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419 results · page 9 of 17

Lectures on Cauchy Problem

Studies initial-value problems for partial differential equations. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Cauchy Problem

Sigeru Mizohata · Long lecture notes · Graduate · English

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Studies initial-value problems for partial differential equations. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Distributions; Sobolev spaces; PDE.

Use: Specialized graduate PDE reading.

Version: TIFR volume 35; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Complex Analytic Manifolds

Treats analytic manifolds and their local structure. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Complex Analytic Manifolds

Laurent Schwartz · Long lecture notes · Graduate · English

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Treats analytic manifolds and their local structure. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Complex analysis; topology.

Use: Classical geometric analysis preparation.

Version: TIFR volume 4; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Condensed Mathematics

Condensed sets, abelian groups and solid modules give an algebraic framework for topological objects.

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Lectures on Condensed Mathematics

Peter Scholze · Long lecture notes · Research · English

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Free PDF at the author or authorized archive.

Condensed sets, abelian groups and solid modules give an algebraic framework for topological objects.

Preparation: Sheaves; homological algebra; category theory.

Use: Enter condensed mathematics before liquid and analytic constructions.

Version: May 2026 revision of the summer 2019 Bonn course · Checked 2026-10-13

Full-text source checked: 2026-11-03

Found via — References: Lectures on Condensed Mathematics

Lectures on Curve Shortening Flow

Uses planar curves to develop maximum principles, monotonicity, Harnack inequalities and convergence to a round point.

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Lectures on Curve Shortening Flow

Robert Haslhofer · Lecture notes · Graduate · English

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The author’s university page links this freely readable PDF.

Uses planar curves to develop maximum principles, monotonicity, Harnack inequalities and convergence to a round point.

Preparation: Curves and curvature; real analysis; elementary PDE.

Use: Enter geometric evolution equations through a lower-dimensional model.

Version: February 20, 2026 · Checked 2026-10-13

Lectures on Cyclic Homology

Develops cyclic and Hochschild homology. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Cyclic Homology

Dale Husemoller · Long lecture notes · Graduate · English

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Develops cyclic and Hochschild homology. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Homological algebra; associative algebras.

Use: Bridge to noncommutative invariants.

Version: TIFR volume 83; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Deformations of Singularities

Studies deformation problems and algebraic singularities. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Deformations of Singularities

Michael Artin · Long lecture notes · Graduate · English

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Studies deformation problems and algebraic singularities. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Local algebra; algebraic geometry.

Use: Background for moduli and deformation theory.

Version: TIFR volume 54; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Diffusion Problems and Partial Differential Equations

Connects diffusion processes with analytical PDE methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Diffusion Problems and Partial Differential Equations

S. R. S. Varadhan · Long lecture notes · Graduate · English

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Connects diffusion processes with analytical PDE methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Measure-theoretic probability; PDE.

Use: Study the probability–analysis interface.

Version: TIFR volume 64; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Discrete Subgroups of Lie Groups

Studies lattices and geometry in Lie groups. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Discrete Subgroups of Lie Groups

George D. Mostow · Long lecture notes · Graduate · English

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Studies lattices and geometry in Lie groups. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Lie groups; differential geometry.

Use: Connect homogeneous spaces and geometric group theory.

Version: TIFR volume 48; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Disintegration of Measures

Studies conditional measure constructions in depth. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Disintegration of Measures

Laurent Schwartz · Long lecture notes · Graduate · English

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Studies conditional measure constructions in depth. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Measure theory; topology.

Use: Advanced probability and measure reference.

Version: TIFR volume 50; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Elliptic Partial Differential Equations

Introduces elliptic boundary-value problems and variational methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Elliptic Partial Differential Equations

Jacques-Louis Lions · Long lecture notes · Graduate · English

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Introduces elliptic boundary-value problems and variational methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Sobolev spaces; functional analysis.

Use: Graduate elliptic PDE study.

Version: TIFR volume 10; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Equations Defining Space Curves

A specialist course connecting equations, ideals and the geometry of space curves. Use after graded commutative algebra and projective geometry.

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Lectures on Equations Defining Space Curves

Lucien Szpiro · Long lecture notes · Research · English

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Complete institutional PDF, authorized for individual use only. Copyright remains with TIFR; retypesetting may retain errors. This is not a redistribution licence.

A specialist course connecting equations, ideals and the geometry of space curves. Use after graded commutative algebra and projective geometry.

Preparation: Commutative algebra; algebraic curves; projective geometry.

Version: TIFR Lectures on Mathematics 62; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Equivariant Stable Homotopy Theory

A finite-group course on orthogonal spectra, transfers, fixed points and norms; the author labels the notes incomplete.

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Lectures on Equivariant Stable Homotopy Theory

Stefan Schwede · Lecture notes · Research · English

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The author’s university page links this freely readable PDF.

A finite-group course on orthogonal spectra, transfers, fixed points and norms; the author labels the notes incomplete.

Preparation: Algebraic topology; spectra; group representations.

Use: Bridge ordinary stable homotopy to equivariant constructions.

Version: February 5, 2023 · Checked 2026-10-13

Lectures on Ergodic Theory

A sustained course on invariant measures, recurrence and ergodic dynamics.

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Lectures on Ergodic Theory

Henk Bruin · Long lecture notes · Graduate · English

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A sustained course on invariant measures, recurrence and ergodic dynamics.

Preparation: Measure theory; real analysis.

Use: Graduate entry into dynamical systems.

Version: May 8, 2023; notes in progress · Checked 2026-10-11

Lectures on Étale Cohomology

Develops étale morphisms, sites and cohomology through base change and the Weil conjectures. These freely available course notes are not the separate 1980 Princeton book.

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Lectures on Étale Cohomology

J. S. Milne · Long lecture notes · Research · English

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Develops étale morphisms, sites and cohomology through base change and the Weil conjectures. These freely available course notes are not the separate 1980 Princeton book.

Preparation: Scheme theory; homological algebra.

Use: First sustained study of étale cohomology.

Version: v2.21, March 2013 · Checked 2026-10-11

Full-text source checked: 2026-11-03

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Lectures on Expansion Techniques in Algebraic Geometry

An algebraic-geometry specialization emphasizing expansion techniques and local algebra. Use after commutative algebra and basic algebraic curves.

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Lectures on Expansion Techniques in Algebraic Geometry

Shreeram S. Abhyankar · Long lecture notes · Research · English

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Complete institutional PDF, authorized for individual use only. Copyright remains with TIFR; retypesetting may retain errors. This is not a redistribution licence.

An algebraic-geometry specialization emphasizing expansion techniques and local algebra. Use after commutative algebra and basic algebraic curves.

Preparation: Local algebra; algebraic geometry.

Version: TIFR Lectures on Mathematics 57; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Exterior Differential Systems

Studies differential systems using geometric and exterior-algebraic methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Exterior Differential Systems

Masatake Kuranishi · Long lecture notes · Graduate · English

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Studies differential systems using geometric and exterior-algebraic methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Differential forms; manifolds; PDE.

Use: Research preparation in geometric PDE.

Version: TIFR volume 25; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Fibre Bundles and Differential Geometry

Develops connections and bundle-theoretic differential geometry. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Fibre Bundles and Differential Geometry

Jean-Louis Koszul · Long lecture notes · Graduate · English

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Develops connections and bundle-theoretic differential geometry. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Smooth manifolds; linear algebra.

Use: Bridge manifolds and geometric structures.

Version: TIFR volume 20; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Forms of Higher Degree

A specialized arithmetic course on higher-degree forms and related local questions. Study field and valuation foundations before its arithmetic constructions.

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Lectures on Forms of Higher Degree

Jun-ichi Igusa · Long lecture notes · Research · English

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Complete institutional PDF, authorized for individual use only. Copyright remains with TIFR; retypesetting may retain errors. This is not a redistribution licence.

A specialized arithmetic course on higher-degree forms and related local questions. Study field and valuation foundations before its arithmetic constructions.

Preparation: Algebraic number theory; local fields.

Version: TIFR Lectures on Mathematics 59; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Frobenius Splittings and B-Modules

Studies positive-characteristic geometric and representation-theoretic methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Frobenius Splittings and B-Modules

Wilberd van der Kallen · Long lecture notes · Graduate · English

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Studies positive-characteristic geometric and representation-theoretic methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Algebraic groups; characteristic-p geometry.

Use: Connect Frobenius techniques and representation theory.

Version: TIFR volume 84; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Galois Cohomology of Classical Groups

Applies cohomological methods to classical algebraic groups. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Galois Cohomology of Classical Groups

Martin Kneser · Long lecture notes · Graduate · English

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Applies cohomological methods to classical algebraic groups. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Galois theory; algebraic groups; cohomology.

Use: Research preparation in arithmetic groups.

Version: TIFR volume 47; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Geodesics in Riemannian Geometry

A sustained course on geodesics and Riemannian methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Geodesics in Riemannian Geometry

Marcel Berger · Long lecture notes · Graduate · English

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A sustained course on geodesics and Riemannian methods. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Riemannian manifolds; differential equations.

Use: Develop geometric intuition alongside formal theory.

Version: TIFR volume 33; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Groups of Transformations

Studies group actions in a geometric setting. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

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Lectures on Groups of Transformations

Jean-Louis Koszul · Long lecture notes · Graduate · English

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Studies group actions in a geometric setting. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Lie groups; smooth manifolds.

Use: Connect symmetry and geometry.

Version: TIFR volume 32; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Holomorphic Curves in Symplectic and Contact Geometry

Develops analytic foundations for holomorphic curves, including elliptic regularity, Fredholm theory, moduli spaces and compactness.

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Lectures on Holomorphic Curves in Symplectic and Contact Geometry

Chris Wendl · Book draft / lecture notes · Graduate · English

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The complete author-deposited PDF opens in the arXiv archive.

Develops analytic foundations for holomorphic curves, including elliptic regularity, Fredholm theory, moduli spaces and compactness.

Preparation: Smooth manifolds; differential forms; complex analysis; functional analysis.

Use: Build the analytic background needed for contact and symplectic research.

Version: Work-in-progress version 3.2, May 28, 2014; arXiv v2 · Checked 2026-10-13

Lectures on Infinitary Model Theory

Develops infinitary languages, back-and-forth methods, Scott analysis and model-existence questions.

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Lectures on Infinitary Model Theory

David Marker · Course notes · Research · English

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Develops infinitary languages, back-and-forth methods, Scott analysis and model-existence questions.

Preparation: First-order model theory; countable structures.

Use: Move from first-order foundations to infinitary classification methods.

Version: Fall 2013 course notes · Checked 2026-10-13

Lectures on Infinity Categories

A sustained course on infinity categories, including the homotopical constructions needed to use them in practice.

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Lectures on Infinity Categories

Vladimir Hinich · Long lecture notes · Graduate · English

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Public full text; checked against the title and contents.

A sustained course on infinity categories, including the homotopical constructions needed to use them in practice.

Preparation: Categories; simplicial sets; elementary homotopy theory.

Use: Use this course to bridge simplicial homotopy theory and technical infinity-category references.

Version: arXiv 1709.06271; inspected electronic version · Checked 2026-11-03

Found via — References: Lectures on Infinity Categories