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Creators/Authors contains: "Tsimerman, Jacob"

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  1. ; (, Forum of Mathematics, Sigma)
    Abstract We prove a functional transcendence theorem for the integrals of algebraic forms in families of algebraic varieties. This allows us to prove a geometric version of André’s generalization of the Grothendieck period conjecture, which we state using the formalism of Nori motives. More precisely, we prove a version of the Ax–Schanuel conjecture for the comparison between the flat and algebraic coordinates of an arbitrary admissible graded polarizable variation of integral mixed Hodge structures. This can be seen as a generalization of the recent Ax–Schanuel theorems of [13, 18] for mixed period maps. 
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    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We prove a mixed version of a conjecture of Griffiths: that the closure of the image of any admissible mixed period map is quasi-projective, with a natural ample bundle. Specifically, we consider the map from the image of the mixed period map to the image of the period map of the associated graded. On the one hand, we show in a precise manner that the parts of this map parametrizing extension data of non-adjacent-weight pure Hodge structures are quasi-affine. On the other hand, extensions of adjacent-weight pure polarized Hodge structures are parametrized by a compact complex torus (the intermediate Jacobian) equipped with a natural theta bundle which is ample in Griffiths transverse directions.Our proof makes heavy use of o-minimality, and recent work with B. Klingler associating an ℝ an , exp {\mathbb{R}_{\mathrm{an},\exp}}-definable structure to mixed period domains and admissible mixed period maps. 
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  3. ; ; ; (, Journal of the European Mathematical Society)
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  4. ; ; ; (, Épijournal de Géométrie Algébrique)
    We generalize the finiteness theorem for the locus of Hodge classes withfixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodgeclasses to self-dual classes. The proof uses the definability of periodmappings in the o-minimal structure $$\mathbb{R}_{\mathrm{an},\exp}$$. 
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  5. ; ; (, Inventiones mathematicae)
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  6. ; (, Journal of Differential Geometry)
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  7. ; (, Compositio Mathematica)
    We prove a bound relating the volume of a curve near a cusp in a complex ball quotient $$X=\mathbb{B}/\unicode[STIX]{x1D6E4}$$ to its multiplicity at the cusp. There are a number of consequences: we show that for an $$n$$ -dimensional toroidal compactification $$\overline{X}$$ with boundary $$D$$ , $$K_{\overline{X}}+(1-\unicode[STIX]{x1D706})D$$ is ample for $$\unicode[STIX]{x1D706}\in (0,(n+1)/2\unicode[STIX]{x1D70B})$$ , and in particular that $$K_{\overline{X}}$$ is ample for $$n\geqslant 6$$ . By an independent algebraic argument, we prove that every ball quotient of dimension $$n\geqslant 4$$ is of general type, and conclude that the phenomenon famously exhibited by Hirzebruch in dimension 2 does not occur in higher dimensions. Finally, we investigate the applications to the problem of bounding the number of cusps and to the Green–Griffiths conjecture. 
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