  We report on preliminary results from the Fermi High-Latitude Extended
Sources Catalog (FHES), a comprehensive search for spatially extended gamma-ray
sources at high Galactic latitudes ($|b|>5^\circ$) based on data from the Fermi
Large Area Telescope (LAT). While the majority of high-latitude LAT sources are
extragalactic blazars that appear point-like within the LAT angular resolution,
there are several physics scenarios that predict the existence of populations
of spatially extended sources. If Dark Matter consists of Weakly Interacting
Massive Particles, the annihilation or decay of these particles in subhalos of
the Milky Way would appear as a population of unassociated gamma-ray sources
with finite angular extent. Gamma-ray emission from blazars could also be
extended (so-called pair halos) due to the deflection of electron-positron
pairs in the intergalactic magnetic field (IGMF). The pairs are produced in the
absorption of gamma rays in the intergalactic medium and subsequently
up-scatter photons of background radiation fields to gamma-ray energies.
Measurement of pair halos could provide constraints on the strength and
coherence length scale of the IGMF. In a dedicated search, we find 21 extended
sources and 16 sources not previously characterized as extended. Limits on the
flux of the extended source components are used to derive constraints on the
strength of the IGMF using spectral and spatial templates derived from Monte
Carlo simulations of electromagnetic cascades. This allows us to constrain the
IGMF to be stronger than $3\times10^{-16}\,$G for a coherence length $\lambda
\gtrsim 10\,$kpc.
