• Agatha Atkarskaya (GTIIT)

Small cancellation rings and Groebner-Shirshov bases

Abstact: Small cancellation groups and their generalisations give a big source of groups with exotic properties (e.g. Burnside groups, Tarskii monster, finitely generated non-finitely presented subgroups of finitely presented groups, a.k.a. Rips construction, etc.). I will speak about a similar theory for algebras, which was recently developed. We expect that it can be used for constructing algebras with exotic properties as small cancellation groups are used for group-theoretic examples. On the other hand, a technique that we developed is of its own interest and can be considered as a generalisation of Groebner-Shirshov bases.

• Amiram Braun (University of Haifa)

Azumaya algebras, old and new

Abstract: Azumaya algebras pervades many topics in algebra. We shall discuss several of these, mostly old results, questions , etc. A new characterization of  Azumaya algebras  will be presented.

• Inna Entova-Aizenbud (Ben Gurion University)

Odd nilpotent elements in quasi-reductive supergroups

Abstract: Given a finite-dimensional complex vector space V and a nilpotent endomorphism f in End(V), one may construct a corresponding action of the group SL_2 on V, so that the infinitesimal action of the unipotent upper-triangular matrices is given by f. In this talk, I will explain a generalization of this construction to Z/2Z-graded vector spaces and supergroups, leading to ``homological'' tensor functors on representation categories of supergroups, and a structure theory for odd elements in Lie superalgebras. No prior knowledge of supergroups is assumed. This is based on a joint work with V. Serganova.

• Evgeny Feigin (Tel Aviv University)

Toda recursion, generalized brick manifolds and path algebras

Abstract: A point of a brick manifold is a collection of vector spaces subject to certain conditions. These manifolds were introduced by Escobar in 2014 and since then proved to be useful in many areas of mathematics. In a recent preprint Labelle suggested a generalization of brick manifolds, whose Poincare polynomials conjecturally solve Toda recursion. We will describe an algebraic framework which allows to study the generalized brick manifolds and their close cousins. Our construction is based on certain bimodules of the path algebras. Joint work with Markus Reineke.   

• Yasmine Fittouhi (Weizmann Institute of Science)

TBA

• Anthony Joseph (Weizmann Institute of Science)

The adjoint action of a parabolic subgroup P of SL(n) on the Lie algebra m of its nilradical

Abstract

• Anton Khoroshkin (University of Haifa)

Grobner Bases for Operadic Structures: From Associative Algebras to Dioperads

Abstract: The theory of Grobner bases, initially motivated by the need to compute effectively within polynomial rings and noncommutative algebras, relies heavily on a well-behaved arithmetic of monomials. Extending this theory to operadic structures is not straightforward, as the symmetric group action often conflicts with standard monomial orderings. In this talk, I will explain the "shuffle" machinery and other specialized techniques required to define Grobner bases for (colored) operads, contractads, and dioperads. We will conclude with several applications, showing how these bases help in the computation of Hilbert series and establishing the Koszul property for different algebraic structures such as (triangular) Lie bialgebras.

• Boris Kunyavsky (Bar Ilan University)

Width in algebras

Abstract: Every element of a simple Lie algebra can be represented as a sum  of finitely many Lie brackets. The least number of brackets needed  to obtain such a representation is called the bracket length of the element. The bracket width of the algebra is then defined as supremum of the lengths of its elements. 

I will give an overview of results and open questions concerning this notion and its various analogues and generalizations. 

• Anna Melnikov (University of Haifa)  

Between geometry and combinatorics: link patterns and classification of orbital varieties with a dense B-orbit in the case (l,k,1)

Abstract: GL_n(C) acts by conjugation on nilpotent matrices. The intersection of a nilpotent orbit with upper-triangular matrices is reducible and its components are equidimentional and are labeled by standard Young tableaux of the form corresponding to the Jordan form of a given orbit. The components are called orbital varieties and they are stable under the action of  Borel subgroup of upper-triangular invertible matrices. But in general they do not admit a dense Borel orbit. We provide a classification of orbital varieties of form (l,k,1) in terms of link patterns.

 Joint work with E. Abed Elfatah

• Ivan Penkov (Constructor University, Bremen)

Three open problems

Abstract: I will try to draw attention to three open problems. They have arisen naturally in my work, and at least two of them should be solvable. The third one, in number theory, seems to be the toughest. Come to the talk to find out more!

• Louis Rowen (Bar Ilan University)

Makar-Limanov’s problem

Abstract

• Alek Vainshtein (University of Haifa)

Poisson-Lie groups and cluster structures

Abstract: It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected complex Lie group G by a pair of classical R-matrices. The key element of the construction is a rational Poisson map from the group with a bracket defined by a pair of suitably chosen standard R-matrices to the same group with an arbitrary pair of R-matrices. In the case of G=SL_n one can build explicitly the corresponding cluster structure and prove its regularity and completeness.

Based on joint work with Misha Gekhtman (Notre Dame) and Michael Shapiro (Michigan State University).

• Uzi Vishne (Bar Ilan University)

Locally Finite Central Simple Algebras

Abstract:  Among Lenny’s most influential contributions to algebra are his construction of an algebraically closed division algebra and his pioneering method for identifying free objects within division rings. Despite these milestones, a comprehensive general theory of infinite-dimensional division algebras remains elusive. In this lecture, I will outline a recently developed theory focusing on a specific class of infinite-dimensional division algebras: those that are locally both finite-dimensional and central simple.