Dan Abramovich studied mathematics at Tel Aviv University and at Harvard, where he received his PhD in 1991. After a postdoctoral fellowship at MIT, he was on faculty at Boston University, where he was Sloan Research Fellow, before moving to Brown University where he is L. Herbert Ballou University Professor. He is Fellow of the American Mathematical Society and the American Association for the Advancement of Science. He works in birational Geometry, Moduli Spaces, and Arithmetic Geometry. His 2018 ICM talk at Rio de Janeiro focused on material described in the present book. Anne Frühbis-Krüger works in computational algebraic geometry and singularity theory. She received her PhD from Kaiserslautern University in 2000. After a visiting professorship at FU Berlin and more than a decade as apl. Professor at Leibniz Universität Hannover, she moved to her current position at Universität Oldenburg in 2019. She has served as the spokespersonof the 'Fachgruppe Computeralgebra' for two periods and is actively involved in the development of the computer algebra systems Singular and OSCAR.
Michael Temkin is the Maurice and Clara Weil Chair in Mathematics at the Hebrew University of Jerusalem. His main research interests lie within non-archimedean geometry, birational geometry and the interplay between them. In particular, he is interested in resolution of singularities and semistable reduction problems. He graduated from the Weizmann Institute of Science in 2006, and after a postdoc at the University of Pennsylvania and a one-year membership at the IAS joined the Hebrew University of Jerusalem in 2010. Since 2020 he is serving as the editor in chief of the Israel Journal of Mathematics.Jaros¿aw W¿odarczyk works in birational geometry and resolution of singularities. He graduated from Warsaw University in 1993. After a visiting position in Ruhr University Bochum and a scholarship at Grenoble University, he joined Warsaw University where he worked till 2000. After that he moved to Purdue University, where he is now a professor at the Department of Mathematics. Jaros¿aw W¿odarczyk was an invited speaker in ICM Madrid 2006, where he presented his work on the weak Factorization Theorem, playing an important role in Algebraic Geometry. He is also a recipient of numerous awards for his research contributions to birational geometry.

Gives an introduction to stacks

Includes an introduction to logarithmic geometry

Presents techniques of resolution of singularities

A Computational View on Hironaka's Resolution of Singularities.- Stacks for Everyone Who Cares About Varieties and Singularities.- Introduction to Logarithmic Geometry.- Birational Geometry Using Weighted Blowing Up.- Relative and Logarithmic Resolution of Singularities.- Weighted Resolution of Singularities. A Rees Algebra Approach.- New Techniques in Resolution of Singularities: Open Problems.