Page 46 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 46
PLENARY SPEAKERS
Statistical Learning: Causal-oriented and Robust
Peter Bühlmann, buehlmann@stat.math.ethz.ch
ETH Zurich, Switzerland
Reliable, robust and interpretable machine learning is a big emerging theme in data science and
artificial intelligence, complementing the development of pure black box prediction algorithms.
Looking through the lens of statistical causality and exploiting a probabilistic invariance prop-
erty opens up new paths and opportunities for enhanced robustness, with wide-ranging prospects
for various applications.
Stable solutions to semilinear elliptic equations are smooth up to
dimension 9
Xavier Cabré, xavier.cabre@upc.edu
ICREA and Universitat Politecnica de Catalunya, Spain
The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970’s.
In dimensions 10 and higher, there exist stable energy solutions which are singular. In this
talk I will describe a recent work in collaboration with Figalli, Ros-Oton, and Serra, where we
prove that stable solutions are smooth up to the optimal dimension 9. This answers to an open
problem posed by Brezis in the mid-nineties concerning the regularity of extremal solutions to
Gelfand-type problems.
Minimal surfaces from a complex analytic viewpoint
Franc Forstnericˇ, franc.forstneric@fmf.uni-lj.si
University of Ljubljana, Slovenia
In this talk, I will describe some recent developments in the theory of minimal surfaces in
Euclidean spaces which have been obtained by complex analytic methods. After a brief history
and background of the subject, I will present a new Schwarz-Pick lemma for minimal surfaces,
describe approximation and interpolation results for minimal surfaces, and discuss the current
status of the Calabi-Yau problem on the existence of complete conformal minimal surfaces with
Jordan boundaries.
Bernoulli Random Matrices
Alice Guionnet, alice.guionnet@gmail.com
ENS Lyon, France
The study of large random matrices, and in particular the properties of their eigenvalues and
eigenvectors, has emerged from the applications, first in data analysis and later as statistical
models for heavy-nuclei atoms. It now plays an important role in many other areas of mathe-
matics such as operator algebra and number theory. Over the last thirty years, random matrix
theory became a field on its own, borrowing tools from different branches of mathematics. The
44
Statistical Learning: Causal-oriented and Robust
Peter Bühlmann, buehlmann@stat.math.ethz.ch
ETH Zurich, Switzerland
Reliable, robust and interpretable machine learning is a big emerging theme in data science and
artificial intelligence, complementing the development of pure black box prediction algorithms.
Looking through the lens of statistical causality and exploiting a probabilistic invariance prop-
erty opens up new paths and opportunities for enhanced robustness, with wide-ranging prospects
for various applications.
Stable solutions to semilinear elliptic equations are smooth up to
dimension 9
Xavier Cabré, xavier.cabre@upc.edu
ICREA and Universitat Politecnica de Catalunya, Spain
The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970’s.
In dimensions 10 and higher, there exist stable energy solutions which are singular. In this
talk I will describe a recent work in collaboration with Figalli, Ros-Oton, and Serra, where we
prove that stable solutions are smooth up to the optimal dimension 9. This answers to an open
problem posed by Brezis in the mid-nineties concerning the regularity of extremal solutions to
Gelfand-type problems.
Minimal surfaces from a complex analytic viewpoint
Franc Forstnericˇ, franc.forstneric@fmf.uni-lj.si
University of Ljubljana, Slovenia
In this talk, I will describe some recent developments in the theory of minimal surfaces in
Euclidean spaces which have been obtained by complex analytic methods. After a brief history
and background of the subject, I will present a new Schwarz-Pick lemma for minimal surfaces,
describe approximation and interpolation results for minimal surfaces, and discuss the current
status of the Calabi-Yau problem on the existence of complete conformal minimal surfaces with
Jordan boundaries.
Bernoulli Random Matrices
Alice Guionnet, alice.guionnet@gmail.com
ENS Lyon, France
The study of large random matrices, and in particular the properties of their eigenvalues and
eigenvectors, has emerged from the applications, first in data analysis and later as statistical
models for heavy-nuclei atoms. It now plays an important role in many other areas of mathe-
matics such as operator algebra and number theory. Over the last thirty years, random matrix
theory became a field on its own, borrowing tools from different branches of mathematics. The
44
