POSTECH 2026 Fall Number Theory Learning Seminar: Arthur-Selberg Trace Formula

• Speaker: Yuchan Lee

• Abstract:

• Note

Goal:

• Brief recall for Group scheme and automorphic forms of a connected reductive group G;

• Definition of the ordinary automorphic representation;

• Adelic quotient of G and its L^2-space;

• definition of the discrete automorphic representation and comparison;

References:

Goal: 

• Hilbert space and generalized basis

• An example assocaited with SL_2(Z)\H 

• Eisenstein theory and Langlands' decomposition

• L^2-expansion of the function in L^2([G]^1)

References:

Goal:

• When [G] becomes compact quotient

• Kernel function of R(f) and identity operator

• spectral and geometric expansions

• (If time allows) considering the kernel function for non-compact quotient and derive the convergence problem

References: