Antonio Giambruno

 

Memorial University of Newfoundland

 Atlantic Association for Research in the Mathematical Sciences

Atlantic Algebra Centre

CRG "Groups, Rings, Lie and Hopf Algebras"

 

 

POLYNOMIAL IDENTITIES, REPRESENTATION THEORY AND GROWTH
FUNCTIONS

 

Mini-course by

Professor Antonio Giambruno

University of Palermo, Italy

September 19 - 23, 2022

 

Professor Antonio Giambruno

 

Professor Giambruno among the participants of the International workshop "PI-algebras. II" , St. John's, 2011

From September 19 to September 23, 2021, Professor Antonio Giambruno from the University of Palermo will give an introductory mini-course on Polynomial Identities in Algebras

The aim of this short course in to present a combinatorial approach to the study of the polynomial identities satisfied by an algebra in characteristic zero. In this setting a major tool is the representation theory of the symmetric or general linear groups. This allows us to investigate various problems related to the growth of the space of polynomial identities.

Lecture 1 A brief introduction to the theory of polynomial identities.  The free algebra, T-ideals, polarization, stability, alternating polynomials, etc.

Lecture 2 A brief introduction to the representation theory of the  symmetric group in characteristic zero and action on multilinear polynomials. Codimensions and cocharacters. The  theorem of Regev on the exponential bound of the codimensions.

Lecture 3 Main properties of the sequence of cocharacters. Amitsur  conjecture and the PI-exponent of an algebra. Fundamental algebras and  Kemer polynomials. Some open problems.

The lectures will be delivered during three time periods, as shown below. They will take place at the St. John's campus of Memorial University and will be broadcast via Webex. All the times are in Newfoundland Daylight Time (NDT=UTC-2:30).

Tuesday, September 20, 10:30-11:45 am 

Wednesday, September 21, 3:30-4:45 pm 

Friday, September 23, 3:30-4:45 pm 

The room is A-2065 (Arts and Administartion Building) or join via Webex. On Tuesday September 20:

Join from the meeting link
https://mun.webex.com/mun/j.php?MTID=m0b1c7c32d64b83af75c942abf0443d2a
Join by meeting number
Meeting number (access code): 2634 265 3930
Meeting password: 6G4gxaHFbb6

On Wednesday, September 21, and Friday, September 23:

Join from the meeting link
Lectures on September 21 and 23
Join by meeting number
Meeting number (access code): 2634 733 8904
Meeting password: 62kpMHgngx6

On Friday, September 23:

Join from the meeting link
https://mun.webex.com/mun/j.php?MTID=m67f422524ea8225d95b0c8e5ec57bc85
Join by meeting number
Meeting number (access code): 2631 095 4545
Meeting password: 62kpMHgngx6