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Adelic line bundles on quasi-projective varieties
A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In th...
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An invitation to modern number theory
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiment...
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Exponential sums, hypergeometric sheaves, and monodromy groups
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck’s creation o...
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Fearless symmetry
Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious pattern...
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Introduction to arithmetic theory of automorphic functions
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoreti...
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Multiplicative hitchin fibrations and the fundamental lemma
A proof of the endoscopic fundamental lemma for spherical Hecke algebras using a new comprehensive framework of multiplicative Hitchin fibrationsThis book develops a comprehensive framework of multiplicative Hitchin fibrations, which is a novel analogue of the classical Hitchin fibrations, and th...
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Number theory
An introductory textbook with a unique historical approach to teaching number theoryThe natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they ...
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Quasi-projective and formal-analytic arithmetic surfaces
A milestone in the geometric understanding of algebraization theorems that also provides an introduction to Arakelov geometryMotivated by questions of transcendental number theory, arithmetic, and Diophantine geometry, this book provides a thorough study of a new kind of mathematical object—forma...
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Supersingular p-adic l-functions, maass-shimura operators and waldspurger formulas
A groundbreaking contribution to number theory that unifies classical and modern resultsThis book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to...
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The irrationals
An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first centuryThe ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their myste...
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