On Monday, December 8, there will take place DAMSI Day event at Aula of the Faculty of Mathematics and Computer Science. The following two lectures by members of the DASMI Center Scientific Council will be preceded by a cookie gathering starting at 3:15 p.m.

16:00 - Pascal Hubert
Title : Complexity of Polygonal Billiards

Abstract : Given a polygon in the plane, one can code a billiard trajectory by the sequence of sides its intersects. The complexity is the number of  words of a given length we get this way starting from any point with any initial direction.  It is a measure of the disorder of the dynamical system.Katok considered this problem as one of the most resistant one in dynamics. For rational polygons, following results of Howard Masur, one can get cubic lower and upper bounds. 

I will explain recent results obtained with Athreya and Troubetzkoy. For regular polygons, we get a cubic asymptotic behavior for this quantity. With Athreya, Forni and Matheus, we find an error term for this counting. 

17:00 - Rafał Bogacz
Title: Computational modelling of learning in the brain
 
Abstract: Biological neural networks store information in the strengths of synaptic connections between neurons. During learning the modification of synaptic connections only relies on information locally available to a synapse such as activity of the two neurons it connects. This is a fundamental constraint on biological neural networks which shapes how they are organized. Hence it is important to understand how effective learning in large networks of neurons can be achieved within the constraint of local plasticity. This talk will review predictive coding, which is an influential model describing information processing in hierarchically organized cortical circuits. The talk will demonstrate that predictive coding network can learn equally or more effectively than artificial neural networks trained with backpropagation despite relying only on the local plasticity.