Abstract: There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot concordance and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth structures.

Speaker’s Bio: Lisa Piccirillo received her PhD in 2019 from UT Austin. After a year of NSF postdoc at Brandeis, she moved to MIT as an assistant professor. Lisa was covered in many newspapers/journals (NY Times, Guardian, Scientific American, Quanta, … ) for resolving a 50 year old question by J. Conway as a graduate student in 2019. The resulting paper was published in Annals of Mathematics. Lisa has authored and co-authored many other important papers since then, and for all this she recently received the first Mirzakhani award given by the Breakthrough Foundation. Further info about Lisa can be found at here: https://sites.google.com/view/lpiccirillo/home