Learning to be a theoretical computer scientist by learning the classical and quantum PAC learning

This is a story how a harmonic analyst may try to enter
the area of theoretical computer science (TCS). PAC=probably approximately
correct is a notion of TCS where one should determine the object
(a function, a matrix,...) by making a “small” number of trials. One
pays the price: trials are random and so the object will be found only
with large probability, another price is that it will be found approximately,
with a possible small error. PAC learning is a classical part of
TCS, where many beautiful results are known. Not long ago a sudden
breakthrough in a classical PAC learning was made by my former student
Paata Ivanisvili jointly with Alexandros Eskenazis. The quantum
analog is PAC learning of big matrices. This will be the main topic of my
talk as it leads to an interesting question a l\'a Marcinkiewicz and Bernstein
inequalities. The talk is based on joint results with Lars Becker,
Ohad Klein, Joseph Slote and Haonan Zhang.