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  1. ; (, Forum of Mathematics, Pi)
    Abstract In this paper, we determine the number of general points through which a Brill–Noether curve of fixed degree and genus in any projective space can be passed. 
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  2. ; ; ; ; ; ; (, Bulletin of the London Mathematical Society)
    Abstract On a projective variety defined over a global field, any Brauer–Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show that this subgroup can require arbitrarily many generators. 
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  3. ; ; (, Forum of Mathematics, Sigma)
    Abstract Let$$\alpha \colon X \to Y$$be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under$$\alpha $$is semistable if the genus ofYis at least$$1$$and stable if the genus ofYis at least$$2$$. We prove this conjecture if the map$$\alpha $$is general in any component of the Hurwitz space of covers of an arbitrary smooth curveY. 
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  4. ; ; (, International Mathematics Research Notices)
    Abstract Let $$\alpha \colon X \to Y$$ be a general degree $$r$$ primitive map of nonsingular, irreducible, projective curves over an algebraically closed field of characteristic zero or larger than $$r$$. We prove that the Tschirnhausen bundle of $$\alpha $$ is semistable if $$g(Y) \geq 1$$ and stable if $$g(Y) \geq 2$$. 
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  5. ; (, Advances in Mathematics)
    Free, publicly-accessible full text available January 1, 2026
  6. ; ; ; ; (, Transactions of the American Mathematical Society, Series B)
    We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck–Witt group. We show that this enrichment is related to the topology of the real points of a lift. For cellular schemes over a field, we prove a rationality result for this enriched logarithmic derivative of the zeta function as an analogue of part of the Weil conjectures. We also compute several examples, including toric varieties, and show that the enrichment is a motivic measure. 
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  7. ; ; (, Journal of the European Mathematical Society)
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  8. ; ; ; ; (, Algebraic Geometry)
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  9. ; ; ; ; ; ; (, American Mathematical Society)
    Accepted Manuscript Full Text Available