“Bulletin Board”

 School of Mathematics - May 27, 2006

Short Course

Mircea Immanuel Mustata
University of Michigan
Michigan, USA

June 6-8, 2006
School of Mathematics, IPM

 
 

Mircea Immanuel Mustata
University of Michigan
Michigan, USA


  • Expository Talk 1: An Invariant of Singularities via Integration
    Tuesday 6 June, 10:30-11:30

    Abstract:
    I will discuss several points of view on an invariant of singularities, the log canonical threshold, that has played recently an important role in the geometry of higher dimensional algebraic varieties. I will start with an analytic approach based on Lebesgue integrals, then I will discuss an arithmetic interpretation via p-adic integration and then I will explain a recent interpretation in terms of spaces of arcs and motivic integration.


  • Expository Talk 2: Invariants of Singularities in Positive Characteristic
    Wednesday 7 June, 10:30-11:30

    Abstract:
    This talk is about an application of commutative algebra in positive characteristic to the study of singularities. I will describe invariants of singularities that can be defined in positive characteristic using the Frobenius morphism. They behave in a similar way with invariants that in characteristic zero are defined via resolution of singularities, like the log canonical threshold or the multiplier ideals. Despite the fact that the definition in characteristic p is very elementary, the corresponding invariants seem to encode more information than their characteristic zero counterparts, in particular revealing some subtle connections with arithmetic.


  • Research Talk: Space of Arcs and Applications
    Thursday 8 June, 10:30-11:30

    Abstract:
    The space of arcs of a variety X consists of all morphisms from the formal disk Spec(k[[t]]) to X. In general, this is an infinite-dimensional space. I will give an introduction to its basic properties, explaining its role in birational geometry and in the study of singularities.


Information:
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran.

 
 
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