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hopf algebras and combinatorics
federico ardila m.san francisco state university . universidad de los andes
The topic. We will study Hopf algebras, with an emphasis on their connections with combinatorics.
Hopf algebras are spaces with a notion of multiplication and comultiplication, which satisfy certain
compatibility relations. They can loosely be thought of as generalizations of groups. They were
defined by topologists in the 40s, and became an object of intensive study in their own right.
Beginning in the 70s, combinatorialists found that many of their favorite objects can be naturally
turned into Hopf algebras. This key observation gives us a rich source of interesting examples of
Hopf algebras, as well as an elegant machinery to prove purely combinatorial theorems.
Instructor. Federico Ardila . firstname.lastname@example.org . Thornton 927 . 1.415.338.7720
Logistics. This course is part of the SFSU-Colombia Combinatorics Initiative, a teaching and
research collaboration between San Francisco State University and the Universidad de Los Andes
in Bogot´a, with guest participants from UC Berkeley and other sites. This course will be offered
jointly at both locations; most lectures will take place at SFSU, and videos will be broadcast at
Los Andes and freely available online. Students will have the opportunity to discuss the course
material and assignments in an internet forum.
Homework. During the first half of the course there will be biweekly assignments. These will range
from fairly routine exercises to challenging problems, and working in groups will be encouraged.