A minimal partition is a decomposition of a manifold into
disjoint sets that minimizes a spectral energy functional. In the
bipartite case minimal partitions are closely related to
eigenfunctions of the Laplacian, but in the non-bipartite case
they...
In a series of papers with Alexander Ritter, we construct a
symplectic cohomology for open non-convex symplectic manifolds that
admit pseudo-holomorphic C*-actions. Out of this construction, we
get a filtration on ordinary cohomology of these...
Cayley graphs provide interesting bridges between graph theory,
additive combinatorics and group theory. Fixing an ambient finite
group, random Cayley graphs are constructed by choosing a
generating set at random. These graphs reflect interesting...
I will talk about a proof of local-global compatibility at p for
higher coherent cohomology mod p in weight one for Hilbert modular
varieties at an unramified prime, assuming we are not in middle
degree. I will discuss some key ingredients to the...
In their 1971 study of telephone switching circuitry, Graham and
Pollak designed a novel addressing scheme that was better suited
for the faster communication required by computers. They introduced
the distance matrix of a graph, and used its...
Finding regular subgraphs can be useful. Many results assume a
graph is regular or are easier to prove when they are. In 1975,
Erdős and Sauer asked for an estimate, for any constant r, on the
maximum number of edges an n-vertex graph can have...
We show that for every quadratic extension of number fields K/F,
there exists an abelian variety A/F of positive rank whose rank
does not grow upon base change to K. By work of Shlapentokh, this
implies that Hilbert's tenth problem over the ring of...
Stars orbiting sufficiently close to massive black holes
inevitably inspiral towards the black hole due to gravitational
wave radiation. The fate of such stars is subtle and depends on an
interplay between tidal heating of the star, mass transfer...