Sandra Nair

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• Andrews, E., Bhamidipati, D., Fox, M., Goodson, H., Groen, S. R., & Nair, S. (2026). On the classification of indecomposable Ekedahl-Oort strata in unitary Shimura varieties, and related Newton polygons.
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  In this paper, we give a complete classification of indecomposable Ekedahl--Oort strata of Shimura varieties associated to the unitary group $\mathsf{GU}(a, b)$ over an odd inert prime. We show that each indecomposable stratum is one of four types: unitary unicycle, unitary bicycle, Serre unicycle, or Serre bicycle; the latter two types are named for a tensor construction of abelian varieties developed by Serre. We provide an algorithm that translates the description of a stratum in terms of words in the alphabet $\{\texttt{f},\texttt{v}\}$ to the corresponding Weyl group coset representative. Finally, using a $p$-adic lift, we construct a `tautological' point in each Ekedahl--Oort stratum, and compute its Newton polygon. As an application, we show that the indecomposable Ekedahl--Oort strata corresponding to unitary unicycles and Serre unicycles always intersect the supersingular locus.[Journal_ref: ]
• Andrews, E., Bhamidipati, D., Goodson, H., Groen, S. R., & Nair, S. (2026). Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties.
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  Let $\mathbb{k}$ be an algebraically closed field of characteristic $p>2$ and let $O_K$ be an imaginary quadratic order in which $p$ is inert. For any $a,b\in \mathbb{Z}_{\geq 0}$ not both 0, denote by $M(a,b)$ the unitary Shimura variety that parametrizes principally polarized abelian varieties over $\mathbb{k}$ with an action of signature $(a,b)$ by $O_K$ (subject to certain compatibility conditions). For any $a,b,c,d \in \mathbb{Z}_{\geq 0}$, there is a natural product map $M(a,b) \times M(c,d) \to M(a+c,b+d)$, which induces a map on Ekedahl-Oort strata. In this paper we focus on product maps where at least one of the factors is superspecial, since most Ekedahl-Oort strata of unitary Shimura varieties contain such a factor. We describe maps with this property completely on the level of Weyl group coset representatives. We also characterize, on the level of Weyl group coset representatives, which Ekedahl-Oort strata of $M(a,b)$ admit a superspecial factor.[Journal_ref: ]
• Andrews, E., Bhamidipati, D., Fox, M., Goodson, H., Groen, S. R., & Nair, S. (2025). Ekedahl-Oort strata in the $\mathsf{GU}(q-2,2)$ Shimura variety.
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  This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(q-2,2)$ Shimura varieties, which classify abelian varieties with additional structure. These Shimura varieties admit two stratifications of interest: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. In this paper, we present several novel techniques that give a better understanding of the Ekedahl-Oort stratification and of the interaction between the two stratifications for a general signature $(q-2,2)$.[Journal_ref: ]
• Andrews, E., Bhamidipati, D., Fox, M., Goodson, H., Groen, S. R., & Nair, S. (2025). The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety.
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  This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an imaginary quadratic field in which $p$ is inert. We completely describe the interaction of two stratifications of these Shimura varieties: the Ekedahl-Oort stratification, based on the isomorphism class of the $p$-torsion subgroup scheme, and the Newton stratification, based on the isogeny class of the $p$-divisible group. We identify which Ekedahl-Oort and Newton strata intersect.[Journal_ref: ]
• Andrews, E., Bhamidipati, D., Fox, M., Goodson, H., Groen, S. R., & Nair, S. (2025). Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups.
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  The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an application, we establish bounds on the isogeny cutoffs for these $p$-divisible groups. Finally, we rephrase our results in the language of the $\mathrm{BT}_m$ stratifications of unitary Shimura varieties of signature $(a,b)$.[Journal_ref: ]
• Bauman, A., Ellers, H., Hu, G., Murayama, T., Nair, S., & Wang, Y. (2025). Variants of normality and steadfastness deform. Michigan Mathematical Journal, 75(1), 145--172.
• Brosowsky, A., Du, H., Krishna, M., Nair, S., Page, J., & Ryan, T. (2022). Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm.
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  In this paper, we study maximal sets of skew lines on Hermitian surfaces. We give a new algorithm to compute these sets and give some computational results for Hermitian surfaces of degrees 3,4, and 5. In more generality, this algorithm solves a new variant of the clique listing problem, which may be more approachable than the classical problem. Finally, we explicitly construct a large skew set of lines on Hermitian varieties of any degree and use it to give a lower bound on the largest size of maximal skew sets and a lower bound on the possible number of maximal skew sets.[Journal_ref: ]