Mathematics Library

Lectures on Quadratic Jordan Algebras

Nathan Jacobson · Long lecture notes · Research · English

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A specialist introduction to nonassociative algebra and quadratic Jordan structures. Follow an ordinary ring-and-module course first.

Preparation: Graduate algebra; nonassociative algebra foundations.

Version: TIFR Lectures on Mathematics 45; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Representations of Complex Semi-simple Lie Groups

Thomas J. Enright · Long lecture notes · Research · English

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A specialist continuation from semisimple Lie algebras to representation-theoretic structure. Follow roots, weights and basic representations first.

Preparation: Lie algebras; Lie groups; representation theory.

Version: TIFR Lectures on Mathematics 66; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Riemann Matrices

Carl Ludwig Siegel · Long lecture notes · Graduate · English

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Studies period matrices and associated analytic structures. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Complex analysis; linear algebra.

Use: Background for abelian and modular geometry.

Version: TIFR volume 28; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Schramm–Loewner Evolution

Nathanaël Berestycki and James R. Norris · Lecture notes · Research · English

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The complete PDF opens publicly from the author’s university resource page.

Connects conformal maps and complex Brownian motion to the basic theory of SLE.

Preparation: Complex analysis; measure-theoretic probability; Brownian motion.

Use: Prepare for research on planar random curves.

Version: August 22, 2023 · Checked 2026-10-13

Lectures on Semi-Group Theory and its Application to Cauchy’s Problem in Partial Differential Equations

Kôsaku Yosida · Long lecture notes · Graduate · English

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Develops operator semigroups for evolution equations. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Functional analysis; differential equations.

Use: Connect abstract operators and PDE.

Version: TIFR volume 8; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Sheaf Theory

C. H. Dowker · Long lecture notes · Graduate · English

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A sustained sheaf-theoretic course linking topology and homological methods. Useful for readers moving beyond categorical vocabulary to local-to-global constructions.

Preparation: Topology; modules; homological algebra.

Version: TIFR Lectures on Mathematics 6; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Siegel Modular Forms and Representation by Quadratic Forms

Yoshiyuki Kitaoka · Long lecture notes · Research · English

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Connects Siegel modular forms and the arithmetic of quadratic forms. A higher-dimensional branch after classical modular forms.

Preparation: Modular forms; quadratic forms; algebraic number theory.

Version: TIFR Lectures on Mathematics 77; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Siegel’s Modular Functions

Hans Maass · Long lecture notes · Graduate · English

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Studies modular objects in higher-dimensional settings. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Modular forms; several complex variables.

Use: Prepare for Siegel modular theory.

Version: TIFR volume 3; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Sieve Methods

Hans-Egon Richert · Long lecture notes · Graduate · English

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A sustained exposition of sieve techniques. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Analytic number theory; asymptotic estimates.

Use: Focused reading in sieve theory.

Version: TIFR volume 55; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Sieve Methods and Prime Number Theory

Yoichi Motohashi · Long lecture notes · Research · English

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A specialist sieve-theoretic route into prime-distribution questions. Read after a first analytic-number-theory course.

Preparation: Analytic number theory; elementary sieves; asymptotic estimates.

Version: TIFR Lectures on Mathematics 72; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Sieves

D. R. Heath-Brown; notes written by Boris Moroz · Long lecture notes · Graduate · English

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Full author-submitted PDF opened publicly in the arXiv archive.

A systematic course in sieve methods, including upper-bound sieves, the large sieve and applications to counting primes.

Preparation: Elementary number theory and analysis; basic analytic number theory.

Use: Study sieve techniques before approaching research on primes and almost-primes.

Version: arXiv v1, 25 September 2002; Bonn lectures January–June 2002 · Checked 2026-10-13

Lectures on Some Aspects of p-adic Analysis

François Bruhat · Long lecture notes · Graduate · English

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Studies analysis over nonarchimedean fields. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: p-adic fields; algebra; analysis.

Use: Prepare for local arithmetic geometry.

Version: TIFR volume 27; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Some Fixed Point Theorems of Functional Analysis

F. F. Bonsall · Long lecture notes · Graduate · English

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Develops fixed-point principles in functional-analytic settings. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Banach spaces; topology.

Use: Connect existence methods and analysis.

Version: TIFR volume 26; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Spaces of Nonpositive Curvature

Werner Ballmann; appendix by Misha Brin · Monograph / author text · Advanced · English (legacy metadata)

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Develops nonpositive curvature, boundaries at infinity and rank rigidity, with an appendix on geodesic-flow ergodicity. A specialized continuation, not a general first Riemannian geometry textbook.

Preparation: Riemannian geometry; topology; some dynamical systems.

Legacy entry retained from October 8, 2026

Lectures on Stochastic Control and Nonlinear Filtering

M. H. A. Davis · Long lecture notes · Research · English

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A stochastic-analysis branch connecting control and filtering. This is a specialized application, not an elementary probability course.

Preparation: Stochastic processes; martingales; SDE.

Version: TIFR Lectures on Mathematics 75; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on Stochastic Differential Equations and Malliavin Calculus

Shinzo Watanabe · Long lecture notes · Graduate · English

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Develops stochastic equations and differential methods on probability spaces. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Brownian motion; stochastic calculus.

Use: Research preparation in Malliavin calculus.

Version: TIFR volume 73; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Stochastic Flows and Applications

Hiroshi Kunita · Long lecture notes · Graduate · English

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Studies stochastic flow constructions and applications. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Stochastic calculus; differential equations.

Use: Advanced stochastic dynamics reference.

Version: TIFR volume 78; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Stochastic Processes

Kiyosi Itô · Long lecture notes · Graduate · English

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Develops the mathematical theory of stochastic processes. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Measure-theoretic probability.

Use: Classical foundations for stochastic analysis.

Version: TIFR volume 24; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Stratification of Complex Analytic Sets

Marie-Hélène Schwartz · Long lecture notes · Graduate · English

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Studies singular analytic spaces via stratifications. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Several complex variables; topology.

Use: Background for singular geometric spaces.

Version: TIFR volume 38; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on Symplectic Geometry

Ana Cannas da Silva · Lecture text · Introductory · English (legacy metadata)

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A graduate introduction to symplectic forms, Hamiltonian geometry and reduction. Efficient for readers with manifold foundations; not an elementary introduction to geometry.

Preparation: Smooth manifolds; differential forms; de Rham cohomology.

Legacy entry retained from October 8, 2026

Lectures on the Algebraic Theory of Fields

K. G. Ramanathan · Long lecture notes · Graduate · English

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A classical field-theoretic course for strengthening algebraic-extension and Galois arguments. Compare the historical presentation with a modern algebra text.

Preparation: Abstract algebra; fields and polynomial rings.

Version: TIFR Lectures on Mathematics 5; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on the Ekeland Variational Principle with Applications and Detours

Djairo G. de Figueiredo · Long lecture notes · Graduate · English

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Develops variational techniques for existence and optimization. Historical notation may differ from current treatments. Individual-use access only; do not redistribute.

Preparation: Functional analysis; nonlinear analysis.

Use: Apply variational principles to nonlinear problems.

Version: TIFR volume 81; retypeset digital edition (see PDF imprint for publication year) · Checked 2026-10-11

Lectures on the Finite Element Method

Philippe G. Ciarlet · Long lecture notes · Graduate · English

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A numerical-PDE specialization with mathematical approximation foundations. Distinguish discretization theory from pure PDE existence and regularity.

Preparation: Sobolev spaces; variational PDE; numerical linear algebra.

Version: TIFR Lectures on Mathematics 49; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on the Fourteenth Problem of Hilbert

Masayoshi Nagata · Long lecture notes · Research · English

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A specialist course on finite generation and invariant-ring phenomena. Read after Noetherian rings and examples in invariant theory.

Preparation: Commutative algebra; invariant theory.

Version: TIFR Lectures on Mathematics 31; authorized retypeset historical edition — original date on title page · Checked 2026-10-11

Lectures on the Geometry of Manifolds

Liviu I. Nicolaescu · Author manuscript · Graduate · English

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The complete PDF opens on the author’s or university’s public site.

A sustained course combining smooth and Riemannian geometry with bundles and global analysis. Use the analytic chapters as preparation for geometric operators and index theory.

Preparation: Analysis; linear algebra; topology; differential equations.

Use: Follow a graduate geometry course, then read selected global-analysis chapters.

Version: Author manuscript dated February 21, 2026 · Checked 2026-10-13