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   Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu (March 2020, International Journal of Number Theory)

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   We first develop some basic facts about hypergeometric sheaves on the multiplicative group [Formula: see text] in characteristic [Formula: see text]. Certain of their Kummer pullbacks extend to irreducible local systems on the affine line in characteristic [Formula: see text]. One of these, of rank [Formula: see text] in characteristic [Formula: see text], turns out to have the Conway group [Formula: see text], in its irreducible orthogonal representation of degree [Formula: see text], as its arithmetic and geometric monodromy groups. 

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2. Experimenting with Symplectic Hypergeometric Monodromy Groups

   https://doi.org/10.1080/10586458.2020.1780516  

   Detinko, A. S.; Flannery, D. L.; Hulpke, A. (June 2020, Experimental Mathematics)

   We present new computational results for symplectic monodromy groups of hypergeometric dif- ferential equations. In particular, we compute the arithmetic closure of each group, sometimes jus- tifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties. 

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3. Braid loops with infinite monodromy on the Legendrian contact DGA

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4. Rigid local systems with monodromy group the Conway group ${\mathsf{Co}}_3$

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   Katz, Nicholas M.; Rojas-León, Antonio; Tiep, Pham Huu (January 2020, Journal of Number Theory)

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5. Geometry of the Wiman–Edge monodromy

   https://doi.org/10.1142/S1793525321500503  

   Stover, Matthew (September 2023, Journal of Topology and Analysis)

   The Wiman–Edge pencil is a pencil of genus 6 curves for which the generic member has automorphism group the alternating group [Formula: see text]. There is a unique smooth member, the Wiman sextic, with automorphism group the symmetric group [Formula: see text]. Farb and Looijenga proved that the monodromy of the Wiman–Edge pencil is commensurable with the Hilbert modular group [Formula: see text]. In this note, we give a complete description of the monodromy by congruence conditions modulo 4 and 5. The congruence condition modulo 4 is new, and this answers a question of Farb–Looijenga. We also show that the smooth resolution of the Baily–Borel compactification of the locally symmetric manifold associated with the monodromy is a projective surface of general type. Lastly, we give new information about the image of the period map for the pencil. 

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