The Langlands programme has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
The article details the recent proof of the geometric Langlands conjecture, a significant advancement in mathematics that validates a decades-old program aiming for a "grand unified theory" of the field. Led by Dennis Gaitsgory and Sam Raskin, the proof—spanning five papers and nearly 1,000 pages—is expected to open new avenues of research and potentially bridge connections between mathematics and theoretical physics, particularly in understanding symmetries in quantum field theory. While not a complete solution to the broader Langlands program, it provides strong evidence for its underlying principles and offers new tools for tackling complex mathematical problems.
The study investigates how well bacterial spores maintain their structural and morphological biosignatures after exposure to harsh conditions simulating the surfaces of Enceladus and Europa. It finds that spore structure remains resilient even after exposure to radiation and temperature extremes, suggesting that methods targeting cell morphology could be valuable for future life detection missions.
consciousness relates to a dynamic process of self-sustained, coordinated brain-scale activity assisting the tuning to a constantly evolving environment, rather than in static descriptions of brain function (3–5). In that respect, neural signals combine, dissolve, reconfigure, and recombine over time, allowing perception, emotion, and cognition to happen (6).
