Ideas from quantum field theory and string theory have had an enormous impact on geometry over the last two decades. One extremely fruitful source of new mathematical ideas goes back to the works of Cecotti, Vafa, et al. around 1991 on the geometry of topological field theory. Their tt*-geometry (tt* stands for topological-antitopological) was motivated by physics, but it turned out to unify ideas from such separate branches of mathematics as singularity theory, Hodge theory, integrable systems, matrix models, and Hurwitz spaces. The interaction among these fields suggested by tt*-geometry has become a fast moving and exciting research area.This book, loosely based on the 2007 Augsburg, Germany workshop ""From tQFT to tt* and Integrability"", is the perfect introduction to the range of mathematical topics relevant to tt*-geometry. It begins with several surveys of the main features of tt*-geometry, Frobenius manifolds, twistors, and related structures in algebraic and differential geometry, each starting from basic definitions and leading to current research. The volume moves on to explorations of current foundational issues in Hodge theory: higher weight phenomena in twistor theory and non-commutative Hodge structures and their relation to mirror symmetry. The book concludes with a series of applications to integrable systems and enumerative geometry, exploring further extensions and connections to physics. With its progression through introductory, foundational, and exploratory material, this book is an indispensable companion for anyone working in the subject or wishing to enter it.
This work was partially supported by NSF grant 1262531 and a Royal Society Wolfson Research Merit Award. c2018 Mark Gross and Bernd Siebert 1More common seems to be the usage of characteristic, but 199 Proceedings of Symposia in Pure ...
This volume contains the proceedings of the conference String-Math 2015, which was held from December 31, 2015-January 4, 2016, at Tsinghua Sanya International Mathematics Forum in Sanya, China.
This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry.
Richard M. Karp, Reducibility among combinatorial problems, Complexity of computer computations (Proc. ... MR779900 Daphne Koller and Nir Friedman, Probabilistic graphical models: Principles and techniques, Adaptive Computation and ...
... Dinesh N. Manocha, Xenia H. Kramer, Reinhard C. Laubenbacher, Rekha R. Thomas, John B. Little David A Cox, PH. ... [Laz2] |Lit] [Man1] References W. Adams and P. Loustaunau, Introduction to Gröbner Bases, AMS, Providence, RI, 1994.
The mast of Gale Stockdale's boat is 32 feet high . If it intercepts an angle of 2 ° 10 ' , how far away is it ? 28. A television tower 530 m high intercepts an angle of 2 ° 40 ' . How far away is the tower ? : Find the areas of each of ...
This book consists of expositions of aspects of modern Hodge theory, with the purpose of providing the nonexpert reader with a clear idea of the current state of the subject.
Examples of Robinson. In the late 1960s at Berkeley, Raphael M. Robinson [77, p. 264 saw “an unpublished example of a ternary sextic worked out recently by W. J. Ellison using Hilbert's method (see $3a). It is, as would be expected, ...
Mathematical Surveys and Monographs
AMS Special Session, the Ubiquitous Heat Kernel, October 2-4, 2003, Boulder, Colorado Jay Jorgenson, American Mathematical Society Lynne Walling. for tables comparing three types of trace formulas. A reference for the continuous trace ...