I'm a postdoc member at IAS during 2021-2023. I was a graduate student of Dennis Gaitsgory.
1. Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor
pdf (last updated Aug. 27, 2020) arXiv
shorter version (with fewer appendices, last updated Aug. 27, 2020)
2. Deligne-Lusztig duality on the moduli stack of bundles
pdf (last updated Sep. 12, 2021) arXiv
Nearby Cycles and Dualities in Geometric Langlands Program
It covers the work of the above two preprints, and several new results on the same theme. It might be more reader-friendly than the preprints.
pdf (last updated Sep. 12, 2021)