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Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
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Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.
Each year thirty-two seniors at American universities are awarded Rhodes Scholarships, which entitle them to spend two or three years studying at the University of Oxford. The program, founded by the British colonialist and entrepreneur Cecil Rhodes and established in 1903, has become the world's most famous academic scholarship and has brought thousands of young Americans to study in England. Many of these later became national leaders in government, law, education, literature, and other fields. Among them were the politicians J. William Fulbright, Bill Bradley, and Bill Clinton; the public policy analysts Robert Reich and George Stephanopoulos; the writer Robert Penn Warren; the entertaine...
Index of the "initial decisions" issued in appeals brought by air traffic controllers protesting their removal after the PATCO organized strike against the Federal government. These decisions were issued by the Board's Regional offices.
In ``The Yang-Mills equations over Riemann surfaces'', Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In ``Yang-Mills Connections on Nonorientable Surfaces'', the authors study Yang-Mills functional on the space of connections on a principal $G_{\mathbb{R}}$-bundle over a closed, connected, nonorientable surface, where $G_{\mathbb{R}}$ is any compact connected Lie group. In this monograph, the authors generalize the discussion in ``The Yang-Mills equations over Riemann surfaces'' and ``Yang-Mills Connections on Nonorientable Surfaces''. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups $SO(n)$ and $Sp(n)$.
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