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I am studying complex analysis and complex geometry, especially around the Oka principle, the homotopy principle in complex analysis, and Gromov ellipticity, the opposite of Kobayashi hyperbolicity.
The Oka principle is a heuristic principle that analytic problems on Stein manifolds have only topological obstructions, which was extolled by Thom as “the most beautiful principle in analysis” when he visited Kyushu University.
I have clarified the relationship between this analytic principle and ellipticity in complex geometry, and am currently studying the Oka principle from a broader perspective, including algebraic geometry and differential geometry.