Moderator:
Malihe Yousofzadeh (ma.yousofzadeh@sci.ui.ac.ir)

This selfcontained minicourse will cover recent progress on connections between interpolation symmetric polynomials
and Lie theory. Our starting point will be the classical Capelli operator, a mysterious element of the enveloping algebra
$U(gl(n,C))$ that was discovered in the 19th century. We will then see how representation theory can be used to generalize
the Capelli operators to other interesting families of operators and their associated nvariable polynomials, such as
KnopSahi, OkounkovOlshanski, and SergeevVeselov polynomials.
The minicourse will be accessible to graduate students. It is tuned for anyone interested in algebra or algebraic
combinatorics.

