Titles and abstracts

Dave Benson: NilCoxeter algebras, their representations, and cohomology.

Abstract: The nilCoxeter algebra of a Coxeter group is the algebra obtained by replacing the relations in the group algebra saying that the distinguished generators square to one, with the relations saying they square to zero. The finite types give rise to local finite dimensional algebras, and I shall describe their cohomology. The affine types are examples of prime affine polynomial identity algebras, which gives us interesting information on the representation theory. Hyperbolic types seem harder to approach, but there are some interesting conjectures.

Alexander Berglund: Poincaré duality homomorphisms and graph complexes

Benjamin Briggs: Derivations on blocks of group algebras

Lars W. Christensen: Rational Poincaré series and Bass series

Rostislav Grigorchuk: Self-similar torsion groups and their applications

Farshid Hajir: A historical survey of the Golod-Shafarevich theorem and its consequences: From Evgenii Golod to Nigel Boston

Abstract. In the early 1960s, Shafarevich articulated the conjecture that a pro-p group whose minimal presentation has “few” relations as compared to its number of generators must be infinite. Soon thereafter, Golod and Shafarevich formulated and proved a very explicit version of this conjecture in their 1964 paper “On Class Field Towers.” This fundamental theorem of group theory had its origins in the investigation of an intriguing problem in algebraic number theory. In this historical talk, I will sketch the influence of the Golod-Shafarevich theorem in algebraic number theory in the ensuing decades, especially with the view to illustrating the group theory - number theory synergies displayed prominently in the contributions of Nigel Boston.

Vladimir Hinich: Lagrangian equivalence relations

Natalya Iyudu: Golod-Shafarevich estimate for potential algebras’

Abstract: We will remind the Golod-Shafarevich lower estimate for the Hilbert series via number of algebra generators and relations, based on which Golod constructed his famous counter-example to the Kurosh problem on whether finitely generated nil algebra should be nilpotent. Then we explain improvement of this estimate we obtained in case the algebra is potential. We also mention our positive answer to the question of Wemyss on whether potential should necessarily have terms of degree three in order algebra to be finite dimensional or of linear growth, based on this improved Golod-Shafarevich type inequality.

Andrei Jaikin: Embeddings of group rings into artinian rings and their applications

Abstract: I will describe several instances of embeddings of group rings into Artinian rings and show how these embeddings can be used to study the corresponding groups.

Steffen Kionke: Hereditarily just-infinite torsion groups

Volodymyr Nekrashevych: Simple torsion groups of intermediate growth

Abstract: We will discuss a method of constructing amenable finitely generated infinite torsion groups from actions of the infinite dihedral group on a Cantor set. Many of the examples will have intermediate growth. We will discuss the methods of finding growth estimates for these groups and properties of random walks on them.

Christian Maire: The Golod–Shafarevich theorem and the groups G_S.

Abstract: In this talk, we will present some consequences of the Golod–Shafarevich theorem in the context of number field extensions with restricted ramification.

Claudia Miller: Cotangent complexes and acyclic closures

Taras Panov: Polyhedral products, Golod rings and moment-angle complexes

Julia Pevtsova: Finite generation of cohomology: From Golod to van der Kallen

Abstract: The question of finite generation of the cohomology ring for a finite group/finite group scheme/finite dimensional Hopf algebra/finite tensor category goes back to the pioneering work of Golod and Venkov over 60 years ago but still has no shortage of open problems and unsettled conjectures. I’ll try to give (an incomplete) historical overview of the subject and describe where it stands now.

Dmitri Piontkovski: Non-commutative geometry and coherent rings

Eduard Schesler: Finite quotients of torsion groups and how to modify them

Liana Sega: Poincare series over rings defined by general forms

Abstract: We will present applications of the concept of Golod homomorphism to the computation of the Poincare series of the residue field of a standard graded ring, in situations when the ring is defined via general forms.

Ryo Takahashi: On the dominance of Golod local rings

Abstract: We call a local ring dominant if the residue field is finitely built from any nonzero object in the singularity category in the sense of Buchweitz and Orlov. In this talk, I will speak about the question asking whether a Golod local ring is dominant. All the new things presented in this talk come from my ongoing joint work with Toshinori Kobayashi.

Mark Walker: On homotopy Lie algebras and deformations

Volkmar Welker: Golod property of quotients of polynomial rings and its applications in combinatorics