Advances in Noncommutative Algebra -- on the occasion of Louis Rowen's retirement BAR ILAN UNIVERSITY | ||

Sunday June 25th, Maxim Hotel | ||

19:00 | Arrival | |

Monday, June 26th, Beck Auditorium | ||

10:00-10:40 | Eli Aljadeff (The Technion) | On the codimension growth of Kemer's fundamental algebras (abstract) |

10:50-11:30 | Andrei Rapinchuk (Virginia) | On the notion of genus for division algebras and algebraic groups (abstract) |

11:50-12:30 | Murray Schacher (UCLA) | Norms of integers in central simple algebras (abstract) |

12:40-13:20 | Lenny Makar-Limanov (Wayne State U) | Freiheitssatz (abstract) |

13:20-14:50 | Lunch (bldg 409) | |

14:50-15:30 | Ed Formanek (Penn State U) | The Jacobian Conjecture in Two Variables (abstract) |

15:40-16:20 | Allan Berele (DePaul) | Invariant theory and trace identities for verbally prime algebras. (abstract) |

16:40-17:20 | Jason Bell (Waterloo) | The Dixmier-Moeglin equivalence for D-groups (abstract) |

17:30-18:10 | Susan Montgomery (USC) | Frobenius-Schur indicators: from groups, through Hopf algebras, to tensor categories (abstract) |

Tuesday, June 27th, Beck Auditorium | ||

10:00-10:40 | Eric Brussel (California Polytechnic State U) | Division algebras of two-dimensional local fields. (abstract) |

10:50-11:30 | Danny Krashen (U Georgia) | The period-index problem for p-adic surfaces |

11:50-12:30 | Kelly McKinnie (Montana) | Essential dimension of generic symbols in characteristic $p$ |

12:40-13:20 | Max Lieblich (U Washington) | Universality questions about Br |

13:30 | Excursion (to Jerusalem) | |

Wednesday, June 28th (Amitsur Symposium), Feldmann Auditorium | ||

10:00-10:40 | Amitai Regev (Weizmann) | Growth for the central polynomials (abstract) |

10:50-11:30 | Amiram Braun (Haifa) | On Humphreys' blocks parametrization conjecture (abstract) |

11:50-12:30 | Miriam Cohen (Ben Gurion U) | The role of left coideal subalgebra in the structure theory of Hopf algebras (abstract) |

12:40-13:20 | Jack Sonn (The Technion) | Quadratic residues, difference sets and Hasse's norm theorem (abstract) |

13:20-14:50 | Lunch | |

14:50-15:30 | Alexander Merkurjev (UCLA) | Rationality problem for classifying spaces of algebraic groups (abstract) |

15:40-16:20 | Claudio Procesi (Universita Di Roma) | Variations on standard identities (abstract) |

16:40-17:20 | Eva Bayer (EPFL, Lausanne) | Hasse principle for multinorm equations (abstract) |

17:30-18:10 | Jean-Pierre Tignol (UC de Louvain) | Around Rowen's crossed product theorem (abstract) |

18:30 | Festive dinner (bldg 1004) | |

Thursday, June 29th, Beck Auditorium | ||

10:00-10:40 | Yoav Segev (Ben Gurion) | Primitive axial algebras of Jordan type admit a Frobenius form (abstract) |

10:50-11:30 | Evgeny Shustin (Tel Aviv) | Refined tropical enumerative invariants (abstract) |

11:50-12:30 | Alexei Belov (Bar Ilan) | Representations of relativelly free algebras and canonization theorems (abstract) |

12:40-13:20 | Eliyahu Matzri (Bar Ilan) | Massey products in Galois cohomology |

13:20-14:50 | Lunch (bldg 306) | |

14:50-15:30 | Be'eri Greenfeld (Bar Ilan) | Frameworks and Approximations for the Kothe Conjecture (abstract) |

15:40-16:20 | Zinovy Reichstein (Vancouver) | Fields of definition for representations of finite groups. (abstract) |

16:40-17:20 | Don Passman (U Wisconsin-Madison) | Logic festival (abstract) |

17:30-18:10 | Surender Jain (Ohio State University) | Almost Injectivity |

By order of appearance

If you are not too familiar with free groups here is a familiar analogy: a linear relation in an $n$ dimensional vector space defines an $n-1$ dimensional subspace.

Surprisingly enough if $A$ is an associative algebra with $n$ generators and one relation it is still not known whether $A$ is non-trivial. Though it seems obvious that $A \neq 0$ the question is still open when characteristic is not zero.

In my talk I'll discuss possible approaches to this question and tell what is already known.

If $x \mapsto F$, $y \mapsto G$ defines an automorphism of $\mathbb{C}[x,y]$, then the chain rule implies that $J(F,G)$ is invertible. The Jacobian Conjecture in two variables asserts the converse: If $J(F,G)$ is invertible, then $x \mapsto F$, $y \mapsto G$ defines an automorphism of $\mathbb{C}[x,y]$.

I will survey some of the partial results on the conjecture.

When evaluated in an algebra this gives rise to a polynomial map equivariant under the automorphism group. We will investigate a class of problems related to this more general construction.

A Frobenius form on an algebra A is a non-zero bilinear form (. , .) that associates with the algebra product, that is, (ab, c) = (a, bc) for all a, b, c \in A.

We prove the claim of the title. (Joint work with Jon Hall and Sergey Shpectorov.)

Joint work of speaker with Louis Rowen and Uzi Vishne discovered relations with non-commutative algebraic geometry and provide new insights for representaion theory.

Consider representation $\rho$ of $k$-algebra $A$ to matrix algebra over algebraic close field $K$, wich is an affine space. Then Zarissky closer of $\rho(A)$ satysfy the same identities and its natural to investigate representations up to Zarissky clousure wich usually not a linea span if $k$ is finite. $\rho(A)$ decomposes into sum of prime components and Pierce components of radical. First canonization theorem says that it can be reduced to upper block-triangular case. Blocks are either {\it glued} (may be up to {\it Frobenious twist}) or independant. Second canonization theorem provides information for quiver or pseudoquiver. Third canonisation theorem says about quiver transformation under factorizing by representable $T$-ideal. And Fourth (projective) canonization theorem provide existence of non-identities of some canonical structure inside non-zero $T$-ideal and Phoenix property (``hiking'') saying that any element of $T$-ideal generated by hiked polynomial can be restituted to the same form.

Because one can provide via substitutions on hiked polynomial structure of Notherean module, Specht properties and local representability follows.

In this talk we focus on two frameworks which turn out to be valuable from the point of view of such approximations, namely: graded-nil algebras and differential polynomial rings. We present both positive and negative approximations and mark some promising directions for further research. (based on joint work with J. P. Bell and with A. Smoktunowicz and M. Ziembowski.)

The classical answer is given by the Schur index of \rho, which is the smallest degree of a finite field extension l/k such that \rho can be defined over l. In this talk, based on joint work with Nikita Karpenko, Julia Pevtsova and Dave Benson, I will discuss another invariant, the essential dimension of \rho, which measures "how far" \rho is from being definable over k in a different way, by using transcendental, rather than algebraic field extensions. This invariant is of interest in both the modular and the non-modular settings.