Professor Tohru Eguchi (University of Tokyo)
Time: 11/2, 11/9, 11/16, 11/23, 11/30, 12/14, 12/21
“String theory and Moonshine phenomenon”
Several years ago we have found some curious phenomenon in string theory, i.e. appearance of exotic discrete symmetries in the theory. This is now called as moon-shine phenomenon and has been under intensive study. In this series of lectures I would like to give you an introduction to moonshine phenomena which may possibly play an interesting role in string theory in the future.

Professor Ryu Sasaki (Shinshu University)
Time: 10/12, 10/19, 10/26
“Simplest Quantum Mechanics”
By pursuing the similarity and parallelism between the ordinary Quantum Mechanics (QM) and the eigenvalue problem of hermitian matrices, we present simplest forms of exactly solvable QM. Its Hamiltonians are a special class of tri-diagonal real symmetric (Jacobi) matrices. The super (sub) diagonal elements of the Jacobi matrices are interpreted as the positive (negative) shift operators acting on vectors which are expressed as functions defined on a finite (infinite) integer lattice, x=0,1,2…. Now the Jacobi matrices are second order difference operators which are Hamiltonians of discrete Quantum Mechanics with real shifts (rdQM) in one dimension. Their eigenfunctions (vectors) are the well known classical orthogonal polynomials of a discrete variable belonging to the Askey scheme of hypergeometric orthogonal polynomials, e.g. the Charlier, Meixner, (dual) Hahn, Racah etc and their q-versions. Here we present the simple QM counterparts of the prominent results of exactly solvable QM; Crum's theorem, shape invariance, Heisenberg operator solutions together with the duality and dual polynomials which are the special features of the discrete QM with real shifts.

Professor W-Y. Pauchy Hwang National Taiwan University
Time: 12/28, 1/4
“Black Holes Do Not Exist in Our Universe”