Rigid Local Systems and Sporadic Simple Groups

Chapters 1. Introduction 2. Almost quasisimple groups containing elements with simple spectra 3. Preliminary results on condition $mathrm {({bf S })}$ 4. $G_mathrm {geom}$ and $G_mathrm {arith}$ 5. Structure of $G_mathrm {geom}$ 6. Rationality, moments, and reduction mod $ell $ of hypergeometric sheaves 7. Descents of hypergeometric sheaves 8. The notational scheme for descents 9. Proving finiteness of $G_mathrm {geom}$ 10. The alternating group $mathsf {A}_6$ 11. The alternating group $mathsf {A}_7$ 12. The Mathieu group $mathrm {M}_{11}$ 13. The Mathieu group ${mathrm M}_{22}$ 14. The Mathieu group $mathrm {M}_{23}$ 15. The Mathieu group $mathrm {M}_{24}$ 16. The MacLaughlin group $mathrm {McL}$ 17. The Janko group $mathrm {J}_2$ 18. The Janko group $mathrm {J}_3$ 19. The Rudvalis group $mathrm {Ru}$ 20. The special linear group $mathrm {PSL}_3(4)$ 21. The special unitary group $mathrm {PSU}_4(3)$ 22. The symplectic group $mathrm {Sp}_6(2)$ 23. The orthogonal group $Omega ^ _8(2)$ 24. The exceptional group $G_2(3)$ 25. The exceptional group $G_2(4)$ and its subgroup $mathrm {SU}_3(4)$ 26. The ""exceptional"" group $mathrm {SU}_3(3) cdot 2 cong G_2(2)$ 27. The Suzuki group ${}^2! B_2(8)$ 28. The ""exceptional"" group $mathrm {SL}_2(8) cdot 3 cong {}^2! G_2(3)$ 29. The Conway group $mathrm {Co}_1$ and the Suzuki group $mathrm {Suz}$ 30. Complex reflection groups 31. Further local systems for $mathrm {Sp}_6(2)$, $mathrm {SU}_3(3)$, ${}^2! G_2(3)$, and $2mathsf {A}_7$ 32. Further multi-parameter local systems