Playlist: https://mediaspace.ucsd.edu/playlist/dedicated/1_x0lpso72/1_nm8mfpzj Jan 4 (M): Kummer theory and the Kronecker-Weber theorem (https://kskedlaya.org/papers/pcm.pdf)). Jan 6 (W): The Hilbert class field (https://kskedlaya.org/cft/sec_hilbert.html. Jan 8 (F): Generalized ideal class groups and the Artin reciprocity law (https://kskedlaya.org/cft/sec_artinrec.html. Jan 11 (M): The principal ideal theorem (https://kskedlaya.org/cft/sec_principal.html. Jan 13 (W): Zeta functions and the Chebotarev density theorem (https://kskedlaya.org/cft/sec_zeta.html. Jan 15 (F): Cohomology of finite groups, I (https://kskedlaya.org/cft/sec_cohom1.html. Note: this lecture is rescheduled to Thursday, January 14 at 4pm. Jan 20 (W): Cohomology of finite groups, II (https://kskedlaya.org/cft/sec_cohom2.html. Jan 22 (F): Extended functoriality; homology and Tate groups (https://kskedlaya.org/cft/sec_homology.html. Jan 25 (M): Herbrand quotient; profinite groups (https://kskedlaya.org/cft/sec_profinite.html. Jan 27 (W): cohomology of profinite groups; overview of local class field theory (https://kskedlaya.org/cft/sec_localrecip.html. Jan 29 (F): overview of local class field theory (https://kskedlaya.org/cft/sec_localrecip.html. Feb 1 (M): cohomology of local fields (https://kskedlaya.org/cft/sec_localcomp.html. Feb 3 (W): cohomology of local fields; Tate’s theorem (https://kskedlaya.org/cft/sec_tatethm.html. Feb 5 (F): local CFT via Tate’s theorem (https://kskedlaya.org/cft/sec_tatethm.html. Feb 8 (M): abstract CFT (https://kskedlaya.org/cft/sec_abstractcft2.html. Feb 10 (W): the abstract reciprocity map and reciprocity law (https://kskedlaya.org/cft/sec_abstractcft3.html. Feb 12 (F): the abstract reciprocity law; the filtration on a local Galois group (https://kskedlaya.org/cft/sec_filtration.html. Feb 17 (W): adèles (https://kskedlaya.org/cft/sec_adeles.html. Feb 19 (F): idèles and class groups (https://kskedlaya.org/cft/sec_ideles.html. Feb 22 (M): adèles and idèles in field extensions; the theorems of adelic CFT (https://kskedlaya.org/cft/sec_adelic-recip.html. Feb 24 (W): local-global compatibility for the reciprocity law; overview of the proofs of global CFT (https://kskedlaya.org/cft/sec_adelic-overview.html. Feb 26 (F): the First Inequality (https://kskedlaya.org/cft/sec_ideles-cohom1.html. Mar 1 (M): the Second Inequality: analytic proof (https://kskedlaya.org/cft/sec_ideles-cohom2.html. Mar 3 (W): the abstract reciprocity map; reductions for the existence theorem (https://kskedlaya.org/cft/sec_existence.html. Mar 5 (F): the key case of the existence theorem; algebraic proof of the Second Inequality (https://kskedlaya.org/cft/sec_existence.html. Mar 8 (M): local-global compatibility (https://kskedlaya.org/cft/sec_connection.html. Mar 10 (W): Brauer groups of number fields (https://kskedlaya.org/cft/sec_connection.html. Mar 12 (F): preview of Math 204C: adelic Fourier analysis (http://dx.doi.org/10.1007/978-1-4757-3085-2/) (the Math 204C textbook (the Math 204C textbook).