Peter Ozsváth and Zoltán Szabó developed Heegaard Floer homology, constructing invariants of three-manifolds from holomorphic-disk counts associated with Heegaard splittings. Their Berkeley lecture record explicitly identifies the joint discovery.[ref]
https://math.berkeley.edu/about/upcoming-events/lecture-series/chern-lectures/2010-chern-lectures. Institutional lecture abstract and joint attribution
Their four-manifold work uses pseudoholomorphic curves on triangular domains to define maps associated with cobordisms and assemble a smooth four-manifold invariant. The construction connects surface diagrams with information about smooth structures in four dimensions.[ref]
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Peter Ozsváth is a mathematician known primarily for his work in the fields of topology and geometry, particularly in relation to three-manifolds and knot theory. He is recognized for his contributions to the development of Heegaard Floer homology, a powerful tool in the study of three-manifolds. Ozsváth has collaborated with other mathematicians, including Zoltán Szabó, to advance the understanding of these complex areas.