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 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 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.[-]