Papers and preprints
- (BAA)-branes from higher Teichmüller theory, with Eric Y. Chen and Enya Hsiao. arXiv:2508.09562
Interpreting certain holomorphic Lagrangians that arise from the relative Langlands program, we construct moduli stacks underlying the generalized Slodowy categories of Collier--Sanders and $G^\mathbb{R}$-Higgs bundles over a Riemann surface. Furthermore, we extend the Cayley correspondence of Bradlow--Collier--García-Prada--Gothen--Oliveira to a morphism of Lagrangians over the Hitchin moduli stack, and initiate the study of its hyperholomorphic mirror partner under $S$-duality.
- Conformal limits in Cayley components and $\Theta$-positive opers, with Georgios Kydonakis, Adv Math (2026). doi:10.1016/j.aim.2026.110969
We study Gaiotto's conformal limit for the $G^\mathbb{R}$-Hitchin equations, when $G^\mathbb{R}$ is a simple real Lie group admitting a $\Theta$-positive structure. We identify a family of flat connections coming from certain solutions to the equations for which the conformal limit exists and admits the structure of an oper. We call this new class of opers appearing in the conformal limit $\Theta$-positive opers. The two families involved are parameterized by the same base space. This space is a generalization of the base of Hitchin's integrable system in the case when the structure group is a split real group.
- A comparison of generalized opers and (G,P)-opers, Indian J Pure Appl Math (2021). doi:10.1007/s13226-021-00170-0
The goal of this paper is to describe the relationship between generalized B-opers, generalized SO(2n,C)-opers and (G,P)-opers. In particular, we show that to each generalized B-oper there is a naturally associated (G,P)-oper, but there are some (G,P)-opers that do not arise as generalized B-opers or SO(2n,C)-opers.
- On the generalized SO(2n,C)-opers, with Indranil Biswas and Laura Schaposnik, Ann Glob Anal Geom (2021). doi:10.1007/s10455-021-09783-4
Since their introduction by Beilinson–Drinfeld (Opers, 1993. arXiv math/0501398; Quantization of Hitchin’s integrable system and Hecke eigensheaves, 1991), opers have seen several generalizations. In Biswas et al. (SIGMA Symmetry Integr Geom Methods Appl 16:041, 2020), a higher rank analog was studied, named generalized B-opers, where the successive quotients of the oper filtration are allowed to have higher rank and the underlying holomorphic vector bundle is endowed with a bilinear form which is compatible with both the filtration and the oper connection. Since the definition did not encompass the even orthogonal groups, we dedicate this paper to study generalized B-opers whose structure group is SO(2n,C) and show their close relationship with geometric structures on a Riemann surface.
- Generalized B-Opers, with Indranil Biswas and Laura Schaposnik, SIGMA 16 (2020). doi:10.3842/SIGMA.2020.041
Opers were introduced by Beilinson-Drinfeld [BD93, BD91], and in [Bis03] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing generalized B-opers (where "B" stands for "bilinear"), obtained by endowing the underlying vector bundle, in the set-up of [Bis03], with a bilinear form which is compatible with both the filtration and the connection. We study the geometry and topology arising through them.