Complex geometry

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Related lectures (32)

Numerical Flow Simulation: Methods and Applications

Explores numerical methods for flow simulation, including finite element, spectral, particle, and lattice Boltzmann methods.

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Riemann Surfaces: Complex Manifolds

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Quotient Criterion

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.

Computational Inverse Design

Explores computational inverse design of deployable structures and geometric computing for materials fabrication and engineering applications.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

Cartier Divisors and Invertible Sheaves

Covers Cartier divisors, invertible sheaves, and their properties in algebraic geometry.

Varieties with nef anti-canonical: Surjective Albanese

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Examples of Collapse

Explores examples of collapse, focusing on the morphing of shapes like the ball, cone, and more complex structures.

Fourier Transform and Residue Calculus

Explores Fourier transform calculation and residue calculus in mathematical analysis.

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