Fifteen years ago\, Boe\, Kujawa and the speaker introduced the concept of detecti ng subalgebras for classical Lie superalgebras. These algebras were constr ucted by using ideas from geometric invariant theory. More recently\, D. G rantcharov\, N. Grantcharov\, Wu and the speaker introduced the concept of a BBW parabolic subalgebra. Given a Lie superalgebra \\({\\mathfrak g}\\) \, one has a triangular decomposition \\({\\mathfrak g}={\\mathfrak n}^{-} \\oplus {\\mathfrak f} \\oplus {\\mathfrak n}^{+}\\) with \\({\\mathfrak b }={\\mathfrak f}\\oplus {\\mathfrak n}^{-}\\) where \\({\\mathfrak f}\\) i s a detecting subalgebra and \\({\\mathfrak b}\\) is a BBW parabolic subal gebra. This holds for all classical "simple" Lie superalgebras\, and one c an view \\({\\mathfrak f}\\) as an analog of the maximal torus\, and \\({\ \mathfrak b}\\) like a Borel subalgebra. This setting also provide a usefu l method to define semisimple elements and nilpotent elements\, and to com pute various sheaf cohomology groups \\(R^{\\bullet}\\text{ind}_{B}^{G} (- )\\).

The goal of my talk is to provide a survey of the main ide as of this new theory and to give indications of the interconnections with in the various parts of this topic. I will also indicate how this treatmen t can further unify the study of the representation theory of classical Li e superalgebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Zaicev (Lomonosov Moscow State University) DTSTART;VALUE=DATE-TIME:20201022T170000Z DTEND;VALUE=DATE-TIME:20201022T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/16 DESCRIPTION:Title: Polynomial identities: anomalies of codimension growth\nby Mik hail Zaicev (Lomonosov Moscow State University) as part of LieJor Online S eminar: Algebras\, representations\, and applications\n\n\nAbstract\nMikha il Zaicev (Lomonosov Moscow State University\, Russia): Polynomial identi ties: anomalies of codimension growth. Polynomi al identities: anomalies of codimension growth.

Mikhail Zaicev (Lomonosov Moscow State University\, Russia)

22/Oct/2020 - 14:00 GMT-3 (Sã\;o Paulo time)

We consider numerical invariants associat ed with polynomial identities of algebras over a field of characteristic z ero. Given an algebra \\(A\\)\, one can construct a sequence of non-negati ve integers \\({c_n(A)}\, n=1\,2\, \\ldots \\)\, called the codimensions o f \\(A\\)\, which is an important numerical characteristic of identical re lations of \\(A\\). In present talk we discuss asymptotic behavior of codi mension sequence in different classes of algebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Natalia Iyudu (University of Edinburgh) DTSTART;VALUE=DATE-TIME:20201119T170000Z DTEND;VALUE=DATE-TIME:20201119T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/17 DESCRIPTION:Title: On the proof of the Kontsevich conjecture on noncommutative birati onal transformations\nby Natalia Iyudu (University of Edinburgh) as pa rt of LieJor Online Seminar: Algebras\, representations\, and applications \n\n\nAbstract\nI will talk about our proof (arxiv 1305.1965\, Duke math J .) of the Kontsevich conjecture (1996) on noncommutative birational transf ormations. It deals with difficulties arising out of the fact that there a re no canonical form for noncommutative rational expressions. Miraculous i dentities proved supposedly reflect some kind of noncommutative group acti ons.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Eli Aljadeff (Technion-Israel Institute of Technology) DTSTART;VALUE=DATE-TIME:20201126T170000Z DTEND;VALUE=DATE-TIME:20201126T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/18 DESCRIPTION:Title: PI theory\, generic objects and group gradings\nby Eli Aljadef f (Technion-Israel Institute of Technology) as part of LieJor Online Semin ar: Algebras\, representations\, and applications\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Agata Smoktunowicz (University of Edinburgh) DTSTART;VALUE=DATE-TIME:20210225T170000Z DTEND;VALUE=DATE-TIME:20210225T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/19 DESCRIPTION:Title: Some questions related to nilpotent rings and braces\nby Agata Smoktunowicz (University of Edinburgh) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nIn around 200 5\, Wolfgang Rump introduced braces\, a generalisation of nilpotent rings to describe all involutive\, non-degenerate set theoretic solutions of the Yang-Baxter equation. This formulation then rapidly found application in other research areas. This talk will review these applications.

Braces h ave been shown to be equivalent to several concepts in group theory such a s groups with bijective 1-cocycles and regular subgroups of the holomorph of abelian groups. In algebraic number theory there is a correspondence be tween braces and Hopf-Galois extensions of abelian type first observed by David Bachiller. There is also connection between R-braces and pre-Lie alg ebras discovered by Wolfgang Rump in 2014. One generator braces have been shown to describe indecomposable\, involutive solutions of the Yang-Baxter equation.

On the other hand\, Anastasia Doikou and Robert West on have recently discovered some fascinating connections between braces an d quantum integrable systems. In particular\, to find solutions of the set -theoretic reflection equation it is needed to solve problems on some poly nomial identities in nilpotent rings. Because previously the theory of pol ynomial identities was mainly developed for prime rings\, and for the refl ection equation we only consider nilpotent rings\, there are no known meth ods for solving such problems. We will mention some open problems on polyn omial identities in nilpotent rings which appear in this situation.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Dotsenko (Université de Strasbourg) DTSTART;VALUE=DATE-TIME:20210304T170000Z DTEND;VALUE=DATE-TIME:20210304T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/20 DESCRIPTION:Title: Diamond Lemma and the Maurer-Cartan equation\nby Vladimir Dots enko (Université de Strasbourg) as part of LieJor Online Seminar: Algebra s\, representations\, and applications\n\n\nAbstract\nI shall outline a ne w approach to the Composition-Diamond Lemma for rewriting systems / Gr&oum lbner-Shirshov bases; more specifically\, I shall explain how the Maure r-Cartan equation in the tangent complex of a monomial algebra leads to ma ny different versions of the Composition-Diamond Lemma\, one for each repr esentative of the tangent complex arising from a multigraded resolution of such algebra. This is joint work with Pedro Tamaroff.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandr Zubkov (UAEU (United Arab Emirates)) DTSTART;VALUE=DATE-TIME:20210311T170000Z DTEND;VALUE=DATE-TIME:20210311T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/21 DESCRIPTION:Title: Harish-Chandra pairs and group superschemes\nby Alexandr Zubko v (UAEU (United Arab Emirates)) as part of LieJor Online Seminar: Algebras \, representations\, and applications\n\n\nAbstract\nThe purpose of my tal k is to discuss the following results recently obtained in collaboration w ith A.Masuoka (Tsukuba University\, Japan). First\, we prove that a certai n category of Harish-Chandra pairs is equivalent to the category of (not n ecessary affine) locally algebraic group superschemes. Using this fundamen tal equivalence we superize the famous Barsotti-Chevalley theorem and prov e that the sheaf quotient of an algebraic group superscheme over its group super-subscheme is again a superscheme of finite type. I will also formul ate some open problems whose solving would bring significant progress in t he supergroup theory.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Gorelik (The Weizmann Institute of Science\, Israel) DTSTART;VALUE=DATE-TIME:20210318T170000Z DTEND;VALUE=DATE-TIME:20210318T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/22 DESCRIPTION:Title: Depths and cores in the light of DS-functors\nby Maria Gorelik (The Weizmann Institute of Science\, Israel) as part of LieJor Online Sem inar: Algebras\, representations\, and applications\n\n\nAbstract\nThe Dul fo-Serganova functors DS are tensor functors relating representations of d ifferent Lie superalgebras. In this talk I will consider the behaviour of various invariants\, such as the defect\, the dual Coxeter number\, the at ypicality and the cores\, under the DS-functor. I will introduce a notion of depth playing the role of defect for algebras and atypicality for modul es. I will mainly concentrate on examples of symmetrizable Kac-Moody and Q -type superalgebras. The talk is based on arXiv:2010.05721\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Apoorva Khare (Indian Institute of Science) DTSTART;VALUE=DATE-TIME:20210325T170000Z DTEND;VALUE=DATE-TIME:20210325T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/23 DESCRIPTION:Title: Polymath14: Groups with norms\nby Apoorva Khare (Indian Instit ute of Science) as part of LieJor Online Seminar: Algebras\, representatio ns\, and applications\n\n\nAbstract\nConsider the following three properti es of a general group \\(G\\):

Algebra: \\(G\\) is abelian and torsion-free.

Analysis: \\(G\\) is a metric space that admits a "nor m"\, namely\, a translation-invariant metric \\(d(.\,.)\\) satisfying: \\( d(1\,g^n) = |n| d(1\,g)\\) for all \\(g \\in G\\) and integers \\(n\\).

While these properties may a priori seem different\, in fact they t urn out to be equivalent (and also to \\(G\\) being isometrically and addi tively embedded in a Banach space\, hence inheriting its norm). The nontri vial implication amounts to saying that there does not exist a non-abelian group with a "norm". We will discuss motivations from analysis\, probabil ity\, and geometry; then the proof of the above equivalences; and fi nally\, the logistics of how the problem was solved\, via a PolyMath proje ct that began on a blog post of Terence Tao.

(Joint - as D.H.J . PolyMath - with Tobias Fritz\, Siddhartha Gadgil\, Pace Nielsen\, Lior S ilberman\, and Terence Tao.)\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Kang Seok-Jin (Korea Research Institute of Arts and Mathematics\, South Korea) DTSTART;VALUE=DATE-TIME:20210401T130000Z DTEND;VALUE=DATE-TIME:20210401T140000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/24 DESCRIPTION:Title: Quantum Borcherds-Bozec algebras and abstract crystals\nby Kan g Seok-Jin (Korea Research Institute of Arts and Mathematics\, South Korea ) as part of LieJor Online Seminar: Algebras\, representations\, and appli cations\n\n\nAbstract\nIn this talk\, we will discuss the basic properties of quantum Borcherds-Bozec algebras and their integrable representations. We also give a brief description of the theory of abstract crystals for q uantum Borcherds-Bozec algebras and their applications.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Evgeny Mukhin (IUPUI School of Science\, USA) DTSTART;VALUE=DATE-TIME:20210408T170000Z DTEND;VALUE=DATE-TIME:20210408T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/25 DESCRIPTION:Title: Supersymmetric analogs of partitions and plane partitions\nby Evgeny Mukhin (IUPUI School of Science\, USA) as part of LieJor Online Sem inar: Algebras\, representations\, and applications\n\n\nAbstract\nWe will explain combinatorics of various partitions arising in the representation theory of quantum toroidal algebras associated to Lie superalgebra gl(m|n ). Apart from being interesting in its own right\, this combinatorics is e xpected to be related to crystal bases\, fixed points of the moduli spaces of BPS states\, equivariant K-theory of moduli spaces of maps\, and other things. This talk is based on a joint project with Luan Bezerra.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/25/ END:VEVENT BEGIN:VEVENT SUMMARY:José María Pérez Izquierdo (Universidad de La Ri oja\, Spain) DTSTART;VALUE=DATE-TIME:20210415T170000Z DTEND;VALUE=DATE-TIME:20210415T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/26 DESCRIPTION:Title: Some aspects of the free nonassociative algebra\nby José María Pérez Izquierdo (Universidad de La Rioja\, Spain) as pa rt of LieJor Online Seminar: Algebras\, representations\, and applications \n\n\nAbstract\nThe free nonassociative algebra provides a simple combinat orial context to extend some constructions from the associative setting. I n this talk\, based on joint work with J. Mostovoy and I. P. Shestakov\, I will briefly discuss three of them related to nonassociative Lie theory: the embedding of the free loop as nonassociative formal power series\, a n onassociative extension of the Baker-Campbell-Hausdorff formula and a nona ssociative version of Solomon's descent algebra.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Belolipetsky (IMPA\, Brazil) DTSTART;VALUE=DATE-TIME:20210422T180000Z DTEND;VALUE=DATE-TIME:20210422T190000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/27 DESCRIPTION:Title: Growth of lattices in semisimple Lie groups\nby Mikhail Beloli petsky (IMPA\, Brazil) as part of LieJor Online Seminar: Algebras\, repres entations\, and applications\n\n\nAbstract\nA discrete subgroup \\(G\\) of a Lie group \\(H\\) is called a lattice if the quotient space \\(H/G\\) h as finite volume. By a classical theorem of Bieberbach we know that the gr oup of isometries of an \\(n\\)-dimensional Euclidean space has only finit ely many different types of lattices. The situation is different for the s emisimple Lie groups \\(H\\). Here the total number of lattices is infinit e and we can study its growth rate with respect to the covolume. This topi c has been a subject of our joint work with A. Lubotzky for a number of ye ars. In the talk I will discuss our work and some other more recent relate d results.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergey Shpectorov (University of Birmingham\, UK) DTSTART;VALUE=DATE-TIME:20210429T170000Z DTEND;VALUE=DATE-TIME:20210429T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/28 DESCRIPTION:Title: 2-generated algebras of Monster type\nby Sergey Shpectorov (Un iversity of Birmingham\, UK) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe class of non-associa tive axial algebras was introduced in 2015 as a broad generalisation of Ma jorana algebras of Ivanov that were modelled after the properties of the G riess algebra\, the algebra whose automorphism group is the Monster sporad ic simple group. Sakuma's theorem classifies 2-generated Majorana algebras \, which in axial terms correspond to algebras of Monster type (1/4\,1/32) . The quest to classify all 2-generated algebras of arbitrary Monster type \\((\\alpha\,\\beta)\\) was started by Rehren who proved an upper bound o n the dimension and generalised the Norton-Sakuma algebras to arbitrary \\ ((\\alpha\,\\beta)\\). Recently\, new results emerged from the work of Fra nchi\, Mainardis and the speaker\, and independently\, of Yabe\, who class ified symmetric 2-generated algebras of Monster type. Several new classes of algebras have been found.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Natasha Rozhkovskaya (Kansas State University\, USA) DTSTART;VALUE=DATE-TIME:20210506T170000Z DTEND;VALUE=DATE-TIME:20210506T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/29 DESCRIPTION:Title: Generating functions of polynomial tau-functions of the soliton hi erarchies\nby Natasha Rozhkovskaya (Kansas State University\, USA) as part of LieJor Online Seminar: Algebras\, representations\, and applicatio ns\n\n\nAbstract\nThe Kademtsev-Petviashvily (KP) equation is a famous evo lution equation with soliton solutions. It was discovered by M.Sato and th e Kyoto school that the KP equation can be regarded as a part of a countab le system of compatible evolution equations\, which is called today the KP hierarchy. The observation allowed the researchers to discover many new e xamples of soliton type hierarchies and to study them with methods of math ematical physics\, algebraic geometry and representation theory. In the ta lk we will describe the explicit construction of polynomial tau-functions of the KP\, BKP hierarchies through their generating functions. The method uses the tools of representation theory and properties of symmetric funct ions. The talk is based on the joint work with V. G. Kac and J. van de Leu r.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Alistair Savage (University of Ottawa\, Canada) DTSTART;VALUE=DATE-TIME:20210513T170000Z DTEND;VALUE=DATE-TIME:20210513T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/30 DESCRIPTION:Title: Affine Hecke algebras and the elliptic Hall algebra\nby Alista ir Savage (University of Ottawa\, Canada) as part of LieJor Online Seminar : Algebras\, representations\, and applications\n\n\nAbstract\nThe ellipti c Hall algebra has appeared in many different contexts in representation t heory and geometry under different names. We will explain how this algebra is categorified by the quantum Heisenberg category\, which is a diagramma tic category modelled on affine Hecke algebras. This categorification can be used to construct large families of representations for the elliptic Ha ll algebra.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Farkhod Eshmatov (Academy of Science of Uzbekistan\, Uzbekistan) DTSTART;VALUE=DATE-TIME:20210520T170000Z DTEND;VALUE=DATE-TIME:20210520T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/31 DESCRIPTION:Title: On transitive action on quiver varieties\nby Farkhod Eshmatov (Academy of Science of Uzbekistan\, Uzbekistan) as part of LieJor Online S eminar: Algebras\, representations\, and applications\n\n\nAbstract\nThe C alogero-Moser space \\({\\mathcal C}_n\\) is the space of conjugacy classe s of pairs of \\(n \\times n\\) matrices such that the matrix \\(XY - Y X + I_n\\) has rank one. These spaces play important role in geometry\, repr esentation theory and integrable systems. A well-known result of Berest an d Wilson states that the natural action of the affine Cremona group \\(GA_ 2\\) on \\({\\mathcal C}_n\\) is transitive. In this talk we will give a q uiver generalization of this statement and discuss some applications.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Kleshchev (University of Oregon\, USA) DTSTART;VALUE=DATE-TIME:20210527T170000Z DTEND;VALUE=DATE-TIME:20210527T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/32 DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups\nb y Alexander Kleshchev (University of Oregon\, USA) as part of LieJor Onlin e Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nWe motivate\, discuss history of\, and present a solution to the following p roblem: describe pairs \\((G\,V)\\) where \\(V\\) is an irreducible repres entation of the symmetric group \\(S_n\\) of dimension \\(>1\\) and \\(G\\ ) is a subgroup of \\(S_n\\) such that the restriction of \\(V\\) to \\(G\ \) is irreducible. We do the same with the alternating group \\(A_n\\) in place of \\(S_n\\). The latest results on the problem are joint with Pham Huu Tiep and Lucia Morotti.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Bavula (The University of Sheffield\, UK) DTSTART;VALUE=DATE-TIME:20210401T170000Z DTEND;VALUE=DATE-TIME:20210401T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/33 DESCRIPTION:Title: The global dimension of the algebras of polynomial integro-differe ntial operators and the Jacobian algebras\nby Vladimir Bavula (The Uni versity of Sheffield\, UK) as part of LieJor Online Seminar: Algebras\, re presentations\, and applications\n\n\nAbstract\nWe review some old and rec ent results about the algebras of polynomial integro-differential operator s and the Jacobian algebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics Uzbekista n Academy of Sciences) DTSTART;VALUE=DATE-TIME:20210415T150000Z DTEND;VALUE=DATE-TIME:20210415T160000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/34 DESCRIPTION:Title: Local and 2-local derivations and automorphisms of Octonian algebr as\nby Shavkat Ayupov (V.I.Romanovskiy Institute of Mathematics Uzbeki stan Academy of Sciences) as part of LieJor Online Seminar: Algebras\, rep resentations\, and applications\n\n\nAbstract\nThe talk is devoted to desc ription of local and 2-local derivations (respectively\, automorphisms) on octonian algebras over fields with zero characteristics. We shall give a general form of local derivations on the real octonion algebra \\(O(\\math bb{R})\\). This description implies that the space of all local derivation s on \\(O(\\mathbb{R})\\) when equipped with Lie bracket is isomorphic to the Lie algebra \\(so_7(\\mathbb{R})\\) of all real skew-symmetric \\(7 \\ times 7\\)-matrices. We also consider 2-local derivations on the octonion algebra \\(O(F)\\) over an algebraically closed field \\(F\\) and prove th at every 2-local derivation on \\(O(F)\\) is a derivation. Further\, we ap ply these results to problems for the simple 7-dimensional Malcev algebra. As a corollary we obtain that the real octonion algebra \\(O(\\mathbb{R}) \\) and Malcev algebra \\(M_7(R)\\) are simple non associative algebras wh ich admit pure local derivations\, that is\, local derivations which are n ot derivation. Further\, we shall give a general form of local automorphis ms on the octonion algebra \\(O(F)\\) over a field \\(F\\). This descripti on implies that the group of all local automorphisms on \\(O(F)\\) is isom orphic to the group \\(O_7(F)\\) of all orthogonal \\(7 \\times 7\\)-matri ces over F. We also consider 2-local automorphisms on the octonion algebra \\(O(F)\\) over an algebraically closed field \\(F\\) and prove that ever y 2-local automorphism on \\(O(F)\\) is an automorphism. As a corollary we obtain descriptions of local and 2-local automorphisms of seven dimension al simple Malcev algebra.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Vyacheslav Futorny (IME-USP\, Brazil) DTSTART;VALUE=DATE-TIME:20210603T170000Z DTEND;VALUE=DATE-TIME:20210603T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/35 DESCRIPTION:Title: Infinite-dimensional representations of Lie algebras\nby Vyach eslav Futorny (IME-USP\, Brazil) as part of LieJor Online Seminar: Algebra s\, representations\, and applications\n\n\nAbstract\nWe will discuss the representation theory of simple finite-dimensional Lie algebras\, Affine Lie algebras and their generalizations. Special focus will be given to the representations of vertex algebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Tony Pantev (University of Pennsylvania\, USA) DTSTART;VALUE=DATE-TIME:20210610T170000Z DTEND;VALUE=DATE-TIME:20210610T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/36 DESCRIPTION:Title: Geometry and topology of wild character varieties\nby Tony Pan tev (University of Pennsylvania\, USA) as part of LieJor Online Seminar: A lgebras\, representations\, and applications\n\n\nAbstract\nWild character varieties parametrize monodromy representations of flat meromorphic conne ctions on compact Riemann surfaces. They are classical objects with remark able geometric and topological properties. \n\nI will recall how intrinsic geometric structures resolve singularities of wild character varieties an d will show that known algebraic symplectic structures extend naturally to the resolutions. This is based on a new universal method for producing sy mplectic structures which is a joint work with Arinkin and Toen. Time perm itting I may also describe recent joint works with Chuang\, Diaconescu\, D onagi\, and Nawata which extract cohomological invariants of wild characte r varieties from enumerative Calabi-Yau geometry and refined Chern-Simons invariants of torus knots.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Geordie Williamson (University of Sydney\, Australia) DTSTART;VALUE=DATE-TIME:20210617T200000Z DTEND;VALUE=DATE-TIME:20210617T210000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/37 DESCRIPTION:Title: Spectra in representation theory\nby Geordie Williamson (Unive rsity of Sydney\, Australia) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nIn geometric representat ion theory cohomology\, intersection cohomology and constructible sheaves show up everywhere. This might seem strange to an algebraic topologist\, w ho might ask: why this emphasis on cohomology\, when there are so many oth er interesting cohomology theories (like K-theory\, elliptic cohomology\, complex cobordism\, ...) out there? They might also ask: is there somethin g like "intersection K-theory"\, or "intersection complex cobordism"? This is something I've often wondered about. I will describe work in progress with Ben Elias\, where we use Soergel bimodules to investigate what KU-mod ules look like on the affine Grassmannian. We have checked by hand that in types A1\, A2 and B2\, one gets something roughly resembling the quantum group. Speaking very roughly\, the intersection K-theory of Schubert varie ties in the affine Grassmannian should recover the irreducible representat ions of the quantum group. Inspirations for this work include a strange Ca rtan matrix discovered by Ben Elias\, and work of Cautis-Kamnitzer.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Vitaly A. Roman'kov (Sobolev Institute of Mathematics RAS\, Omsk B ranch\, Omsk\, Russia) DTSTART;VALUE=DATE-TIME:20210624T170000Z DTEND;VALUE=DATE-TIME:20210624T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/38 DESCRIPTION:Title: Embedding theorems for solvable groups\nby Vitaly A. Roman'kov (Sobolev Institute of Mathematics RAS\, Omsk Branch\, Omsk\, Russia) as p art of LieJor Online Seminar: Algebras\, representations\, and application s\n\n\nAbstract\nIn this talk\, we present a series of results on group em beddings in groups with a small number of generators. We show that each fi nitely generated group \\(G\\) lying in a variety M can be embedded in a 4 -generated group \\(H\\) in a variety MA\, where a A means the variety of abelian groups. If \\(G\\) is a finite group\, then \\(H\\) can also be f ound as a finite group. It follows\, that any finitely generated (finite) solvable group \\(G\\) of the derived length \\(l\\) can be embedded in a 4-generated (finite) solvable group \\(H\\) of length \\(l+1\\). Thus\, we answer the question of V. H. Mikaelian and A.Yu. Olshanskii. It is also s hown that any countable group \\(G\\) in M\, such that the abelianization \\(G_{ab}\\) is a free abelian group\, is embeddable in a 2-generated grou p \\(H\\) in MA.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitry V. Artamonov (Lomonosov State University\, Moscow) DTSTART;VALUE=DATE-TIME:20210701T170000Z DTEND;VALUE=DATE-TIME:20210701T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/39 DESCRIPTION:Title: \\(3j\\)-symbols for the algebra \\(gl_3\\)\nby Dmitry V. Arta monov (Lomonosov State University\, Moscow) as part of LieJor Online Semin ar: Algebras\, representations\, and applications\n\n\nAbstract\nThe probl em of caculation of Clebsh-Gordan coefficients for a tensor product of two irreducible representations of the Lie algebra \\(gl_2\\) is well-investi gated. It's solution plays an importan role in quantum mechanics. Analogou s problem for the algebra \\(gl_3\\) is also improtant (in the theory of q uarks)\, but it it much l more difficult. In some sence it was solved in t he 60-s in a series of papers by Biedenharn\, Louck\, Baird. But their solution is very cumbersome and not explicit. Thus the problem of findind of an explicit and simple formula for a Clebsh-Gordan coefficient remained unsolved.

In the talk an explicit and simple formula for a Cleb sh-Gordan coefficient for the algebra \\(gl_3\\) will be presented. The a nswer will be given as a value at \\(1\\) of some \\(A\\)-hypergeometric f unction.

As a byproduct I shall give an explicit description of i nvariants in triple tensor product and a projection on the corresponding trivial representation.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Kotchetov (Memorial University of Newfoundland\, Canada) DTSTART;VALUE=DATE-TIME:20210708T170000Z DTEND;VALUE=DATE-TIME:20210708T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/40 DESCRIPTION:Title: Fine gradings on classical simple Lie algebras\nby Mikhail Kot chetov (Memorial University of Newfoundland\, Canada) as part of LieJor On line Seminar: Algebras\, representations\, and applications\n\n\nAbstract\ nGradings by abelian groups have played an important role in the theory of Lie algebras since its beginning: the best known example is the root spac e decomposition of a semisimple complex Lie algebra\, which is a grading b y a free abelian group (the root lattice). Involutive automorphisms or\, e quivalently\, gradings by the cyclic group of order 2\, appear in the clas sification of real forms of these Lie algebras. Gradings by all cyclic gro ups were classified by V. Kac in the late 1960s and applied to the study o f symmetric spaces and affine Kac-Moody Lie algebras.\n\nIn the past two d ecades there has been considerable interest in classifying gradings by arb itrary groups on algebras of different varieties including associative\, L ie and Jordan. Of particular importance are the so-called fine gradings (t hat is\, those that do not admit a proper refinement)\, because any gradin g on a finite-dimensional algebra can be obtained from them via a group ho momorphism\, although not in a unique way. If the ground field is algebrai cally closed and of characteristic 0\, then the classification of fine abe lian group gradings on an algebra (up to equivalence) is the same as the c lassification of maximal quasitori in the algebraic group of automorphisms (up to conjugation). Such a classification is now known for all finite-di mensional simple complex Lie algebras.\n\nIn this talk I will review the a bove mentioned classification and present a recent joint work with A. Eldu que and A. Rodrigo-Escudero in which we classify fine gradings on classica l simple real Lie algebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Lubotzky (Hebrew University\, Jerusalem\, Israel) DTSTART;VALUE=DATE-TIME:20210715T170000Z DTEND;VALUE=DATE-TIME:20210715T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/41 DESCRIPTION:Title: First order rigidity of high-rank arithmetic groups\nby Alex L ubotzky (Hebrew University\, Jerusalem\, Israel) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Berest (Cornell University\, USA) DTSTART;VALUE=DATE-TIME:20210722T170000Z DTEND;VALUE=DATE-TIME:20210722T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/42 DESCRIPTION:Title: Spaces of quasi-invariants and homotopy Lie groups\nby Yuri Be rest (Cornell University\, USA) as part of LieJor Online Seminar: Algebras \, representations\, and applications\n\n\nAbstract\nQuasi-invariants are natural algebraic generalizations of classical invariant polynomials of fi nite reflection groups. They first appeared in mathematical physics --- in the work of O. Chalykh and A. Veselov on quantum integrable systems --- i n the early 1990s\, and since then have found many interesting application s in other areas: most notably\, representation theory\, algebraic geometr y and combinatorics.\n\nIn this talk\, I will explain how the algebras of quasi-invariants arise in topology: as cohomology rings of certain spaces naturally attached to compact connected Lie groups. Our main result is a g eneralization of a well-known theorem of A. Borel that realizes the algebr a of classical invariant polynomials of a Weyl group W(G) as the cohomolog y ring of the classifying space BG of the corresponding Lie group G. Perha ps most interesting here is the fact that our construction of spaces of qu asi-invariants is purely homotopy-theoretic. It can therefore be extended to some non-Coxeter (p-adic pseudo-reflection) groups\, in which case the compact Lie groups are replaced by the so-called p-compact groups (a.k.a. homotopy Lie groups).\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Onofrio Mario Di Vincenzo (Università di Basilicata\, Potenza\, I taly) DTSTART;VALUE=DATE-TIME:20210729T170000Z DTEND;VALUE=DATE-TIME:20210729T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/43 DESCRIPTION:Title: Algebras and superalgebras with (super-)involutions and their poly nomial identities\nby Onofrio Mario Di Vincenzo (Università di Basili cata\, Potenza\, Italy) as part of LieJor Online Seminar: Algebras\, repre sentations\, and applications\n\n\nAbstract\nIn this talk we consider the *-polynomial identities of algebras with involutions. The positive solutio n of Specth's problem\, given by Aljadeff\, Giambruno and Karasik in [E. A ljadeff\, A. Giambruno\, Y. Karasik Polynomial identities with involution\ , super-involutions and the Grassmann envelope\, Proc. Amer. Math. Soc. 14 5 (2017)\, no. 5\,1843-1857]\, for the T*-ideals of the free algebra with involution\, show the decisive role of the identities of finite dimensiona l superalgebras with superinvolution. In this talk we consider block-trian gular matrix algebras related to any sequence of such *-simple superalgebr as. These *-simple superalgebras are also involved in determining the exac t value of the correponding exponent as proved in [A. Ioppolo The exponent for superalgebras with superinvolution\, Linear Algebra and its Applicati ons Amer. Math. Soc. 555 (2018)\, 1-20]. We review the results in this are a and we show that that every minimal affine variety of superalgebras with superinvolution is generated by one of the block triangular matrix algebr as we introduced\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexei Kanel-Belov (Bar Ilan University\, Israel) DTSTART;VALUE=DATE-TIME:20210805T170000Z DTEND;VALUE=DATE-TIME:20210805T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/44 DESCRIPTION:Title: Evaluations of nonassociative polynomials on finite dimensional al gebras\nby Alexei Kanel-Belov (Bar Ilan University\, Israel) as part o f LieJor Online Seminar: Algebras\, representations\, and applications\n\n \nAbstract\nLet \\(p\\) be a polynomial in several non-commuting variable s with coefficients in an algebraically closed field \\(K\\) of arbitrary characteristic. It has been conjectured that for any \\(n\\)\, for \\(p\\) multilinear\, the image of \\(p\\) evaluated on the set \\(M_n(K)\\) of \ \(n\\) by \\(n\\) matrices is either zero\, or the set of scalar matrices\ , or the set \\(sl_n(K)\\) of matrices of trace 0\, or all of \\(M_n(K)\\) .

In this talk we will discuss the generalization of this result for non-associative algebras such as Cayley-Dickson algebra (i.e. algebra of octonions)\, pure (scalar free) octonion Malcev algebra and basic low rank Jordan algebras.\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolay Romanovskiy (Novosibirsk State University\, Russia) DTSTART;VALUE=DATE-TIME:20210812T170000Z DTEND;VALUE=DATE-TIME:20210812T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/45 DESCRIPTION:by Nikolay Romanovskiy (Novosibirsk State University\, Russia) as part of LieJor Online Seminar: Algebras\, representations\, and applic ations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugeny Plotkin (Bar-Ilan University\, Israel) DTSTART;VALUE=DATE-TIME:20210819T170000Z DTEND;VALUE=DATE-TIME:20210819T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/46 DESCRIPTION:by Eugeny Plotkin (Bar-Ilan University\, Israel) as part of Li eJor Online Seminar: Algebras\, representations\, and applications\n\nAbst ract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Askar Dzhumadil'daev (Academy of Sciences of Kazakhstan\, Kazakhst an) DTSTART;VALUE=DATE-TIME:20210826T170000Z DTEND;VALUE=DATE-TIME:20210826T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/47 DESCRIPTION:Title: Dimension formula for Koszul operads\nby Askar Dzhumadil'daev (Academy of Sciences of Kazakhstan\, Kazakhstan) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\n\nAbstract\nWe g ive recurrence formula for dimensions of Koszul operads. For example\, dim ensions of multi-linear parts of Lie-admissible operad satisfy the followi ng recurrence relations \\(d_n=\\sum_{i=1}^{n-1}\\mu k B_{n-1\,k}(d_1\,\\l dots\,d_{n-1})\,\\) where \\(B_{n\,k}\\) are Bell polynomial and \\(\\mu_k =k!\\sum_{i=0}^k (k-i+1)^i/i!\\). If \\(p>3\\) is prime\, then \\(d_{p-1}\ \equiv 1 (mod p)\,\\) \\(d_{p}\\equiv -1(mod p)\,\\) \\(d_{p+1}\\equiv -1( mod p)\,\\) \\(d_{p+2}\\equiv -6(mod p)\,\\) \\(d_{p+3}\\equiv -56 (mod p) \,\\) \\(d_{p+4}\\equiv -725(mod p).\\)\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitry Leites (New York University Abu Dhabi\, United Arab Emirat es and Stockholm University\, Sweden) DTSTART;VALUE=DATE-TIME:20210902T170000Z DTEND;VALUE=DATE-TIME:20210902T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/48 DESCRIPTION:by Dimitry Leites (New York University Abu Dhabi\, United Arab Emirates and Stockholm University\, Sweden) as part of LieJor Online Semi nar: Algebras\, representations\, and applications\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Ofelia Ronco (Universidad de Talca\, Chile) DTSTART;VALUE=DATE-TIME:20210909T170000Z DTEND;VALUE=DATE-TIME:20210909T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/49 DESCRIPTION:by Maria Ofelia Ronco (Universidad de Talca\, Chile) as part o f LieJor Online Seminar: Algebras\, representations\, and applications\n\n Abstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Petr Vojtechovsky (Denver University\, USA) DTSTART;VALUE=DATE-TIME:20210916T170000Z DTEND;VALUE=DATE-TIME:20210916T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/50 DESCRIPTION:by Petr Vojtechovsky (Denver University\, USA) as part of LieJ or Online Seminar: Algebras\, representations\, and applications\n\nAbstra ct: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Valery Bardakov (Sobolev Institute of Mathematics\, Novosibirsk\, Russia) DTSTART;VALUE=DATE-TIME:20210923T170000Z DTEND;VALUE=DATE-TIME:20210923T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/51 DESCRIPTION:by Valery Bardakov (Sobolev Institute of Mathematics\, Novosib irsk\, Russia) as part of LieJor Online Seminar: Algebras\, representation s\, and applications\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Semrl (University of Ljubljana\, Slovenia) DTSTART;VALUE=DATE-TIME:20210930T170000Z DTEND;VALUE=DATE-TIME:20210930T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/52 DESCRIPTION:by Peter Semrl (University of Ljubljana\, Slovenia) as part of LieJor Online Seminar: Algebras\, representations\, and applications\n\nA bstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael J. Larsen (Indiana University\, USA) DTSTART;VALUE=DATE-TIME:20211007T170000Z DTEND;VALUE=DATE-TIME:20211007T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/53 DESCRIPTION:by Michael J. Larsen (Indiana University\, USA) as part of Lie Jor Online Seminar: Algebras\, representations\, and applications\n\nAbstr act: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Rowen (Bar-Ilan University\, Israel) DTSTART;VALUE=DATE-TIME:20211014T170000Z DTEND;VALUE=DATE-TIME:20211014T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/54 DESCRIPTION:by Louis Rowen (Bar-Ilan University\, Israel) as part of LieJo r Online Seminar: Algebras\, representations\, and applications\n\nAbstrac t: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Oksana Bezuschak (Kyiv Taras Shevchenko University\, Ukraine) DTSTART;VALUE=DATE-TIME:20211021T170000Z DTEND;VALUE=DATE-TIME:20211021T180000Z DTSTAMP;VALUE=DATE-TIME:20210804T213534Z UID:LieJor_Seminar/55 DESCRIPTION:by Oksana Bezuschak (Kyiv Taras Shevchenko University\, Ukrain e) as part of LieJor Online Seminar: Algebras\, representations\, and appl ications\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/LieJor_Seminar/55/ END:VEVENT END:VCALENDAR