Abstract: Any birational geometer would agree that the best algorithm

for resolution of singularities should run by defining a simple invariant of

the singularity and iteratively blowing up its maximality locus.

The only problem is that already the famous example of Whitney umbrella

shows that this is impossible, and all methods following Hironaka had

to use some history and resulted in more complicated algorithms.

Nevertheless, in a recent work with Abramovich and Wlodarczyk we did

construct such an algorithm, and an independent description of a similar

algorithm was done by McQuillan and Marzo. The novelty is in enlarging

the pool of admissible blow ups: we allow weighted blow ups of smooth

centers, and working with orbifolds we achieve that the ambient space

nevertheless remains smooth.

In this talk I will explain some ideas of the old and new algorithms and describe

simple examples, including the Whitney umbrella, in the old and new

algorithms.

for resolution of singularities should run by defining a simple invariant of

the singularity and iteratively blowing up its maximality locus.

The only problem is that already the famous example of Whitney umbrella

shows that this is impossible, and all methods following Hironaka had

to use some history and resulted in more complicated algorithms.

Nevertheless, in a recent work with Abramovich and Wlodarczyk we did

construct such an algorithm, and an independent description of a similar

algorithm was done by McQuillan and Marzo. The novelty is in enlarging

the pool of admissible blow ups: we allow weighted blow ups of smooth

centers, and working with orbifolds we achieve that the ambient space

nevertheless remains smooth.

In this talk I will explain some ideas of the old and new algorithms and describe

simple examples, including the Whitney umbrella, in the old and new

algorithms.

## Date:

Mon, 13/05/2019 - 14:30 to 16:00

## Location:

Ross 70