Research Methods: Setting Up Experiments and Interview Guides

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Related lectures (32)

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Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Setting up Experiments: Compactness, Isometries, Quasi-Isometry

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Continuous Functions on Compact Sets

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Interior Points and Compact Sets

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.