GLn (R) actions on Posn(R) -- Measures, Integration, and Quadratic Model -- Special Functions on Posn(R) -- Invariant Differential Operators on Posn(R) -- Poisson duality and zeta functions -- Eisenstein Series: First Part -- Geometric and Analytic Estimates -- Eisenstein Series: Second Part.Posn(R) and Eisenstein Series provides an introduction, requiring minimal prerequisites, to the analysis…
Absolute Values -- Valuations -- Extension of Valuations -- Henselian Fields -- Structure Theory -- Applications of Valuation Theory.Absolute values and their completions -like the p-adic number fields- play an important role in number theory. Krull's generalization of absolute values to valuations made applications in other branches of mathematics, such as algebraic geometry, possible. In valu…
Solving Polynomial Equations -- Resultants -- Computation in Local Rings -- Modules -- Free Resolutions -- Polytopes, Resultants, and Equations -- Polyhedral Regions and Polynomials -- Algebraic Coding Theory -- The Berlekamp-Massey-Sakata Decoding Algorithm.In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpens…
Characteristic Classes of Singular Varieties -- Lectures on the Geometry of Flag Varieties -- Combinatorial K-theory -- Morse Functions and Cohomology of Homogeneous Spaces -- Integrable Systems and Gromov-Witten Theory -- Multiplying Schubert Classes -- Lectures on Characteristic Classes of Constructible Functions -- Algebraic K-theory of Schemes -- Gromov-Witten Invariants and Quantum Cohomol…
Inroduction -- Rogers-Ramanujan Continued Fraction and Its Modular Properties -- Explicit Evaluations of the Rogers-Ramanujan Continued Fraction -- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions -- The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series -- Finite Rogers-Ramanujan Continued Fractions -- Other q-continued Fractions -- Asymp…
to Projective Duality -- Actions with Finitely Many Orbits -- Local Calculations -- Projective Constructions -- Vector Bundles Methods -- Degree of the Dual Variety -- Varieties with Positive Defect -- Dual Varieties of Homogeneous Spaces -- Self-dual Varieties -- Singularities of Dual Varieties.Projective duality is a very classical notion naturally arising in various areas of mathematics, suc…
Supplementary Thoughts on Symplectic Groups -- Automorphisms of the Modular Curve -- Reducing the Fontaine-Mazur Conjecture to Group Theory -- Relating Two Genus 0 Problems of John Thompson -- Relatively Projective Groups as Absolute Galois Groups -- Invariants of Binary Forms -- Some Classical Views on the Parameters of the Grothendieck-Teichmüller Group -- The Image of a Hurwitz Space Under …
Arithmetic over Function Fields: A Cohomological Approach -- Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial -- On a Problem of Miyaoka -- Monodromy Groups Associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic -- Irreducible Values of Polynomials: A Non-Analogy -- Schemes over -- Line Bundles and p-Adic Characters -- Arithmetic Eisenstein Classes on…
Notations and Conventions -- Groups Acting on Lattices -- Permutation Lattices and Flasque Equivalence -- Multiplicative Actions -- Class Group -- Picard Group -- Multiplicative Invariants of Reflection Groups -- Regularity -- The Cohen-Macaulay Property -- Multiplicative Invariant Fields -- Problems.Multiplicative invariant theory, as a research area in its own right within the wider spectrum …
Results on topological spaces -- Rings and modules -- Integral extensions -- Factorial rings -- Field extensions -- Finitely generated algebras -- Gradings and filtrations -- Inductive limits -- Sheaves of functions -- Jordan decomposition and some basic results on groups -- Algebraic sets -- Prevarieties and varieties -- Projective varieties -- Dimension -- Morphisms and dimension -- Tangent s…