A partial Latin square is a n x n grid of cells, each of which is either blank or contains a symbol {1,...n}, so that no symbol is repeated in any row or column; a completion of a partial Latin square is just a way to place symbols in all of the blank cells without repeating a symbol in any row or column. (If this reminds you of Sudoku, you're not wrong.)

Surprisingly, however, these relatively simple objects are connected to a wide swath of applications and research areas in mathematics! In this talk, we will introduce the concept of Latin squares, discuss a few of their applications, and explore a series of open questions around completing certain classes of partial Latin squares. No prerequisites beyond some mathematical sophistication are required to follow this talk.