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Abstract: Given a smooth closed n-manifold M and a k-tuple of basepoints in M, we define a Morse-type A∞-algebra called the based multiloop A∞-algebra and show the equivalence with the higher-dimensional Heegaard Floer A∞-algebra of k disjoint cotangent fibers of T*M.
Around 10 years ago, Donaldson and Sun discovered that metric limits of Ricci positive Kähler–Einstein manifolds are algebraic varieties, and their metric tangent cones also underlie some algebraic structure. I will talk about a general algebraic geometry theory behind this phenomenon. In…
The local volume of a Kawamata log terminal (klt) singularity is an invariant that plays a central role in the local theory of K-stability. By the stable degeneration theorem, every klt singularity has a volume preserving degeneration to a K-semistable Fano cone singularity. I will talk about a…