# # Talks

A lightning talk is a short presentation meant to quickly introduce a topic or concept to an audience. At SUMS, we host lightning talks related to mathematics and related fields and industries. In other words, if your talk is marginally related to math, we'd love to host your talk!

SUMS lightning talks typically last anywhere between 15 minutes and an hour. Anyone can give a lightning talk, including undergraduate and graduate students, faculty, and staff. Attendance is open to the public.

## # Give a Talk

If you'd like to give a talk, please sign up here.

After filling out the form, all you'll have to do is present your talk. We can take care of event logistics and publicity for you!

## # Past Talks

### # 2020-2021

#### # "Algebraic Integers and Integer Sequences Lightning Talk" by *Michael Bradley*

Many mathematicians have a keen interest in *integer sequences*.
For a real world example of this interest, see the *On-Line Encyclopedia of Integer Sequences (OEIS)*, an easily searchable archive of the sequences mathematicians have considered most interesting.
The *Fibonacci numbers* are an example of an integer sequence defined by a relatively simple recursive relation F_{n+1} = F_{n-1} + F_n.
Many people have heard that the ratio of successive Fibonacci numbers approaches the *golden ratio*, a member of a class of numbers called the *algebraic integers*.
This hints at a deeper relationship between the Fibonacci numbers and the golden ratio.
But even more, this hints at a deeper relationship between certain integer sequences and algebraic integers generally.
This lightning talk will explore these relationships in a way that is both casual and detailed.

#### # "Differential Geometry Lite with Mathematica" by *Parsia Hedayat*

When we want to study the geometric properties of objects in some kind of space, how should we go about it? What branch of math might we look to first for help? In this talk, youâ€™ll learn the basics of Differential Geometry, supplemented with graphics in Mathematica, to get a grasp of how Calculus and Linear Algebra can be used to solve problems regarding geometry. The topics to be covered will be curves and surfaces.

#### # "Local and Global Principle Orientation of Number Theory" by *Tomoki Oda*

How can we distinguish between the relations x^2 + y^2 = 1 and x^2 + y^2 = 3? Geometrically speaking, they only differ in scale. How about in terms of rational solutions? The relation x^2 + y^2 = 1 has an obvious rational solution of (1, 0), and another solution (3/5, 4/5) which makes use of Pythagorean triples. In fact, there are infinitely many rational solutions! What about the relation x^2 + y^2 = 3? We probably have not learnt of any rational solutions on this circle, and indeed there are no rational solutions!! There are a variety of ways to explain why the rational solutions do not exist, but we shall be taking a Number Theory approach - one of the explanations is through Local and Global Principal by Hasse! This talk does not require any fancy knowledge of mathematics, but just curiosity! Let's discuss one of the deepest results of modern mathematics!

### # 2019-2020

#### # "Machine Learning" by *Yi Fu*

The first talk of a three-quarter series on Machine Learning, which will introduce students in math major to the theoretical framework behind machine learning techniques and provide insights about the application of upper-division math courses. Topics will include an introduction to machine learning, linear regression models, dimensionality reduction techniques (Principal Component Analysis, Laplacian eigenfunction).

The rest of the past talks have not been added to the new site yet, but they can be found at our old site here.