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Grobner Bases and Convex Polytopes
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the …
Why the Boundary of a Round Drop Becomes a Curve of Order Four
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot …
Lyapunov Exponents and Smooth Ergodic Theory
This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the …
Some Points in Analysis and Their History
This book is a collection of small essays containing the history and the proofs of some important and interesting theorems of analysis and partial differential operators in this …
Ricci Flow and Geometrization of 3-Manifolds
Interpolation and Sampling in Spaces of Analytic Functions
This book contains the latest developments in a central theme of research on analysis of one complex variable. The material is based on lectures at the University of Michigan. The …
Dynamics of Infinite-dimensional Groups
The "infinite-dimensional groups" in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of …
Lectures on the Theory of Pure Motives
Torus Actions and Their Applications in Topology and Combinatorics
This book presents the study of torus actions on topological spaces that is presented as a bridge connecting combinatorial and convex geometry with commutative and homological …
Functions with Disconnected Spectrum
Complex Analysis and CR Geometry
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools …
Lectures on Harmonic Analysis
'There were lots of young analysts who flocked to Chicago in those years, but virtually from the start it was clear that Tom had a special brilliance...Eventually, the mathematical …