# Kiddie Colloquium

Organizer: Carl Schildkraut

## Past Events

An “abstract polyhedron” means, roughly, a graph that “might be the edges and vertices of a polyhedron”. When can we promote “might be” to “is”? This question is answered by a beautiful theorem about circle packings on the sphere. I will explain the proof of this theorem, as well as some…

We will show how to differentiate computer programs (lambda-expressions, Turing machines, etc) by encoding them in a new system called linear logic that endows the space of programs/proofs with the structure of a differential k-algebra. We will discuss this theory from the perspective of the…

This talk plans to design an immersive game for people who are still kids at heart to experience learning mathematics from the very beginning, but in a completely non-traditional way. We will start analysis without \epsilon-\delta, start algebra without writing operators and laws, start topology…

Calculus is hard. In most textbooks and calculus classes, the chain rule (f∘g)′(x) = f′(g(x))∘g′(x) is either not proved, or only partially proved. The reason is that the proof requires knowledge of topology not covered in the first two years of university, and most importantly, the result fails…

Inkscape is a free and open-source vector graphics editor, utilizing the standardized Scalable Vector Graphics (SVG) file format as its main format.

In this talk, we will explore its power in crafting mathematical illustrations. Join us to delve into the fundamentals of Inkscape as…

Given a subset of Euclidean space, we may ask about the space of harmonic functions vanishing on that particular set. In two dimensions, it is easy to see that this space is either trivial or infinite dimensional. Surprisingly, this question becomes drastically different in three dimensions!…

How many lines can one find in high-dimensional space, every pair of which meets at the same angle? How large a multiplicity can the second-largest eigenvalue of a sparse graph have? How can one generate abelian extensions of a real quadratic field? What are the "nicest" generalized measurements…

Suppose that some subset of the entries of an m x n matrix are filled in with generic complex numbers. If we are allowed to fill in the remaining entries in any way that we want, what is the smallest rank that we can make it? I will explain some techniques to address this problem and what little…

In the 1970s, Lovász provided a stunning proof of the Kneser conjecture, which stated that a certain family of graphs had large chromatic number. Lovász proved the result by lower-bounding the chromatic number in terms of the (topological) connectivity of an associated topological space, in…

Given two smooth manifolds M and N with boundaries dM and dN, together with a diffeomorphism between dM and dN, how do we glue M and N along the diffeomorphism to obtain a smooth manifold? The standard method in differential topology is to choose collar neighborhoods, and it can be proven that…