12 citations · 28 across the 17 of their papers we have counts for
26 papers
Can one hear the shape of a lattice random walk?
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We construct distinct high-dimensional mean-zero finite range lattice random walks having pairwise-equal return probabilities for all step counts. The same examples provide pairwis…
Torsors on moduli spaces of principal -bundles
Indranil Biswas, Swarnava Mukhopadhyay
Let be a semisimple complex algebraic group with a simple Lie algebra , and let denote the moduli stack of topologically trivial stable -bu…
Motivic factorisation of KZ local systems and deformations of representation and fusion rings
Prakash Belkale, Najmuddin Fakhruddin, Swarnava Mukhopadhyay
Let be a simple Lie algebra over . The KZ connection is a connection on the constant bundle associated to a set of finite dimensional irreducible rep…
Torelli theorem for moduli stacks of vector bundles and principal G-bundles
David Alfaya, Indranil Biswas, Tomás L. Gómez +1
Given any irreducible smooth complex projective curve , of genus at least , consider the moduli stack of vector bundles on of fixed rank and determinant. It is proved tha…
A parabolic analog of a theorem of Beilinson and Schechtman
Indranil Biswas, Swarnava Mukhopadhyay, Richard Wentworth
For a simple, simply connected, complex group G, we prove an explicit formula to compute the Atiyah class of parabolic determinant of cohomology line bundle on the moduli space of…
Graph potentials and symplectic geometry of moduli spaces of vector bundles
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We give the first examples of Fano manifolds with multiple optimal tori, i.e.~we construct monotone Lagrangian tori , such that the weighted number of holomorphic Maslov index t…
Graph potentials and topological quantum field theories
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. We show that the birational type of the graph potential only depends on the h…
Geometrization of the TUY/WZW/KZ connection
Indranil Biswas, Swarnava Mukhopadhyay, Richard Wentworth
Given a simple, simply connected, complex algebraic group G, a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-…
A Hitchin connection on non abelian theta functions for parabolic G-bundles
Indranil Biswas, Swarnava Mukhopadhyay, Richard Wentworth
For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistabl…
Decompositions of moduli spaces of vector bundles and graph potentials
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently form…
Crossed modular categories and the Verlinde formula for twisted conformal blocks
Tanmay Deshpande, Swarnava Mukhopadhyay
In this paper, we give a Verlinde formula for computing the ranks of the bundles of twisted conformal blocks associated with a simple Lie algebra equipped with an action of a finit…
Spectral data for spin Higgs bundles
Swarnava Mukhopadhyay, Richard Wentworth
In this paper we determine the spectral data parametrizing Higgs bundles in a generic fiber of the Hitchin map for the case where the structure group is the special Clifford group…
Admissible subcategories in derived categories of moduli of vector bundles on curves
Pieter Belmans, Swarnava Mukhopadhyay
We show that the Poincaré bundle gives a fully faithful embedding from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of b…
Examples violating Golyshev's canonical strip hypotheses
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay
We give the first examples of smooth Fano and Calabi-Yau varieties violating the (narrow) canonical strip hypothesis, which concerns the location of the roots of Hilbert polynomial…
Hyperplane arrangements and tensor product invariants
Prakash Belkale, Patrick Brosnan, Swarnava Mukhopadhyay
In the first part of this paper, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a loc…
On higher Chern classes of vector bundles of conformal blocks
Angela Gibney, Swarnava Mukhopadhyay
Here we consider higher Chern classes of vector bundles of conformal blocks on , giving explicit formulas for them, and extending various results…
Fundamental group of moduli of principal bundles on curves
Indranil Biswas, Swarnava Mukhopadhyay, Arjun Paul
Let be a compact connected Riemann surface of genus at least two, and let be a connected semisimple affine algebraic group defined over . For any $δ\in π_1({G}…
Generalized theta functions, strange duality, and odd orthogonal bundles on curves
Swarnava Mukhopadhyay, Richard Wentworth
This paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial Stiefel-Whitney class and the associated space of twisted spin bundles. In parti…
Strange Duality of Verlinde spaces for G_2 and F_4
Swarnava Mukhopadhyay
We prove that the pull back of the canonical theta divisor for E_8-bundles at level one induces a strange duality between Verlinde spaces for G_2 and F_4 at level one on smooth cur…
Nonvanishing of conformal blocks divisors on
Prakash Belkale, Angela Gibney, Swarnava Mukhopadhyay
We introduce and study the problem of finding necessary and sufficient conditions under which a conformal blocks divisor on is nonzero. We give necessary conditions…
Remarks on level one conformal blocks divisors
Swarnava Mukhopadhyay
We show that conformal blocks divisors of type B_r and D_r at level one are effective sums of boundary divisors of . We also prove that the conformal blocks divisor…
Diagram automorphisms and Rank-Level duality
Swarnava Mukhopadhyay
We study the effect of diagram automorphisms on rank-level duality. We use it to prove new symplectic rank-level dualities on genus zero smooth curves with marked points and chosen…
Vanishing and identities of conformal blocks divisors
Prakash Belkale, Angela Gibney, Swarnava Mukhopadhyay
Conformal block divisors in type A on are shown to satisfy new symmetries when levels and ranks are interchanged in non-standard ways. A connection with the quant…
Rank-Level duality and Conformal Block divisors
Swarnava Mukhopadhyay
We describe new relations among conformal block divisors in . These relations appear from various rank-level dualities of conforma…