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Geometry, Symmetry and Physics

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A description of affine canonical basis elements

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CFT and representations of quantum (super)algebras:quantization of (super)KdV hierarchies.

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An algebraic and a diagramatical description of Perverse sheaves on Grassmannians

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Hochschild cohomology of preprojective algebras

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E8 guage theory, WZW models, and supersymmetry.

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Geometric Langlands conjecture and the Hitchin system: from quantization to reduction mod p.

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Moonshine beyond the Monster *joint with Lie Algebras & Rep.Theory

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Cherednik and Hecke algebras of orbifolds

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A new methodology in Geometric Transversal Theory

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Knot homology and its applictions

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