Nikolay Grantcharov

Limited-Term Assistant Professor of Mathematics
University of Georgia

I am a geometric representation theorist currently working at the University of Georgia. My research interests include Higgs and Coulomb branches, symplectic duality, DAHAs, deformation theory, and algebraic geometry.

I received my Ph.D. in Mathematics from the University of Chicago, where I was supported by an NSF Graduate Research Fellowship and advised by Victor Ginzburg. Before that, I earned my Bachelor's degree in mathematics from the University of California, Berkeley.

Email: nikolayg@uga.edu

Curriculum Vitae

Announcements

Cohomology on Cotangent Bundles of Partial Flag Varieties in Type A

Preprint, September 4, 2026.

We prove higher cohomology vanishing and describe global sections of vector bundles on \(T^*(\mathrm{SL}_n/P)\) obtained by pulling back bundles on \(\mathrm{SL}_n/P\) associated to \(\mathrm{SL}_n\)-dominant weights. Using the Braverman–Kazhdan intertwiners constructed in earlier joint work with Aaron Slipper, we then give explicit generators for \(\mathbf{C}[T^*(\mathrm{SL}_n/[P,P])]\). In a joint appendix with Tom Gannon, we show that its spectrum has terminal singularities. arXiv

Deformation theory of the \((C_n^\vee,C_n)\)-DAHA

Preprint, June 28, 2026.

We provide a zeros-and-residues realizations of the double affine Hecke algebra associated with the non-reduced affine root system of type \((C_n^\vee,C_n)\). We also show it is the universal deformation of a crossed product algebra of a quantum torus and finite Weyl group. arXiv

Quasi-classical Braverman-–Kazhdan intertwiners via quiver varieties

Preprint, June 12, 2026.

With Aaron Slipper, we construct isomorphisms between affinized cotangent bundles of Braverman–Kazhdan spaces in type A using reflection functors for quiver varieties with an SL-gauge group. arXiv

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