ask any professional mathematician what they most like to exploit, and the top two answers will most likely be graduate 2022年亚洲世界杯预选赛 and symmetry. this talk will feature one of the former speaking about the latter. specifically, i will be talking about symmetric functions and trying to make the case that if you were stranded on a desert island and could bring only one mathematical object with you, the algebra of symmetric functions would make an excellent choice; one would almost certainly die of thirst/starvation before getting bored. after demonstrating some beautiful (and fundamental) algebraic and combinatorial properties of this algebra, i will show how they can be applied by sketching a proof of the hook-length formula and (if time permits) explaining the basics of polya enumeration.