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  1. ; ; (, Forum of Mathematics, Sigma)
    Abstract We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with$$12$$nodal fibers, and that its degree is larger than$$1$$. This settles the final case of infinitesimal Torelli for a generic elliptic surface. 
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    Full Text Available 
  2. ; ; (, International Mathematics Research Notices)
    Given a smooth quasi-projective complex algebraic variety $$\mathcal{S}$$, we prove that there are only finitely many Hodge-generic non-isotrivial families of smooth projective hypersurfaces over $$\mathcal{S}$$ of degree $$d$$ in $$\mathbb{P}_{\mathbb C}^{n+1}$$. We prove that the finiteness is uniform in $$\mathcal{S}$$ and give examples where the result is sharp. We also prove similar results for certain complete intersections in $$\mathbb{P}_{\mathbb C}^{n+1}$$ of higher codimension and more generally for algebraic varieties whose moduli space admits a period map that satisfies the infinitesimal Torelli theorem. 
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    Free, publicly-accessible full text available August 1, 2026
  3. ; ; (, Duke Mathematical Journal)
    A fullerene, or buckyball, is a trivalent graph on the sphere with only pentagonal and hexagonal faces. Building on ideas of Thurston, we use modular forms to give an exact formula for the number of oriented fullerenes with a given number of vertices. 
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    Free, publicly-accessible full text available February 15, 2026