Mathematics Colloquia and Seminars

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The L-space conjecture predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3-manifold Y. In particular, it predicts exactly which 3-manifolds admit a "taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections, with a focus towards "braid positive knots" (i.e. the knots realized as the closure of positive braids). I'll also present some applications, including obstructions to braid positivity, and a new unknot detector. Finally I'll briefly sketch a strategy for building taut foliations in manifolds obtained by Dehn surgery along knots in the three-sphere. No background in foliations or Floer homology theories will be assumed. All are welcome!