# Kiddie Colloquium

## Past Events

May
20

### Two vignettes in complexity theory

Date11:30 AM
Location
384H
Speaker
Carl Schildkraut (Stanford)

Complexity theory is an interesting subject. I will show you the fastest¹ algorithm for any² problem, as well as how to compute anything³ using only three bits of memory.⁴ If time permits, I will explain why these are (at least somewhat) useful.

May
13

Date11:30 AM
Location
384H
Speaker
Josef Greilhuber (Stanford)

How do the eigenfrequencies of a vibrating membrane change if one deforms the boundary? It turns out that this depends only on the behavior of the membrane at the boundary itself, as encapsuled in a famous formula of Jacques Hadamard from 1909. I will talk about this and some more odd facts…

May
06

### Polynomial positivity

Date11:30 AM
Location
384H
Speaker
Nitya Mani (MIT)

When is a multivariate polynomial nonnegative (over the reals or some other semi algebraic set)? We’ll start with some easy methods to certify positivity, discussing Hilbert’s 17th problem and its positive resolution along the way.

Apr
29

### Construction of the Lebesgue Integral

Date11:00 AM
Location
384H
Speaker
Yizhen Chen (Stanford)

The Riemann integral does not work well with limits, so naturally one wishes to make something better. Thus, every high school or undergraduate math student should attempt to develop a better integral before learning any measure theory. Naturally, they come up with many strange ways to do it,…

Apr
22

### At the intersection of Ramsey and Turán

Date11:30 AM
Location
384H
Speaker
Maya Sankar (Stanford)

Ramsey and Turán numbers are both central quantities in graph theory. Both maximize some quantity — the number of edges (Turán) or independence number (Ramsey) — over n-vertex graphs containing no copy of a fixed forbidden subgraph. In this talk, I'll tell you about a quantity that combines the…

Apr
08

### Combinatorial inequalities via algebraic geometry

Date11:30 AM
Location
384H
Speaker
Matt Larson (Stanford)

I will explain the proof of the following statement: given n vectors in a vector space, let a_k be the number of sets of k of the n vectors which are linearly independent. Then the sequence a_0, a_1, a_2, ... is unimodal. The proof is an application of the Hodge index theorem in algebraic…

Mar
11

### Circles, Graphs, Orbifolds

Date11:30 AM
Location
384H
Speaker
Judson Kuhrman (Stanford)

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…

Feb
26

### How to take the derivative of a computer program

Date11:30 AM
Location
384H
Speaker
Ben Church (Stanford)

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…

Feb
12

### Restart Mathematical Life

Date11:30 AM
Location
384H
Speaker
Jiahao Niu (Stanford)

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…

Feb
05

### The chain rule in calculus

Date11:30 AM
Location
384H
Speaker
Yizhen Chen (Stanford)

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…