Saltman, J.:

Lectures on Division Algebras

This volume is based on lectures on division algebras given at 

a conference held at Colorado State University. 

Although division algebras are a very classical object, 

this book presents this "classical" material in a new way, 

highlighting current approaches and new theorems, and illuminating the connections 

with a variety of areas in mathematics.


	

May 1999			120 pp.




0-8218-0979-2 	 			3,980.	




A. M. S. 




代数学　No.313-116




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Colloquium Publications, Vol. 47:
 

Manin, Yu. :

Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces



		   

This is the first monograph dedicated to the systematic exposition 

of the whole variety of topics related to quantum cohomology. 

The subject first originated in theoretical physics (string theory) 

and has continued to develop extensively over the last decade.

The author's approach to quantum cohomology is based on 

the notion of the Frobenius manifold. 

The first part of the book is devoted to this notion 

and its extensive interconnections with algebraic formalism of operads, 

differential equations, perturbations, and geometry. 



In the second part of the book, the author describes the construction 

of quantum cohomology and reviews the algebraic geometry mechanisms involved 

in this construction (intersection and deformation theory of 

Deligne-Artin and Mumford stacks).


	

1999		 		297 pp. 




0-8218-1917-8		 		10,170.	




A. M. S.

	 



Colloquium Publications, Vol. 46: 
 

Bourgain, J. :

Global Solutions of Nonlinear Schrodinger Equations



	  

This volume presents recent progress in the theory of nonlinear 

dispersive equations, primarily the nonlinear Schrodinger (NLS)equation.

 

The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. 

New techniques and results are described on global existence and 

properties of solutions with Large Cauchy data.

 

Current research in harmonic analysis around Strichartz's 

inequalities and its relevance to nonlinear PDE is presented. 



Several topics in NLS theory on bounded domains are reviewed. 

Using the NLS as an example, the book offers comprehensive 

insight on current research related to dispersive equations and Hamiltonian PDEs.


	

May 1999 				182 pp. 




0-8218-1919-4 		 		6,330.




A. M. S.