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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents 14B05 31 results

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Motivic invariants via non-archimedean geometry - Lecture 2 - Forey, Arthur (Author of the conference) | CIRM H

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These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how these methods can be applied to a singularity arising as the quotient of a smooth variety by a linear group. When the group is finite, the orbifold formula of Batyrev and Denef–Loeser provides a motivic version of the McKay correspondence. In collaboration with Loeser and Wyss, we establish a similar formula for a general linear group.[-]
These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how ...[+]

03C98 ; 14B05 ; 14J17 ; 32S25 ; 32S55

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Motivic invariants via non-archimedean geometry - Lecture 3 - Forey, Arthur (Author of the conference) | CIRM H

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These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how these methods can be applied to a singularity arising as the quotient of a smooth variety by a linear group. When the group is finite, the orbifold formula of Batyrev and Denef–Loeser provides a motivic version of the McKay correspondence. In collaboration with Loeser and Wyss, we establish a similar formula for a general linear group.[-]
These lectures will revolve around applications of Hrushovski and Kazhdan's theory of motivic integration. It associates motivic invariants to semi-algebraic sets in algebraically closed valued fields. Following the work of Hrushovski and Loeser, and in collaboration with Yin, we shall see that when applied to the non-archimedean Milnor fiber, the motivic volumes recover some classical invariants of the Milnor fiber. Finally, we will see how ...[+]

03C98 ; 14B05 ; 14J17 ; 32S25 ; 32S55

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Teissier singularities - Mourtada, Hussein (Author of the conference) | CIRM H

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We will introduce a new class of singularities, Teissier singularities, which are particularly significant in positive characteristics. We will explain why these singularities are candidates to play, in positive characteristics, a role similar to that played by quasi-ordinary singularities in the Jungian approach to the resolution of singularities in characteristic zero. Joint work with Bernd Schober.

14B05 ; 32S05 ; 14E15

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A singular path through toric geometry - Gonzalez Perez, Pedro Daniel (Author of the conference) | CIRM H

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I will speak about some of the aspects of the work of Bernard Teissier concerning singularities, toric geometry and valuations.

14M25 ; 14E15 ; 14B05

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Nash blowup fails to resolve singularities in dimensions four and higher - Leyton-Álvarez, Maximiliano (Author of the conference) | CIRM H

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In this talk, we present a recent joint work with Federico Castillo, Daniel Duarte, and Alvaro Liendo, where we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension 4 or higher over an algebraically closed field of arbitrary characteristic.

14E15 ; 14B05 ; 14M25

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Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 1 - Popescu-Pampu, Patrick (Author of the conference) | CIRM H

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I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that should have been delivered by Angelica Cueto.[-]
I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that ...[+]

14B05 ; 14A21 ; 14M25 ; 14T90 ; 32S05 ; 32S55

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Tropical and logarithmic techniques for the study of Milnor fibers - lecture 2 - Popescu-Pampu, Patrick (Author of the conference) | CIRM H

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I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that should have been delivered by Angelica Cueto.[-]
I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that ...[+]

14B05 ; 14A21 ; 14M25 ; 14T90 ; 32S05 ; 32S55

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Tropical and logarithmic techniques for the study of Milnor fibers - Lecture 3 - Popescu-Pampu, Patrick (Author of the conference) | CIRM H

Multi angle

I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that should have been delivered by Angelica Cueto.[-]
I will explain how to combine tools of local tropical geometry and logarithmic geometry in order to study the structure of Milnor fibers of smoothings of isolated complex singularities, up to homeomorphisms. I will partly follow the paper “The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof”, written in collaboration with Marıa Angelica Cueto and Dmitry Stepanov.This course replaces a course on the same topic that ...[+]

14B05 ; 14A21 ; 14M25 ; 14T90 ; 32S05 ; 32S55

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Arc spaces and singularities in the minimal model program - Lecture 2 - de Fernex, Tommaso (Author of the conference) | CIRM H

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The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.[-]
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...[+]

14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30

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Arc spaces and singularities in the minimal model program - Lecture 3 - de Fernex, Tommaso (Author of the conference) | CIRM H

Multi angle

The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the second lecture. The last two lectures are devoted to some applications of arc spaces toward a conjecture on minimal log discrepancies known as inversion of adjunction. Minimal log discrepancies are invariants of singularities appearing in the minimal model program, a quick overview of which is given in the third lecture.[-]
The space of formal arcs of an algebraic variety carries part of the information encoded in a resolution of singularities. This series of lectures addresses this fact from two perspectives. In the first two lectures, we focus on the topology of the space of arcs, proving Kolchin's irreducibility theorem and discussing the Nash problem on families of arcs through the singularities of the variety; recent results on this problem are proved in the ...[+]

14E18 ; 14E15 ; 13A18 ; 14B05 ; 14E30

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