Talk #1: Fixed Points and Nonlinear Differential Equations in Meromorphic Modular Forms

• Speaker: Isra Al-shbeil, University of Jordan
• Abstract: In this paper, we introduce a map from $M_4(\Gamma)$, the space of meromorphic weight 4 modular forms for a subgroup of the modular group, into itself. This map is built using two tools, namely the Schwarz derivative and the rational equivariant functions. The fixed points of this map turn out to satisfy the same nonlinear differential equations of order 4 with constant coefficients. We will provide 4 examples of fixed points using the Eisenstein series and the Jacobi theta functions.
• Recording: https://youtu.be/cuTEQkgqVpY

Talk #2: The Power of Transition Functions

• Speaker: Sasha Zotine, Queen's University
• Abstract: I’ll describe two ways in which understanding transition functions helps us to understand self-maps of projective bundles on elliptic curves.
• Recording: https://youtu.be/sKgdt66vyIY

Talk #3: An Investigation of Tropical Curve Covers

• Speaker: Eve Pidcock, Colorado State University
• Abstract: We intend to briefly explore the notion of a cover of an abstract tropical curve, the connection between these covers and (ramified) covers of the Riemann sphere, and covers that are "compatible" with a group action. Exact content covered will depend on the time limit.
• Recording: https://youtu.be/VTI2tYrQvXk

Talk #4: The Koszul Complex and DG-Algebras

• Speaker: Sterling Saint Rain, University of California, Berkeley
• Abstract: In this talk, we will introduce the Koszul complex and state some nice facts about its behavior, particularly highlighting that one can view it as a graded algebra endowed with a differential. Time permitting, we will explore the concept of differential graded algebras more generally and discuss their utility and related results.
• Recording: https://youtu.be/pmhOTZjmXM8

Talk #5: Hitchin Truncation for Relative Reductive Groups

• Speaker: Connor Halleck-Dube, University of California, Berkeley
• Abstract: In this flash talk, I will introduce the Hitchin fibration as an algebraic object associated to a relative reductive group over a curve. I'll outline how imposing certain Harder-Narasimhan stability conditions truncates the stack of Higgs bundles in order to obtain a more tractable geometric object (a proper morphism of smooth DM stacks). 
• Recording: https://youtu.be/w1JWT8lIUXA