Some definitions of the word symmetry include "correct or pleasing proportion of the parts of a thing," "balanced proportions," and "the property of remaining invariant under certain changes, as of orientation in space." One might think of snowflakes, butterflies, and our own faces as naturally symmetric objects - or at least close to it. Mathematically one can also conjure up many symmetric objects: even and odd functions, fractals, certain matrices, and modular forms, a type of symmetric complex function. All of these things, mathematical or natural, arguably exhibit a kind of beauty in their symmetries, so would they lose some of their innate beauty if their symmetries were altered? Alternatively, could some measure of beauty be gained with some symmetric imperfections? In this talk, we will explore these questions guided by the topic of modular forms and their variants. What can be gained by perturbing modular symmetries in particular?

Biography: Amanda Folsom is Professor of Mathematics and Department Chair at Amherst College, and specializes in number theory, on modular forms, harmonic Maass forms, and applications to combinatorics and other areas. She hails from the north shore of Boston, and received undergraduate and doctoral mathematics degrees from the University of Chicago and UCLA, respectively. Beyond Amherst, Amanda has held assorted positions at the Max Planck Institute for Mathematics, University of Wisconsin-Madison, Yale University, and the Institute for Advanced Study Princeton. Amanda believes in the visibility of LGBTQ+ mathematicians like herself. She is a member of Spectra, was a Joint Mathematics Meetings AWM panelist on Queer Families and Mathematical Careers, and has given numerous research talks including some at LGBTQ+ mathematics conferences. Some of Amanda's additional outreach involves research with undergraduates and women in mathematics, including her work as a research project leader with the Women in Numbers program.