Rahbar Virk

Jun 2026

• Realizations of exponential sheaves and Fourier transform
  This is unstable and will be updated periodically (current version matches with that on the arXiv). Remark 7.9 is not quite correct: nearby cycles will not be isomorphic to a realization (roughly, although "topologically" the realizations/fibres are the same, their exponential type is different). It is simply limiting behavior.
• Vanishing(!) vanishing cycles
  A simple result about vanishing cycles that I don't understand as well as I would like to.

May 2026

• For just Fourier inversion (re: the note(s) on exponential sheaves above), the more notationally digestible case of the affine line (that nevertheless encapsulates the essence of the general version) can be found here.

Aug 2025

• On the Clemens-Schmid exact sequence
• Monodromy triangle for nearby cycles
  Via the octahedron axiom. I.e., without invoking any explicit constructions.
• Hodge-Grothendieck classes and monodromy invariants of nearby cycles sheaves

Jul 2025 (tomography rabbit hole)

• Quiver and standard operations for monodromic perverse sheaves on a trivial line bundle
• Dualizing complex for a manifold with boundary
• Fourier-Sato transform for monodromic mixed Hodge modules
• Nearby cycles vs specialization for conic sheaves

Aug 2022 miscellanea

• Line fields on manifolds

Sep-Dec 2021 sundries

• Homotopy limits and fixed point stacks
  More general version of `On fixed point stacks' below. A version halfway between the two is here.
• On fixed point stacks
• A remark on Ehresmann's fibration theorem
• Fixed points and Langlands parameter spaces for real groups
• Discussion around integration along the fiber
• Discussion around integration along the fiber for motivic sheaves (complex varieties)

Some of these notes will end up on the arXiv as permanent repository.

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Oct 2010 - 14 Oct 2020

25 Oct 2010 - 23 Jul 2019

21 Jan 2019

???? - 2016

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Last updated: 20 Jun, 2026