|Introduction to cluster algebras|
|Time：||Mon/Wed 15:10-17:00, 2016-07-06~ 2016-08-03|
|Instructor：||Linhui Shen [Northwestern University]|
|Place：||Conference Room 4, Floor 2, Jin Chun Yuan West Building|
The class on August 1 will be changed to 15:10-17:00 July 29 at Room 3.
The course will be on cluster algebras and their applications and connections with representation theory, integrable systems, Donaldson-Thomas theory and mirror symmetry.
Cluster algebras are commutative rings with a set of distinguished generators having a remarkable combinatorial structure. They were introduced in 2000 by Fomin and Zelevinsky to capture the combinatorics of canonical bases and total positivity in semisimple algebraic groups, but have since appeared in many other contexts, e.g. Teichmuller theory, discrete integrable systems, canonical bases, Poisson geometry, Wall-crossing …
Basic knowledge on Representation theory of Algebraic groups will be helpful.
Fock V., Goncharov A.: Cluster ensembles, quantization and the dilogarithm, Ann. Sci. Ec. Norm. Super. (4) 42 (2009), no.6, 865-900
Williams L.: Cluster algebras: an introduction. Bull. Amer. Math. Soc. (N.S.) 51(2014), no.1, 1-26.