**SMS scnews item created by Eduardo Altmann at Mon 13 Mar 2017 1724**

Type: Seminar

Modified: Tue 14 Mar 2017 0901; Fri 7 Apr 2017 1655; Thu 13 Apr 2017 1321

Distribution: World

Expiry: 8 May 2017

**Calendar1: 19 Apr 2017 1400-1515**

**CalLoc1: Carslaw 535A**

CalTitle1: Mathematical Aspects of Embodied Intelligence

Auth: ega@como.maths.usyd.edu.au

### Applied Maths Seminar

# Information Geometry and its Application to Complexity Theory

### Ay

** Speaker: Prof. ** Nihat Ay (Max-Planck-Institute for the Mathematics in the Sciences, Leipzig, Germany)

** Title:**Information Geometry and its Application to Complexity Theory

** Abstract: **In the first part of my talk, I will review information-geometric structures and highlight the important role of divergences. I will present a novel approach to canonical divergences which extends the classical definition and recovers, in particular, the well-known Kullback-Leibler divergence and its relation to the Fisher-Rao metric and the Amari-Chentsov tensor.

Divergences also play an important role within a geometric approach to complexity. This approach is based on the general understanding that the complexity of a system can be quantified as the extent to which it is more than the sum of its parts. In the second part of my talk, I will motivate this approach and review corresponding work.

References:

1. N. Ay, S.I. Amari. A Novel Approach to Canonical Divergences within Information Geometry. Entropy (2015) 17: 8111-8129.

2. N. Ay, J. Jost, H. V. Le, L. Schwachhöfer. Information geometry and sufficient statistics. Probability Theory and Related Fields (2015) 162: 327-364.

3. N. Ay, J. Jost, H. V. Le, L. Schwachhöfer. Parametrized measure models. Bernoulli (2016) accepted. arXiv:1510.07305.

4. N. Ay, J. Jost, H. V. Le, L. Schwachhöfer. Information geometry. Ergebnisse der Mathematik und Ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics, Springer 2017, forthcoming book.

5. N. Ay. Information Geometry on Complexity and Stochastic Interaction. Entropy (2015) 17(4): 2432-2458

Webpage of the Applied Maths Seminars: http://www.maths.usyd.edu.au/u/SemConf/Applied.html