Lectures related to Integration Theory: Berkovich Spaces

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.

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

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

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

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Explores the Albanese morphism of varieties with Kodaira dimension zero in positive characteristic.

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

Covers the basics of real analysis, including limits, sequences, and continuous functions.

Explores real number sequences, convergence, limits, boundedness, and monotonicity.

Covers the analysis of worst time complexity for algorithms and time complexity with real numbers and integers.

Discusses Cauchy sequences, sub-sequences, and numerical series with parameters.

Covers the Archimedean property and the proposition for all x in a set, there exists a positive real number n such that n*x is greater than y.

Introduces the course content by linking familiar mathematics with upcoming topics.

Covers selected mathematical topics including numbers, approximations, algebraic structures, limits, and series.

Explores the concept of real numbers through decimal notation and fraction representation.

Explains interior points, convergence of sequences, and the dense property in real numbers.