lie superalgebra $osp(n|m)$ where $m$ or $n$ equa ls $\\infty$.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Ostrik (University of Oregon) DTSTART:20210504T181500Z DTEND:20210504T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/13 DESCRIPTION:Title: Frobenius exact symmetric tensor categories\nby Vi ctor Ostrik (University of Oregon) as part of Springfest in honor of Vera Serganova\n\n\nAbstract\nI will report on a joint work in progress with K. Coulembier and P.Etingof. We give a characterization of symmetric tensor c ategories over fields of positive characteristic which admit an exact tens or functor to the Verlinde category\; in particular we give a characteriza tion of Tannakian categories. A crucial\ningredient of this characterizati on is exactness of the Frobenius twist functor which mimics the Frobenius twist for representations of algebraic groups.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Catharina Stroppel (University of Bonn) DTSTART:20210505T153000Z DTEND:20210505T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/14 DESCRIPTION:Title: Based tilting theory\nby Catharina Stroppel (Unive rsity of Bonn) as part of Springfest in honor of Vera Serganova\n\n\nAbstr act\nIn this talk I would like to talk about based quasihereditary algebra s and generalisations thereof and describe the corresponding theory of til ting modules and Ringel duality\, some kind of based tilting theory. We gi ve a general setup in which one can study both semiinfinite highest weight categories as well as examples of algebras with triangular decompositions . Important examples arise in practise when the notion of highest weight c ategories is weakened to categories with (nice) stratifications. We will i n particular study such categories when the strata are symmetric and descr ibe the relevance to the representation theory.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Vyacheslav Futorny (University of Sao Paulo) DTSTART:20210505T181500Z DTEND:20210505T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/15 DESCRIPTION:Title: Strongly tame Gelfand-Tsetlin modules for Lie (super)a lgebras and vertex algebras ​\nby Vyacheslav Futorny (University of Sao Paulo) as part of Springfest in honor of Vera Serganova\n\n\nAbstract \nFor Lie algebras and superalgebras in type A we will discuss infinite-d imensional simple modules which admit a basis of Gelfand-Tsetlin tableaux and the action via the classical Gelfand-Tsetlin formulas based on recen t joint results with L.E.Ramirez\, V.Serganova and J.Zhang. We will also d escribe the connection with the admissible representations of simple affin e vertex algebras.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Siddhartha Sahi (Rutgers University) DTSTART:20210506T153000Z DTEND:20210506T163000Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/16 DESCRIPTION:Title: Interpolation polynomials\, Capelli operators\, and Li e superalgebras\nby Siddhartha Sahi (Rutgers University) as part of Sp ringfest in honor of Vera Serganova\n\n\nAbstract\nThe interpolation polyn omials are a family of inhomogeneous symmetric polynomials that are charac terized by rather simple vanishing (interpolation) conditions. They were i ntroduced by the speaker in connection with joint work with Bertram Kostan t on the eigenvalues of generalized Capelli-type operators associated to J ordan algebras. Of particular interest is a one parameter subfamily\, whic h was studied by Friedrich Knop and the speaker\, and by Okunkov-Olshanski \, and which is closely related to Jack polynomials and Macdonald polynomi als.\n\nWe will describe two recent developments in this direction. The fi rst set of results is joint work with Hadi Salmasian and Vera Serganova\, which solves the Capelli eigenvalue problem in the setting of Lie superalg ebras and Jordan superalgebras. The second is joint work with Yusra Naqvi and Emily Sergel\, which proves a long-conjectured positivity property of interpolation polynomials.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Arkady Vaintrob (University of Oregon) DTSTART:20210506T181500Z DTEND:20210506T191500Z DTSTAMP:20260404T095120Z UID:SpringfestSerganova/17 DESCRIPTION:Title: Mirror symmetry for invertible singularities\nby A rkady Vaintrob (University of Oregon) as part of Springfest in honor of Ve ra Serganova\n\n\nAbstract\nA cohomological field theory (CohFT) is an alg ebraic structure underlying the properties of the Gromov-Witten invariants and quantum cohomology of projective varieties. For a quasi-homogeneous p olynomial W with an isolated singularity at the origin there are several k nown constructions of CohFTs\, the so-called A- and B- Landau-Ginzburg (LG ) models. The corresponding invariants play a prominent role in various mi rror symmetry correspondences connecting LG models with other kinds of qua ntum invariants. If the polynomial W is invertible (i.e. when the number o f monomials in W is equal to the number of variables)\, then the dual poly nomial W' with the transposed matrix of exponents also has an isolated sin gularity\, and we can talk about relations between LG models for W and W'. Correspondences of this type were first considered by physicists Berglund and Huebsch in the early 1990s\, but their mathematical understanding was developed only recently. I will talk about a joint work with Weyong He\, Alexander Polishchuk\, and Yefeng Shen on a mirror symmetry theorem connec ting a B-model of W and a A-model of W' based\, respectively\, on Saito's theory of primitive forms and on the CohFT constructed in my earlier work with Polishchuk using categories of matrix factorizations.\n LOCATION:https://stable.researchseminars.org/talk/SpringfestSerganova/17/ END:VEVENT END:VCALENDAR