Short answers, pulled from the story.
Jacques Lacan was a French psychoanalyst and psychiatrist, born on the 13th of April 1901 in Paris and died on the 9th of September 1981. He has been described as "the most controversial psycho-analyst since Freud" and held annual public seminars in Paris from 1952 to 1980. His work had a major impact on post-structuralism, critical theory, feminist theory, and film theory, as well as on clinical psychoanalytic practice.
The mirror stage is Lacan's concept of how the ego forms in the infant. At around six months, before a child has motor co-ordination, it can recognise its reflection as a whole image. The contrast between that unified image and the child's felt bodily fragmentation creates an aggressive tension, resolved when the child identifies with the reflection. Lacan called this identification "alienation," because the ego is constituted from an outside image rather than from within.
The IPA set a condition in August 1963 that the Société Française de Psychanalyse could only be registered as a member body if Lacan was removed from its list of analysts. The SFP complied in November 1963. The primary issues were Lacan's use of variable-length sessions and his broader critical stance toward psychoanalytic orthodoxy. In response, Lacan founded the École Freudienne de Paris on the 21st of June 1964.
Lacan proposed that the unconscious shares with language a complex structure, not that both have a single identical structure. He argued in "The Instance of the Letter in the Unconscious, or Reason Since Freud" that psychoanalytic experience discovers in the unconscious the whole structure of language. For Lacan, the unconscious is not a primitive or archaic layer of the mind but a formation as sophisticated as consciousness itself, which means the self has no stable reference point to which to return following trauma.
The Real, in Lacan's framework, is neither synonymous with ordinary reality nor simply opposed to the Imaginary. It is exterior to the Symbolic order and resists symbolisation absolutely. In Seminar XI, Lacan defined the Real as "the impossible," meaning it cannot be imagined, integrated into the Symbolic, or attained. It is the object of anxiety, described as something faced with which "all words cease and all categories fail."
Lacan replaced the standard fifty-minute analytic session with variable-length sessions that could last from a few seconds to several hours. Between 1979 and 1980 he saw an average of ten patients an hour, a rate critics said reduced psychoanalysis "to zero." He was also accused of physical aggression toward patients, charging exorbitant fees, and fostering dependency among students and followers. Former student Didier Anzieu described him as a "danger" in a 1967 article titled "Against Lacan."