Links of strata in singular spaces are fundamental invariants
which govern the topology of small neighbourhoods around points in
those strata. This talk will focus on inferring links of strata
from incomplete information in three completely...
Using the arithmetics of quantum numbers we construct some
“approximations” of tilting modules for reductive
algebraic groups that might be useful for understanding the
generational patterns of tilting characters conjectured by Lusztig
We are surrounded by functional networks, from fluid transport
in plants and animals to macroscopic elastic scaffoldings and
microscopic crystals and materials, and engineered power grids.
Often, such networks can be seen as optimized for their...
In this talk, I will give an overview of some recent results
motivated by the computation and applications of persistent
homology, a theory that creates a bridge between the continuous
world of topology and the discrete world of data, and...
I'll talk about two related projects, with two different groups,
both aiming to see three-dimensional manifolds "from the inside".
That is, we generate images assuming that light travels along
geodesics in the geometry of the manifold. The first...
Polymers are macromolecules that cannot cross each other without
breaking their bonds. This leads to polymer chain entanglement
which determines bulk viscoelastic responses of the material.
Understanding the relation between entanglement and...
We first describe mathematical foundation of DSGRN (Dynamic
Signatures Generated by Regulatory Networks), an approach that
provides a queryable description of global dynamics of a network
over its entire param- eter space. We describe a connection...
DNA rearrangement is observed at developmental and evolutionary
scale. The recombination process can be directly modeled by
4-regular graphs and Gauss codes, also called double occurrence
words. We discuss properties of these graphs, their spatial...
Motivated by thematic similarities between persistent homology and
magnitude homology, we describe a simplicial construction
associated to a metric space. This construction is determined by
(apart from the metric space itself) a choice of two...
We use persistent homology to analyze predictions of protein
folding by trying to identify global geometric structures that
contribute to the error when the protein is misfolded. The goal is
to find correlations between global geometric structures...