List of contributors; Preface; 1. Projectivity of the moduli of curves Raymond Cheng, Carl Lian and Takumi Murayama; 2. The stack of admissible covers is algebraic Elsa Corniani, Neeraj Deshmukh, Brett Nasserden, Emanuel Reinecke, Nawaz Sultani and Rachel Webb; 3. Projectivity of the moduli space of vector bundles on a curve Jarod Alper, Pieter Belmans, Daniel Bragg, Jason Liang and Tuomas Tajakka; 4. Boundedness of semistable sheaves Haoyang Guo, Sanal Shivaprasad, Dylan Spence and Yueqiao Wu; 5. Theorem of the Base Raymond Cheng, Lena Ji, Matt Larson and Noah Olander; 6. Weil restriction for schemes and beyond Lena Ji, Shizhang Li, Patrick McFaddin, Drew Moore and Matthew Stevenson; 7. Heights over finitely generated fields Stephen McKean and Soumya Sankar; 8. An explicit self-duality Nikolas Kuhn, Devlin Mallory, Vaidehee Thatte and Kirsten Wickelgren; 9. Tannakian reconstruction of coalgebroids Yifei Zhao.
