Linear Algebra & The Periodic Table

Created over 150 years ago, the periodic table of elements reveals many interesting similarities, and periodic behaviors in the elementary constituents of nature. Elements with similar chemical properties are placed on top of one another into columns, and the number of columns populated increases as one moves down the table. But inside this organizational tool one can find many mathematical patterns, which historically provided welcome hints to the nature of quantum theory itself. One such pattern is simply noting that the number of elements in any given row of the table is always twice a perfect square. Why is that? Amazingly, this feature of nature is forced upon us by symmetry and mathematics. In this talk, we use the periodic table as a lighthouse, illuminating our way on a journey through infinite dimensional linear algebra, symmetries, eigenvalues, eigenfunctions, and separable PDEs.