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Explore the complexities of fermion systems in this comprehensive lecture by Carlos SĂ¡ de Melo from Georgia Tech, Atlanta, USA. Delve into the transition from SU(2) to SU(N) fermions with spin-orbit coupling, examining open issues that extend beyond charge and spin density waves. Over the course of 1 hour and 28 minutes, gain insights into advanced concepts in quantum physics and condensed matter theory. Presented at the prestigious Institut Henri PoincarĂ© in Paris, this talk offers a deep dive into cutting-edge research in the field of fermionic systems and their properties.