Archimedean Zeta Integrals for $GL(3)times GL(2)$
Author: Miki Hirano
Publisher: American Mathematical Society
Published: 2022-07-18
Total Pages: 136
ISBN-13: 1470452774
DOWNLOAD EBOOKView the abstract.
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Representations of the Infinite Symmetric Group
Author: Alexei Borodin
Publisher: Cambridge University Press
Published: 2017
Total Pages: 169
ISBN-13: 1107175550
DOWNLOAD EBOOKAn introduction to the modern representation theory of big groups, exploring its connections to probability and algebraic combinatorics.
Sasakian Geometry
Author: Charles Boyer
Publisher:
Published: 2008-01-24
Total Pages: 648
ISBN-13:
DOWNLOAD EBOOKThis book offers an extensive modern treatment of Sasakian geometry, which is of importance in many different fields in geometry and physics.
Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Author: Jan H. Bruinier
Publisher: Springer
Published: 2004-10-11
Total Pages: 159
ISBN-13: 3540458727
DOWNLOAD EBOOKAround 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
50 Years of First-Passage Percolation
Author: Antonio Auffinger
Publisher: American Mathematical Soc.
Published: 2017-12-20
Total Pages: 169
ISBN-13: 1470441837
DOWNLOAD EBOOKFirst-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved. In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a learning tool for researchers.
