In Print: ‘New Techniques in Resolution of Singularities’

Purdue faculty dedicate countless hours to exploring the frontiers of their respective fields, pushing the boundaries of knowledge and contributing to the ever-evolving landscape of academia. To celebrate our faculty’s excellence in scholarship, Purdue Today’s weekly book series will highlight faculty expertise across a diversity of subjects and disciplines. Today’s feature focuses on Jaroslaw Wlodarczyk, professor of mathematics, and his book, “New Techniques in Resolution of Singularities.”

Publication title

New Techniques in Resolution of Singularities

Purdue author

Jaroslaw Wlodarczyk

Authors

Dan Abramovich

Anne Fruhbis-Kruger

Michael Temkin

Jaroslaw Wlodarczyk

Publisher

Birkhauser Cham

Publication date

September 2023

About the book (from the publisher)

Resolution of singularities is notorious as a difficult topic within algebraic geometry. Recent work, aiming at resolution of families and semistable reduction, infused the subject with logarithmic geometry and algebraic stacks, two techniques essential for the current theory of moduli spaces. As a byproduct a short, a simple and efficient functorial resolution procedure in characteristic 0 using just algebraic stacks was produced.

The goals of the book, the result of an Oberwolfach Seminar, are to introduce readers to explicit techniques of resolution of singularities with access to computer implementations, introduce readers to the theories of algebraic stacks and logarithmic structures, and to resolution in families and semistable reduction methods.

About the Purdue author

Jaroslaw Wlodarczyk is a professor of mathematics at Purdue University. He has been published in the Journal of the American Mathematical Society, Journal of Algebraic Geometry and Inventiones Mathematicae. Wlodarczyk graduated from Warsaw University in 1993 and later earned a visiting position at Ruhr University Bochum and a scholarship at Grenoble University.

He was an invited speaker at International Congress of Mathematicians Madrid 2006, where he presented his work on the weak Factorization Theorem. Wlodarczyk is also a recipient of numerous awards for his research contributions to birational geometry.