Benjamin Bakker (UIC) TBA
Philip Engel (UIC) TBA
Ludmil Katzarkov (Miami/Sofia) TBA
Samuel Johnston (Imperial/MIT) TBA
Lisa Marquand (NYU) TBA
Davesh Maulik (MIT) TBA
Sam Raskin (Yale) TBA
Michael Temkin (Hebrew U., Jerusalem) New techniques in resolution of singularities.
Since Hironaka's famous resolution of singularities in characteristic zero in 1964, it took about 40 years of intensive work of many mathematicians to simplify the method, describe it using conceptual tools and establish its functoriality. However, one point remained quite mysterious: despite different descriptions of the basic resolution algorithm, it was essentially unique. Was it a necessity or a drawback of the fact that all subsequent methods relied on Hironaka's ideas essentially?
The situation changed in the last decade, when logarithmic, weighted and foliated analogues and generalizations were discovered in works of Abramovich-Temkin-Wlodarzcyk, McQuillan, Quek, Abramovich-Temkin-Wlodarzcyk-Belotto and others. At this stage we can already try to figure out general ideas and principles shared by all these methods and the picture is quite surprising -- it seems that each method is quite determined by its basic setting consisting of the class of geometric objects and basic blowings up one works with. In particular, the classical method is probably the only natural resolution (via principalization) method obtained by blowing up smooth centers in the ambient manifold.
In my talk I'll describe the settings and the methods on a very general level and will add some details about the classical algorithm, the logarithmic one and the simplest dream (or weighted) method, which has no memory and improves the singularity invariant by each weighted blowing up.