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Mircea Immanuel Mustata
University of Michigan
Michigan, USA
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- 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.
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Information: |
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran.
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