What is... Series
These are expository talks in the style of the “What is. . . ” column in the Notices of the AMS, which are given by graduate students at a level accessible to undergraduate students with minimal background prerequisites.
Upcoming "What is..." talks
On Thursday March 31, 2022, Luis Torres will give an expository talk:
Title: "What are braids?"
Abstract: Braids of strings encode elements of an algebraic mathematical object known as a braid group. These groups have wide-reaching applications in mathematics, and play an important role in group theory and low-dimensional topology, particularly in the theory of knots. We'll learn some basics about braids, braid groups, and how they can be used to investigate knots! Join us in PMA 5.104 for a fun evening with braided Challah bread, pizza, and braids!
Past "What is..." talks
On Thursday September 16, 2021, Nicky Reyes will give an expository talk.
Title: "What is a Fourier transform?"
Abstract: Coming soon!
On April 29, 2021, Luis Torres will give an expository talk:
Title: "What is the Euler characteristic?"
Abstract: In 1750, Leonhard Euler noticed that any polyhedron made up of V vertices, E edges, and F faces satisfies the equation V-E+F = 2. This formula is known as Euler's polyhedron formula and is a particular instance of what later became known as Euler characteristic. Join us for a fun journey through history full of surprises and mysteries as we learn about Euler and his polyhedron formula; how the Greeks missed the formula entirely; how Descartes almost discovered it; how 19th century mathematicians widened the formula's scope; and how 20th century mathematicians discovered that every shape has its own Euler characteristic. Along the way, we'll see a lot of examples and applications, some of them beautiful and unexpected!
On February 11, 2021, Nicky Reyes will give an expository talk.
Title: "What is a differential form?"
Abstract: Differential forms are a way to formalize certain types of measurement in math. For example, we could measure some quantity like temperature at a point in 3D space, or we could measure the total human population in some region of a map. The first example is a kind of ‘0-dimensional” measurement because it takes place at individual points, and we say points have dimension 0 in math. The second example is a kind of ‘2-dimensional” measurement because regions on a map are 2-dimensional. There are also ways to relate measurements of different dimensions. I will introduce differential forms by discussing what they do for us. As much as possible I will avoid the full technical machinery in favor of an intuitive approach that still allows us to deduce the major properties of differential forms and the relevant formulas and equations.
On November 13th, Cas Monroe will give an expository talk.
Title: "What is a graph?"
Abstract: Graph theory is the study of modelling relationships. In this talk, we'll go over what a graph is, different kinds of graphs, some cool things we can do with them, and some surprisingly hard questions we can ask about them! This will be a talk with lots of pictures and some fun real world examples.
On October 9th, Nicky Reyes will give an expository talk.
Title: "What is a category?"
Abstract: Since it’s introduction in the early 40s, the language of categories has been creeping into more and more branches of math as well as taking on a life of its own. A category is an algebraic gadget (like a group or ring if you have seen those) consisting of some data and operations, which turns out to be a great system for speaking about a branch of math as a whole. In a sense, they formalize the language we use to discuss a subject in math, and even allow us to translate problems in seemingly unrelated fields to one another. A common example is the way we solve geometric problems with algebra and vice versa, by relating things like intersecting shapes to solving systems of equations. But category theory is exposing far reaching generalizations of this concept of “translating between two types of math.” Categories are broad enough to encode branches of computer science, physics, music theory, linguistics, logic, and more, but rigid enough to express seemingly unrelated concepts as shadows of the same underlying principle. In this talk I will introduce categories, with examples, and give few examples of apparently unrelated concepts as different instances of the same categorical process.
On September 11th, Jonathan Johnson will give an expository talk.
Title: "What is a Knot Invariant?".
Abstract: Ever see a picture of a knot and think “You look familiar. I swear I saw you last week.”? Maybe it’s the same knot. Maybe the knots just look very similar. Maybe you’re just going crazy. How can you know? To find out, come learn what is a knot invariant.