Harald Cramèr's **Mathematical Methods of Statistics** is a landmark both for Mathematics and Statistics. 2016 is the 70th anniversary of its first publication. Again, after 70 years, mathematics and statistics seem to be falling more and more apart. Numerous statistical procedures are based on ad hoc methods supported by intensive computer assisted simulations, while mathematicians and mathematical statisticians not always know, face and confront the real issues of modern statistics. A much better understanding between statisticians and mathematicians is essential for development of both these fields: a new ** Mathematical Methods of Modern Statistics** remains to be written.

**Our aim is to gather in Luminy world class statisticians, who use excellent mathematics, and mathematicians who work in their area of interest. We plan to discuss recent achievements in modern statistics requiring an extensive use of deep mathematical methods and models. We would like to put emphasis on detailed exposition of mathematics behind the tools used in statistics.**

The major unifying topic will be the ** analysis of large dimensional data**.

The conference includes the following topics:

1. methods of multiple testing

2. model selection theory

3. notions of model sparsity

4. regularization techniques

5. missing data treatments

6. hierarchical and graphical models

7. modern nonparametric Bayes methods (BNP)

8. interactions between the above topics.

9. random matrices

10. mathematical methods applied in the above topics

The subject of the conference will be viewed from:

(a) the frequentist perspective

(b) the Bayesian perspective