ECH (embedded contact homology) capacities give obstructions to
symplectically embedding one four-dimensional symplectic manifold
with boundary into another. These obstructions are known to be
sharp when the domain is a "concave toric domain" and...
Embedded contact homology gives a sequence of obstructions to
four-dimensional symplectic embeddings, called ECH capacities.
These obstructions are known to be sharp in several interesting
cases, for example for symplectic embeddings of one...
We give a geometric theory of vector-valued modular forms attached
to Weil representations of rank 1 lattices. More specifically, we
construct vector bundles over the moduli stack of elliptic curves,
whose sections over the complex numbers...
When a variety \(X\) is equipped with the action of an algebraic
group \(G\), it is natural to study the \(G\)-equivariant vector
bundles or coherent sheaves on \(X\). When \(X\) furthermore has a
mirror partner \(Y\), one can ask for the...
The physical mechanism behind the acceleration of the universe
remains one of the great mysteries of modern cosmology. Given the
proliferation of dark energy models on the market, an obvious
question is: How can we rule out whole classes of dark...
Infrared observations from Spitzer Space Telescope and Herschel
Space Observatory are used to study the interstellar dust in M31. A
physical dust model is used to map the dust surface density,
dust/gas ratio, starlight heating intensity, and the...
We consider a Rankin-Selberg integral representation of a cuspidal
(not necessarily generic) representation of the exceptional group
\(G_2\). Although the integral unfolds with a non-unique model, it
turns out to be Eulerian and represents the...
The advent of wide-field synoptic imaging has re-invigorated the
venerable field of time domain astronomy. Our framework of optical
transients no longer has a wide six-magnitude luminosity "gap"
between the brightest novae and faintest supernovae...
A classic problem posed by long gamma ray bursts (GRB) is that
the energy output requires gravitational energy release so deep
within the host star that the prompt gamma rays should, upon naive
consideration, have been obscured. It is suggested that...
Although the existence of a symplectic filling is well-understood
for many contact 3-manifolds, complete classifications of all
symplectic fillings of a particular contact manifold are more rare.
Relying on a recognition theorem of McDuff for closed...
