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 with the participants of his mini course
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. |
| 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 |