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个人简介
Barannikov is known for his work on mirror symmetry, Morse theory, and Hodge theory. In mirror symmetry, he is a co-author of construction of Frobenius manifold, mirror symmetric to genus zero Gromov–Witten invariants.
He is one of authors of hypothesis of homological mirror symmetry for Fano manifolds.In the theory of exponential integrals, Barannikov is a co-author of the theorem on the degeneration of analogue of Hodge–de Rham spectral sequence.
In the theory of noncommutative varieties, Barannikov is the author of the theory of noncommutative Hodge structures.
Barannikov is known for: Barannikov–Morse complexes,Barannikov modules,Barannikov–Kontsevich construction,and Barannikov–Kontsevich theorem
研究兴趣
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Doklady Mathematicsno. 2 (2024): S325-S332
Doklady Mathematicsno. S2 (2023): S333-S347
arxiv(2023)
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CoRR (2023)
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