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The Sanibel Symposium on the Quantum Theory of Matter, embracing Quantum Chemistry, Quantum Biology and Solid-State Physics, have been held annually since their beginning in 1961. The 1996 symposium represents the 36th meeting. The Sanibel Symposia, which are uniquely influential in the field of Quantum Theory of matter, address the critical areas of research where modern quantum theoretical methods are playing key roles in the elucidation of current concepts and topics of great interest. Today the format for these symposia consists of a single eight-day meeting composed of various topical subsymposia that cover a wide range of current topics in molecular and materials sciences. This compact schedule, with no reduction in the total number of plenary and poster sessions, meets the original goals of the Sanibel Symposium, which are to stimulate the ex- change of ideas on a cross disciplinary, international level and to report on the current state-of-the-art methodology for quantum theoretical computational methods. Typically, more than 300 scientists from 30-40 different nations come to this symposium. We expect a similar sized meeting for 1996.

The Sanibel Symposium on the Quantum Theory of Matter, embracing Quantum Chemistry, Quantum Biology and Solid-State Physics, have been held annually since their beginning in 1961. The 1996 symposium represents the 36th meeting. The Sanibel Symposia, which are uniquely influential in the field of Quantum Theory of matter, address the critical areas of research where modern quantum theoretical methods are playing key roles in the elucidation of current concepts and topics of great interest. Today the format for these symposia consists of a single eight-day meeting composed of various topical subsymposia that cover a wide range of current topics in molecular and materials sciences. This compact schedule, with no reduction in the total number of plenary and poster sessions, meets the original goals of the Sanibel Symposium, which are to stimulate the ex- change of ideas on a cross disciplinary, international level and to report on the current state-of-the-art methodology for quantum theoretical computational methods. Typically, more than 300 scientists from 30-40 different nations come to this symposium. We expect a similar sized meeting for 1996.

Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the defining equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.

Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the defining equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.

Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the defining equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.

We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number theory. On the elementary side, summation by parts, Euler Maclaurin summation, and Mobius inversion play a prominent role. In the slightly less elementary sphere, we find tools from analysis, such as Poisson summation, generating function methods, Cauchy's residue theorem, asymptotic methods, and the fast Fourier transform. We then describe conjectures and experiments that connect number theory and random matrix theory.

The 34th annual Sanibel Symposium, organized by the faculty and staff of the Quantum Theory Project of the University of Florida, was held on February 12- 19, 1994 at the Marriott at Sawgrass Resort, Ponte Vedra Beach, Florida. More than 300 participants gathered for 8 days of lectures and informal discussions. The format of the symposium adopted for the past few years was followed again this year with a compact 8-day schedule with an integrated program of quantum biology, quantum chemistry, and condensed matter physics. The topics of the sessions covered by these proceedings include Propagator and Resolvent Theory, Perturbation Theory, Density Functional Theory for Molecules, High Performance Parallel Computing Algorithms, Weakly Bound Molecular Systems, Theoretical Inorganic Chemistry, Temporal Phenomena, Quantum Dynamics at Interphases, Energy Depositions, Non-Linear Optical Phenomena, and Novel Condensed Systems. The articles have been subjected to the ordinary refereeing procedures of the International Journal of Quantum Chemistry. (jg)

The 34th annual Sanibel Symposium, organized by the faculty and staff of the Quantum Theory Project of the University of Florida, was held on February 12- 19, 1994 at the Marriott at Sawgrass Resort, Ponte Vedra Beach, Florida. More than 300 participants gathered for 8 days of lectures and informal discussions. The format of the symposium adopted for the past few years was followed again this year with a compact 8-day schedule with an integrated program of quantum biology, quantum chemistry, and condensed matter physics. The topics of the sessions covered by these proceedings include Propagator and Resolvent Theory, Perturbation Theory, Density Functional Theory for Molecules, High Performance Parallel Computing Algorithms, Weakly Bound Molecular Systems, Theoretical Inorganic Chemistry, Temporal Phenomena, Quantum Dynamics at Interphases, Energy Depositions, Non-Linear Optical Phenomena, and Novel Condensed Systems. The articles have been subjected to the ordinary refereeing procedures of the International Journal of Quantum Chemistry. (jg)

With the advent of powerful computing tools and numerous advances in mathematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and interna1 pressures gave a powerful impetus to the development of more powerful algorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of applications, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc . . .

The 32nd annual Sanibel Symposium was held March 14 to 21, 1992. The format of the symposium adopted for the past 2 years was followed again this year providing a compact 8-day schedule with an integrated program of quantum biology, quantum chemistry, and condensed matter physics. The topics of the sessions covered by these proceedings include Thirty-five Years of Progress in Electronic Structure Theory, Density Matrices and Other Revelations of 1955, Non-Born-Oppenheimer Methods, Atomic and Molecular Phenomena in Astrophysics, Photoinduced Phenomena, Reactive Molecular Collisions, Quantum Monte Carlo, Density-Functional Theory, Thin Films and Surfaces. A special session on Theoretical Inorganic Chemistry was held in memory of Arnold Karo, one of the real old-timers at Sanibel. All the articles have been subjected to the ordinary refereeing procedures of the The International Journal of Quantum Chemistry. The articles presented in the sessions on quantum biology and associated poster sessions are published in a separate volume of the The International Journal of Quantum Chemistry.... Quantum chemistry, Condensed matter theory, Symposium.

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. Available from the Open Textbook Library:  https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=187

All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. Available from the Open Textbook Library:  https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=187

The 33rd annual Sanibel Symposium, organized by the faculty and staff of the Quantum Theory Project of the University of Florida, was held March 13 to 20, 1993, at the Ponce de Leon Conference Center located at the north gate of the city of St. Augustine, Florida. The topics of the sessions covered by these proceedings include Advanced Scientific Computing, Interaction of Photons and Matter, Quantum Molecular Dynamics, Electronic Structure Methods, Polymeric Systems, and Quantum Chemical Methods for Extended Systems.

The 33rd annual Sanibel Symposium, organized by the faculty and staff of the Quantum Theory Project of the University of Florida, was held March 13 to 20, 1993, at the Ponce de Leon Conference Center located at the north gate of the city of St. Augustine, Florida. The topics of the sessions covered by these proceedings include Advanced Scientific Computing, Interaction of Photons and Matter, Quantum Molecular Dynamics, Electronic Structure Methods, Polymeric Systems, and Quantum Chemical Methods for Extended Systems.

Speaker : Stan Wagon

Speaker : Stan Wagon