The FIRST class is January 11, 2022.
The class is meeting online on Tuesday and Thursday from 13:00 to 14:20.
[When it will be possible some of us might meet in person at York University in room LUM 306]
For registered students, the link to the ZOOM meeting will be sent
by email after you register at Fields. To register, please follow the link
(it is free for sponsor universities)
You will also be registered to "canvas" which is the LMS(Learning Management System) for Fields Institute for this course.
Nantel Bergeron
e-mail: bergeron (at) yorku (dot) ca
Book
Hopf Agebra and Combinatorics
Darij Grinberg, Victor Reiner, arXiv:1409.8356.
This will be the main reference but there will of course be several other references as we go along.
I plan as follow:
What is a Hopf algebra? (algebra, coalgebra, antipodes);
Review of symmetric functions as Hopf algebra;
Zelevinsky's structure theory of positive self-dual Hopf algebras;
Quasisymmetric functions and P-partitions;
Polynomial generators for QSym and Lyndon words;
Aguiar-Bergeron-Sottile theory of characters and universal property of QSym;
Malvenuto Reutenauer Hopf algebra of permutations;
and further topics (Including Hopf algebra of trees and more as time allows).
Evaluation:
Students will be evaluated on three aspects (which are parts of the life of any living mathematician).
I will make an average of the three aspects below.
For me A is well done;
B is ok, need some improvement; and C is insufficent
(close to bad). Any grade below that you are simply not doing anything!
1 Project/Homework (working on an extended project or working on exercises) [to be emailed to instructor regularly]. Group work is encouraged but each participants must submitt their own work in their own words.
2 Oral Presentation (Presenting some special topic or some proofs). [This would be a zoom presentation to the class]
3 Participation in class (Being there, asking questions, being curious, etc.)
is ALSO an important aspect of the evaluation.
Academic Integrity:
All Students are Expected to Engage in Academically Honest Work Academic integrity benefits everyone in our community. It not only helps
you reach the real goal of this class-learning, but also allows for the university and
program to be perceived positively by others. When students are dishonest, they
lose out on valuable learning that will help them perform well in their career. It can
also negatively impact all of the students in the program and at the institution by
creating negative mindsets which may result in fewer outside learning opportunities
for students. Academic dishonesty is any attempt by a student to gain academic
advantage through dishonest means or to assist another student with gaining an
unfair advantage. Academic integrity is important regardless of whether the work
is graded or ungraded, group or individual, written or oral. Dishonest acts are major academic offences and carry serious penalties, ranging from a failing grade on
the plagiarized work to expulsion from the course/university.
This is particularly important in these time of isolation with the pandemic.
Nantel Bergeron
Office: 2029 Dahdaleh Building
tel: 416-736-2100 x 33968
email address: bergeron at yorku dot ca
Department of Mathematics and Statistics.
2029 Dahdaleh Building
York University
North York, Ontario M3J 1P3, Canada
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