ncku-talk2011-12-29

NCTS(South)/ NCKU Math Colloquium

DATE 2011-12-29　15:00-16:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Dr. Jen-Chieh Hsiao（Purdue University）

TITLE F-singularities and singularities in birational geometry

ABSTRACT The fascinating connections between the theory of F-singularities (evolved from the tight closure theory) and singularities arising from birational geometry (in particular, from the minimal model program) have been discovered and explored for decades.In this talk, I will try to illustrate some of them by discussing three of my works.
More precisely, I will begin with mild introductions on the notions (rational, log terminal, log canonical singularities, multiplier ideals) in characteristic 0 and (F-rationality, strong F-regularity, F-purity, test ideals) in positive characteristics. I will then explain some connections between these concepts. At the end, the talk will be concluded by mentioning the following works of mine.
1. Determinantal varieties are log terminal in the sense of de Fernex and Hacon.
2. New proof of normality and rationality of singularities of Schubert varieties.
3. (jointed with K. Schwede and W. Zhang) The correspondence between Cartier modules and certain generalization of ideals defining unions of log canonical centers on toric varieties.

NCTS(South)/ NCKU Math Colloquium

DATE	2011-12-29　15:00-16:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Dr. Jen-Chieh Hsiao（Purdue University）

TITLE	F-singularities and singularities in birational geometry

ABSTRACT	The fascinating connections between the theory of F-singularities (evolved from the tight closure theory) and singularities arising from birational geometry (in particular, from the minimal model program) have been discovered and explored for decades.In this talk, I will try to illustrate some of them by discussing three of my works. More precisely, I will begin with mild introductions on the notions (rational, log terminal, log canonical singularities, multiplier ideals) in characteristic 0 and (F-rationality, strong F-regularity, F-purity, test ideals) in positive characteristics. I will then explain some connections between these concepts. At the end, the talk will be concluded by mentioning the following works of mine. 1. Determinantal varieties are log terminal in the sense of de Fernex and Hacon. 2. New proof of normality and rationality of singularities of Schubert varieties. 3. (jointed with K. Schwede and W. Zhang) The correspondence between Cartier modules and certain generalization of ideals defining unions of log canonical centers on toric varieties.