Description:

This handbook of geometric analysis—the first of the two to be published in the ALM series—presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas.

Description:

This much-anticipated revised second edition of Christopher Sogge’s 1995 work provides a self-contained account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations.

Description:

This twelfth volume of the annual Surveys in Differential Geometry examines recent developments on a number of geometric flows and related subjects, such as Hamilton’s Ricci flow, formation of singularities in the mean curvature flow, the Kähler-Ricci flow, and Yau’s uniformization conjecture.

Contents:

• The Sato-Tate conjecture (L. Clozel)
• Gauge theory, ramification, and the geometric Langlands program (S. Gukov & E. Witten)
• Complex singularities of the Burgers system and renormalization group method (D. Li & Y.G. Sinai)
• A biased view of symplectic cohomology (P. Seidel)
• Global behaviour of nonlinear dispersive and wave equations (T. Tao)

Contents:

• Complex geometry and supergeometry (E.D. Hoker & D.H. Phong)
• String topology: background and present state (D. Sullivan)
• The stability of matter and quantum electrodynamics (E.H. Lieb)
• Holographic algorithm (J.-Y. Cai)
• The fundamental lemma: what is it and what do we know? (S. DeBacker)
• The additivity conjecture in quantum information theory (P.W. Shor)
• Modularity of 2-dimensional Galois representations (M. Kisin)

Description:

Life insurance and life annuities are about cash flows, the time value of money, and the randomness of policyholders' death time. This book intends to present the actuarial model as a combination of these three factors. It also describes how to set premiums and reserves for those insurance products.

The subjects are closely related to the Society of Actuaries (SOA) course MLC requirements. Some examples and exercise problems come from past SOA Course 3, Course M, and Course MLC examinations.

Description:

The works included in this new volume, edited by Jeffrey Cheeger and Karsten Grove, treat important recent developments in metric geometry and comparison geometry. Both these areas are vital and expanding components of modern geometry.