Borsuk–Ulam Theorems for Maps into Higher-Dimensional Codomains

Explore an in-depth lecture on Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Delve into the topology of simplicial complexes defined on spheres and their connection to these theorems. Examine quantitative statements about points "near" the sphere hitting the origin for odd maps from S^n to R^k with k greater than n. Investigate the concept of nontrivial sets of points with diameter strictly less than pi that satisfy specific properties. Learn about ongoing research aimed at obtaining sharper bounds for arbitrary odd maps in higher dimensions. Gain insights into joint work with Henry Adams and Florian Frick on this advanced topic in applied algebraic topology.