In this overview talk we will explore a variational approach to
the problem of Spectral Minimal Partitions (SMPs). The
problem is to partition a domain or a manifold into k subdomains so
that the first Dirichlet eigenvalue on each subdomain is as...
Apart from the usual transversality problems in defining curve
counting invariants, when defining the open Gromov-Witten
invariants of a Lagrangian one has to deal with the fact that the
moduli spaces have boundary. Thus a homological (virtual)...
The theme of the lecture is the notion of points over F1, the
field with one element. Several heuristic computations led to
certain expectations on the set of F1-points: for example the Euler
characteristic of a smooth projective complex variety X...
The Poisson-Furstenberg boundary is a measure space that
describes asymptotics of infinite trajectories of random walks. The
boundary is non-trivial if and only if the defining measure
admits non-constant bounded harmonic functions.
Suppose Alice wants to convince Bob of the correctness of k NP
statements. Alice could send the k witnesses to Bob, but as k grows
the communication becomes prohibitive. Is it possible to convince
Bob using smaller communication? This is the...
Schubert Calculus studies cohomology rings in (generalized) flag
varieties, equipped with a distinguished basis - the fundamental
classes of Schubert varieties - with structure constants satisfying
many desirable properties. Cotangent Schubert...
Vertex decomposition, introduced by Provan and Billera in 1980,
is an inductive strategy for breaking down and understanding
simplicial complexes. A simplicial complex that is vertex
decomposable is shellable, hence Cohen--Macaulay. Through
the...
We will discuss recent results towards the quantum unique
ergodicity conjecture of Rudnick and Sarnak, concerning the
distribution of Hecke--Maass forms on hyperbolic arithmetic
manifolds. The conjecture was resolved for congruence surfaces
by...
Distinct Hamiltonian isotopy classes of monotone Lagrangian tori
in $\mathbb{C} P^2$ can be associated to Markov triples. With two
exceptions, each of these tori are symplectomorphic to exactly
three Hamiltonian isotopy classes of tori in the ball...
A d-dimensional framework is a pair (G,p⃗ ) consisting of a
finite simple graph G and an embedding p⃗ of its vertices in
ℝd. A framework is called rigid if every continuous motion of the
vertices in ℝd that starts at p⃗ , and preserves the lengths...
