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In this paper we study Zimmer's conjecture for $$C^{1}$$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the manifold, then the action factors through a finite group. For lattices in $${\rm SL}(n, {{\mathbb {R}}})$$ , the dimensional bound is sharp. 

Optical SETI (Search for Extraterrestrial Intelligence) instruments that can explore the very fast time domain, especially with large sky coverage, offer an opportunity for new discoveries that can complement multimessenger and time domain astrophysics. The Panoramic SETI experiment (PANOSETI) aims to observe optical transients with nanosecond to second duration over a wide field-of-view (∼2,500 sq.deg.) by using two assemblies of tens of telescopes to reject spurious signals by coincidence detection. Three PANOSETI telescopes, connected to a White Rabbit timing network used to synchronize clocks at the nanosecond level, have been deployed at Lick Observatory on two sites separated by a distance of 677 meters to distinguish nearby light sources (such as Cherenkov light from particle showers in the Earth’s atmosphere) from astrophysical sources at large distances. In parallel to this deployment, we present results obtained during four nights of simultaneous observations with the four 12-meter VERITAS gamma-ray telescopes and two PANOSETI telescopes at the Fred Lawrence Whipple Observatory. We report PANOSETI’s first detection of astrophysical gamma rays, comprising three events with energies in the range between ∼15 TeV and ∼50 TeV. These were emitted by the Crab Nebula, and identified as gamma rays using joint VERITAS observations. 

HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R 100,000 spectroscopy between 0.98 – 2.5 μm, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.