Por Muhammad Ali Khan (FCUP).

Por Alberto Bressan (Penn State University).

Por Daniel Barlet (Inst. Élie Cartan, Lorraine).

Abstract: We shall explain how the classical intersection theory of cycles in a complex manifold is generalized to an ambient nearly smooth complex space. A key point is the local moving lemma for cycles in a complex manifold. The new phenomenon is the fact that the intersection multiplicity of two integral cycles may be a rational not integral number in this context.

Por Gabriele Pulcini (FCT, Universidade Nova de Lisboa).

Por Paulo Amorim (Instituto de Matemática - Universidade Federal do Rio de Janeiro).

Pigeons do not jump high / Using o-minimality to compute lower bounds on sample complexity of neural networks (part 2)

Pigeons do not jump high 15h00

Por Ludovic Patey (Institut Camille Jordain, Lyon).

Por Alexandre Baraviera (Instituto de Matemática e Estatística - Universidade Federal do Rio Grande do Sul).

Por Alex Usvyatsov (Universidade de Lisboa, CMAF-CIO).

Abstract: I will discuss the concept of sample complexity in statistical learning theory. Then I will show how definability of many hypothesis classes (for example, essentially all artificial neural networks used in practice) in o-minimal structures, helps to compute tighter lower bounds on sample complexity for these hypothesis classes.

Por Herwig Hauser (Fakultät für Mathematik, Universität Wien).

Por Lucio Boccardo (Dipartimento di Matematica, "Sapienza" Università di Roma).

Abstract: We present a review on the Stampacchia-Calderon-Zygmund theory for linear elliptic operators of second order with discontinuous coefficients and the corresponding theory for nonlinear operators of Leray-Lions type with nonregular data.

We shall also discuss classical and recent results, including work in progress, on the continuous dependence of the solutions with respect to right hand sides.