CMSA/Tsinghua Math-Science Literature Lecture: Robert Gompf: On classifying smoothings of R^4–from the beginning to the present
CMSA/Tsinghua Math-Science Literature Lecture
Date: September 16, 2026
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street & via Zoom Webinar
Please register to attend
Speaker: Robert E. Gompf, University of Texas, Austin
Title: On classifying smoothings of R^4–from the beginning to the present
Abstract: The field of 4-manifold topology was born around 1981 with two independent revolutionary breakthroughs, by Fields medalists Michael Freedman and Simon Donaldson. Freedman showed that topological 4-manifolds obeyed the well-developed theory of higher-dimensional manifolds, while Donaldson used nonlinear analysis (gauge theory) to show that smooth 4-manifolds are quite different from their high-dimensional counterparts. The clash between the two theories makes 4-manifold topology uniquely intricate within manifold theory. One of the most startling consequences is that unlike in other dimensions, Euclidean 4-space R^4 admits exotic smoothings. Equivalently, there are smooth 4-manifolds that are homeomorphic, but not diffeomorphic, to R^4. We will trace the classification theory of these manifolds from their discovery to the most recent development (joint with Aristotelis Panagiotopoulos) that they cannot be classified by any countable family of numerical invariants.
Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.