Lecture notes use condensed mathematics to reprove finiteness of coherent cohomology, Serre duality, GAGA, and Hirzebruch-Riemann-Roch for compact complex manifolds.
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Proves algebraic hyperbolicity and big Picard theorems for Kähler manifolds with zero-dimensional period maps from polarized VHS, plus hyperbolicity and general type properties for their compactifications.
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Condensed Mathematics and Complex Geometry
Lecture notes use condensed mathematics to reprove finiteness of coherent cohomology, Serre duality, GAGA, and Hirzebruch-Riemann-Roch for compact complex manifolds.
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Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
Proves algebraic hyperbolicity and big Picard theorems for Kähler manifolds with zero-dimensional period maps from polarized VHS, plus hyperbolicity and general type properties for their compactifications.