Seminar
A framework for non-local, non-linear diffusion
Diffusion is a ubiquitous notion in the theory of PDEs. The most obvious case is the heat equation and it has many derivations, including both non-local and non-linear examples (fractional Laplacian, fractional p-Laplacian, porous medium). We will discuss
how to make your own diffusion operator from scratch and why it will have (some of) the properties you would like it to have. Joint work with G. Karch (Wrocław) and M. Kassmann (Bielefeld).
Virtual Gelfand-Zetlin Polytopes
Beyond Classical Thermodynamics
Weakly Whitney preserving maps III
We introduce the family of Weakly Whitney preserving maps and show its relationships with other classes of maps.
Weakly compact sets in ell^infinity
Beukers' proofs of irrationality of $\zeta(3)$ and Brown's program of irrationality proofs for zeta values.
Compactness in ell_1
Introduction to quasiconformal mappings
Sequences, topology, and inferring the dimension of a sensory space from neural responses
Abstract: The brain builds its internal sensory representations based on the structure of neural activity. A number of modalities, such as the early visual system and the spatial map in hippocampus, are relatively well-characterized. However some sensory systems, such as olfaction, remain enigmatic. The primary difficulty is that the underlying perceptual space is not well-understood. Can we "build" the sensory space from neural activity alone, without a prior understanding of how the stimuli are organized?