## Undergraduate Mathematics Seminar

The Johns Hopkins Undergraduate Mathematics Seminar hosts regular talks given by speakers of all academic levels about advanced topics in mathematics, geared to an undergraduate audience. The Fall 2023 semester marks the sixth semester of the undergraduate seminar. The talks will be held in **Krieger 413** on **Mondays at 4:30**.

If you are interested in giving a talk, please submit *this form*.

Below is a list of talks that will be updated through the Fall 2023 semester. For a list of talks given in previous semesters, please take a look at our *archive of talks.*

## Schedule of Talks - Fall 2023

**September 11th**

*Prof. Emily Riehl*:

**A Reintroduction To Proofs**

**Abstract:** An introduction to proofs course aims to teach how to write proofs informally in the language of set theory and classical logic. In this talk, I'll explore the alternate possibility of learning instead to write proofs informally in the language of dependent type theory. I'll argue that the intuitions suggested by this formal system are closer to the intuitions mathematicians have about their praxis. Furthermore, dependent type theory is the formal system used by many computer proof assistants both "under the hood" to verify the correctness of proofs and in the vernacular language with which they interact with the user. Thus, there is an opportunity to practice writing proofs in this formal system by interacting with computer proof assistants such as Coq and Lean.
**Prerequisites**: None

## Schedule of Talks - Spring 2023

**March 13th**

*Prof. Victoria Akin*:

**Harry Houdini’s Magic Math Trick**

**Abstract:** What theorem is so mystifying that Harry Houdini was writing about it in his 1922 book, Paper Magic? In this talk, we’ll hint at the proof of a surprising theorem and demonstrate some magic of our own! Along the way, we’ll develop some mathematical machinery for paper folding and paper flattening. We’ll also explore some cutting, unfolding, and flattening of polyhedra. With any luck, we’ll state an open question or two.
**Prerequisites**: None

**April 14th**

*Dr. Ben Dees*:

**Buffon's Needle**

**Abstract:**Suppose that I draw a bunch of lines parallel to each other, spaced one inch apart, and drop my standard-issue one-inch needle onto them at random. How likely is it that the needle will cross one of the lines? More generally, what if the needle is longer, shorter, or is actually a squiggly piece of uncooked pasta? There are, broadly speaking, two approaches to this. One of them involves setting up some number of integrals to figure out these probabilities. This approach is entirely valid and will work, but there’s another approach that just relies on probability theory. In this talk, we will compute no integrals, and use no calculus. Instead, we will see a marvelous display of the glorious power called “linearity of expectation,” and that’s all we’ll need.
**Prerequisites**: None

**April 28th**

*Yoyo Jiang*:

**Introduction to Monoidal Categories**

**Abstract:** In this talk, we will introduce categories, look at some examples, and see how category theory can help us describe mathematical objects. We will attempt to reconstruct the integers with the familiar properties that we know and love using categorical language, and use that to motivate the definition of a monoidal category. We will finish by seeing some fun examples of monoidal categories. No background is required, although some exposure to linear algebra or abstract algebra will be helpful.
**Prerequisites**: None