New Developments in Four Dimensions

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This award supports travel for US-based participants in the conference “New Developments in Four Dimensions” held at the University of Victoria, British Columbia, Canada, during June 13-17, 2022. The meeting will focus on the branch of low-dimensional topology concerned with understanding four-dimensional manifolds. Low-dimensional topology is the mathematical study of spaces (manifolds) of dimension two, three, and four. Two-dimensional and three-dimensional spaces are intuitive: The surfaces of tables, bagels, or the earth are all examples of two-dimensional spaces and the spatial world we inhabit and the inside of a bagel are examples of three-dimensional spaces. Four-dimensional spaces are considerably more difficult to imagine (and study) with the most salient example being the spacetime conceptualization of the universe. In this sense, four-dimensional topology is the study of the possible shapes that our physical universe might realize. Surfaces have been well-studied classically, and major advances in the late 1900s and early 2000s have given researchers a clear understanding of three-dimensional manifolds. Four-dimensional manifolds represent the unknown frontier of low-dimensional topology, and there remain myriad open conjectures and unanswered question in this field of mathematics.There has been an explosion of activity within four-dimensional topology in the last few years, particularly in the study of diffeomorphism groups of four-manifolds, the construction and detection of exotic structures and embeddings, and the introduction of trisections as a new tool in the field. The purpose of this conference is to gather an international group of experts to explore these recent developments in the study of four-dimensional manifolds, disseminate contemporary research in the field, promote the research of early-career mathematicians working in the field, include and promote the research of mathematicians from underrepresented groups, and to give a venue for new collaborations to occur and old collaborations to continue.Conference Website: https://math.stanford.edu/~maggiehm/developmentsin4DThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.