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  1. ; (, Rendiconti Lincei, Matematica e Applicazioni)
    We develop the general theory of Airy sheaves of Laurent type, the local systems whose trace functions have a particular “Airy-Laurent” shape. The main goal is to provide tools for the later determination of their monodromy groups. See [Eur. J. Math. 10 (2024), article no. 65] for instances of such determinations. 
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    Free, publicly-accessible full text available March 23, 2027
  2. ; ; (, Rendiconti Lincei, Matematica e Applicazioni)
    We prove two results on some special generators of finite simple groups and use them to prove that every non-abelian finite simple groupSadmits a non-congruence presentation (as conjectured by Chen, Lubotzky, and Tiep (2024)), and that ifShas a non-trivial Schur multiplier, then it admits a smooth cover (as conjectured by Chen, Fan, Li, and Zhu (2024)). 
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    Free, publicly-accessible full text available March 23, 2027
  3. ; (, Journal of Algebra)
    Free, publicly-accessible full text available December 1, 2026
  4. ; ; (, Journal of Algebra)
    Free, publicly-accessible full text available November 1, 2026
  5. ; (, Princeton University Press)
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  6. ; ; (, Memoirs of the American Mathematical Society)
    We continue the program set up in [Geom. Funct. Anal.31(2021), no. 3, 562–662] to study the monodromy groups of hypergeometric and Kloosterman sheaves. We gave there easy to apply criteria on these sheaves that their monodromy groups satisfy the group-theoretic condition (S+) \mathrm {(\textbf {S+})} , and showed that many of the finite almost quasisimple groups occur as monodromy groups of such sheaves. Here, we show that precisely 12 of the 26 sporadic simple groups occur in this way (and explain why the others cannot occur this way). We also treat some small rank finite groups of Lie type, as well as certain primitive complex reflection groups. 
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  7. (, Cambridge University Press)
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  8. ; (, Pacific Journal of Mathematics)
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  9. ; (, Forum of Mathematics, Sigma)
    Abstract We determine the geometric monodromy groups attached to various families, both one-parameter and multi-parameter, of exponential sums over finite fields, or, more precisely, the geometric monodromy groups of the$$\ell $$-adic local systems on affine spaces in characteristic$$p> 0$$whose trace functions are these exponential sums. The exponential sums here are much more general than we previously were able to consider. As a byproduct, we determine the number of irreducible components of maximal dimension in certain intersections of Fermat surfaces. We also show that in any family of such local systems, say parameterized by an affine spaceS, there is a dense open set ofSover which the geometric monodromy group of the corresponding local system is a fixed known group. 
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  10. ; ; (, Mathematische Zeitschrift)
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