Programme

12h30-13h50: General Assembly for all BMS members.

13h40-13h55: Welcome coffee

14h00-14h50: Marc Hallin (mathematical statistics, time series analysis, time-series econometrics)

Chair: Thomas Verdebout

Title: Ordering Rd, d ≥ 2. Distribution and quantile functions: a measure transportation approach

Abstract: Unlike the real line, the real space Rd, for d ≥ 2, is not canonically ordered. As a result, such fundamental concepts as distribution and quantile functions, in dimension d ≥ 2, are not canonically defined. The classical definition of a multivariate distribution function, based on marginal orderings, does not enjoy any of the quintessential properties of the univariate concept; in particular, its inverse defines an essentially meaningless quantile function. We show how a measure transportation characterization of the univariate concept readily extends to Rd, leading to distribution-specific orderings in population, data-driven ones in samples. Contrary to the many concepts that can be found in the literature, the empirical counterparts of the resulting distribution and quantile functions possess all the properties that make their univariate counterparts successful tools for data analysis and statistical inference.

14h50-15h00: Coffee

15h00-15h50: Kathryn Hess (homotopy theory, category theory, applications of algebraic topology)

Chair: Nero Budur

Title: Topological insights in neuroscience

Abstract: Over the past decade, and particularly over the past five years, research at the interface of topology and neuroscience has grown remarkably fast. Topology has, for example, been successfully applied to objective classification of neuron morphologies and to automatic detection of network dynamics. In this talk I will focus on the algebraic topology of brain structure and function, describing results obtained by members of my lab in collaboration with the Blue Brain Project on digitally reconstructed microcircuits of neurons in the rat cortex. I will also describe our on-going work on the topology of synaptic plasticity. The talk will include an overview of the Blue Brain Project and a brief introduction to the topological tools that we use.

16h00-17h00: Drink