# Undergraduate Colloquium Spring 2017

**April 6, 2017**

**No Seminar**

**April 13, 2017**

**No Seminar**

**April 20, 2017**

**No Seminar**

**April 27, 2017****Francois Monard****An Excursion through the Art, Math, and Applications of Origami**Origami, a traditional paper-folding discipline from 17th-century Japan, has known new exciting developments over the past three decades: from the beginning of computer-assisted crease pattern design, which helps paper-folders design more and more complex creations, to its use in engineering (blood stents, airbags, and so forth), to the emergence of new forms of artistic origami. The link between origami and mathematics is constantly reinforced and examples abound where these two disciplines feed off of one another. We will go over some of the developments just mentioned, discussing along the way potential creative directions via modular origami or tessellations, or mathematical problems such as the fold-and-cut problem.

**May 3, 2017****Alvin Jin****Knot theory, Not theory**Knots are occur commonly in every day life, as well as mathematics. One of the major questions in knot theory is: how can we tell if a knot is equivalent to the unknot? If it is equivalent to the unknot, how "far" from the unknot is it? In more concrete terms, if I have a jumbled up piece of string, how can I tell if I can untangle it? How long will it take to untangle it? Here are where knot invariants come in. I will discuss some of these invariants in this talk. Typically, the stronger the invariant, the more uncomputable it is.

**May 10, 2017**

**Steven Flynn****An introduction to ordinals and their arithmetic**We will cover the formal definition of an ordinal number and interpret what it means to add, multiply and exponentiate them. Time permitting, we will delve into details about transfinite recursion.

**May 18, 2017**

**No Seminar**

**May 25, 2017**

**Gabriel Martins***What is a theory of everything?*We will start by talking about some very basic concepts of quantum mechanics and relativity. The first goal will be to understand what are some of the main difficulties of putting these two theories together. Along the way we will see various familiar mathematical concepts that are important to understanding this puzzle. Towards the end, if time permits, we will discuss some initial notions of quantum field theory, the most successful attempt of solving this problem so far.

**May 31, 2017**

**Nate Sievers****Places Where Stuff Happens: Category Theory By Examples**This talk aims to introduce aspects of category theory in an intuitive and (relatively) concrete way. We use the running example of the list monad from computer science to guide our discussion, starting first with the definition of a category and ending with the kleisli construction.

**June 7, 2017**

**Natalya Jackson****More Primes than Squares**We will prove, using techniques accessible at the Math 19B level, that there are, in some sense, more primes than squares. No prior number theory experience is assumed, but we will also discuss related theorems and conjectures regarding the frequency and distribution of the primes. One million dollars will be paid to the first person who provides the solution to the last problem in this talk!

**June 15, 2017**

**TBA**