Kiran Kedlaya's Books

The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Bjorn Poonen,Ravi Vakil

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The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Bjorn Poonen,Ravi Vakil

This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.

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Page Count

353

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470451247

ISBN 13

9781470451240

Perfectoid Spaces

Lectures from the 2017 Arizona Winter School

By: Bhargav Bhatt,Ana Caraiani,Kiran S. Kedlaya,Peter Scholze,Jared Weinstein

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Perfectoid Spaces

Lectures from the 2017 Arizona Winter School

By: Bhargav Bhatt,Ana Caraiani,Kiran S. Kedlaya,Peter Scholze,Jared Weinstein

Introduced by Peter Scholze in 2011, perfectoid spaces are a bridge between geometry in characteristic 0 and characteristic $p$, and have been used to solve many important problems, including cases of the weight-monodromy conjecture and the association of Galois representations to torsion classes in cohomology. In recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2018. This book, originating from a series of lectures given at the 2017 Arizona Winter School on perfectoid spaces, provides a broad introduction to the subject. After an introduction with insight into the history and future of the subject by Peter Scholze, Jared Weinstein gives a user-friendly and utilitarian account of the theory of adic spaces. Kiran Kedlaya further develops the foundational material, studies vector bundles on Fargues–Fontaine curves, and introduces diamonds and shtukas over them with a view toward the local Langlands correspondence. Bhargav Bhatt explains the application of perfectoid spaces to comparison isomorphisms in $p$-adic Hodge theory. Finally, Ana Caraiani explains the application of perfectoid spaces to the construction of Galois representations associated to torsion classes in the cohomology of locally symmetric spaces for the general linear group. This book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.

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Page Count

297

Publisher

American Mathematical Society

Published Date

ISBN 10

1470465108

ISBN 13

9781470465100

p-adic Differential Equations

By: Kiran S. Kedlaya

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p-adic Differential Equations

By: Kiran S. Kedlaya

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.

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Page Count

399

Publisher

Cambridge University Press

Published Date

ISBN 10

1139489208

ISBN 13

9781139489201

The William Lowell Putnam Mathematical Competition 2001–2016: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Daniel M. Kane,Jonathan M. Kane,Evan M. O’Dorney

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The William Lowell Putnam Mathematical Competition 2001–2016: Problems, Solutions, and Commentary

By: Kiran S. Kedlaya,Daniel M. Kane,Jonathan M. Kane,Evan M. O’Dorney

The William Lowell Putnam Mathematics Competition is the most prestigious undergraduate mathematics problem-solving contest in North America, with thousands of students taking part every year. This volume presents the contest problems for the years 2001–2016. The heart of the book is the solutions; these include multiple approaches, drawn from many sources, plus insights into navigating from the problem statement to a solution. There is also a section of hints, to encourage readers to engage deeply with the problems before consulting the solutions. The authors have a distinguished history of engagement with, and preparation of students for, the Putnam and other mathematical competitions. Collectively they have been named Putnam Fellow (top five finisher) ten times. Kiran Kedlaya also maintains the online Putnam Archive.

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