Title: Homotopy spheres and the 4D Poincaré conjecture

Speaker: Jae Choon Cha(POSTECH)

Abstract: Since Poincaré posed the question in dimension three in 1904, the Poincaré conjecture in arbitrary dimensions has been a major driving force in the study of topology. The smooth case of the Poincaré conjecture in dimension four (SPC4) remains the last unsettled case. In this talk, we will discuss relevant background, review known results on the SPC4 and potential counterexamples, and report on recent progress. The talk is intended for a broad audience, including graduate students and non-experts.