PIMS Network Wide Colloquium: Melanie Wood
Topic
Finite quotients of 3-manifold groups
Speakers
Details
It is well-known that for any finite group G, there exists a closed 3-manifold M with G as a quotient of the fundamental group of M. However, we can ask more detailed questions about the possible finite quotients of 3-manifold groups, e.g. for G and H_1,...,H_n finite groups, does there exist a 3-manifold group with G as a quotient but no H_i as a quotient? We answer all such questions. To prove non-existence, we prove new parity properties of the fundamental groups of 3-manifolds. To prove existence of 3-manifolds with certain finite quotients but not others, we use a probabilistic method, by first proving a formula for the distribution of the fundamental group of a random 3-manifold, in the sense of Dunfield-Thurston. This is joint work with Will Sawin.
Additional Information
Speaker Bio:
Melanie Matchett Wood is a professor of mathematics at Harvard University and a Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study. Her work spans number theory, algebraic geometry, algebraic topology, additive combinatorics, and probability. Wood has been awarded an American Institute of Mathematics Five-Year Fellowship, a Sloan Research Fellowship, a Packard Fellowship for Science and Engineering, and the AWM-Microsoft Research Prize in Algebra and Number Theory. She is a Fellow of the American Mathematical Society. In 2021, Wood received the National Science Foundation's Alan T. Waterman Award, the nation's highest honor for early-career scientists and engineers, and in 2022 Wood received a MacArthur Fellowship.