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Lightning Talk Schedule:

Session 1:

Room: PMA 9.166

11:15am - 11:25am

Ryan Lowe

Really Old Numbers

An exploration into why numbers originating from ancient times have the values they do and still persist today, and how these numbers point to the deeper mathematical concept of Anti-Primes (Highly Composite Numbers). Tying the ancient mathematics of people like the Sumerians to one of the most intelligent modern minds of mathematics: Srinivasa Iyengar Ramanujan.

11:30am - 11:40am

Donovan Fox

Transforming Pascal's Triangle into an Iterative Function

From the standard method of constructing Pascal's Triangle, an equivalent representation can be developed in the form of an iterative function. By applying induction, one can prove that this function is equivalent to the formula for binomial coefficients, which is the subject of this talk and what I will be demonstrating.

11:45am - 11:55am

Seemya Momin

1729: The Most Interesting Boring Number

Numbers that look ordinary can sometimes hide amazing surprises. The number 1729 seems boring at first, but it is actually the smallest number that can be written as the sum of two cubes in two different ways. We tell the famous story of Srinivasa Ramanujan and G. H. Hardy, including how Ramanujan claimed that many of his ideas came to him in dreams, sometimes inspired by visions of Indian gods. Along the way, the talk reveals how even simple numbers can have hidden patterns and surprising properties, and why mathematicians like Ramanujan find beauty in unexpected places.

Room: PMA 10.176

11:15am - 11:25am

Kate Sur

The REAL deal

In this talk, we will explore the question: what is the DEAL with REAL numbers? We will begin with a basic introduction to ideas like LUB and GLB properties and understanding why they make the reals different from the rationals. Then, we will work our way up through some set theory definitions and exercises. Together we will conquer neighborhoods and sets of various kinds, finally working our way up to some cool and easily digestible proofs (possibly Cantor's diagonalization argument, possibly something else of similar conceptual difficulty). 

11:30am - 11:40am

Jeffery M

A Method for Factoring Quartic Polynomials

The fundamental theorem of algebra says that any polynomial can be factored as a product of linear and quadratic polynomial factors. But how can those factors be found? This talk describes one method for polynomials of degree four, and demonstrates it with some practical examples.

11:45am - 11:55am

Maya Donovan

Zero-Probability events

Impossible events are easy to define. If you are given a probabilistic event that has a limited sample space, there is always an event (or several) that cannot occur. Thus, impossible events have a probability of 0, but a zero-probability event, which also has a probability of 0, is not considered an impossible event. While this seems oxymoronic, continuous distributions, in which we find the probability via integration, have a 0 probability to give a single, unique real number. Despite this, a continuous distribution must yield a single, unique real number when a continuous event occurs. Thus, a Zero-probability event is, mathematically, not an impossible event.

Room: PMA 11.176

11:15am - 11:25am

Alejandro Lopez

Level Sets & Relativity

Why does gravity keep us anchored to the Earth? Could there be a universe where gravity would send us flying away into deep space? This talk will answer these questions by proving the celebrated 'positive mass theorem' of Schoen-Yau by studying the level sets of real-valued functions defined on the universe. 

11:30am - 11:40am

Krithi Prasad

Symmetric Spaces of Algebraic Tori

The topological torus, or the doughnut, is a familiar mathematical shape that can be viewed as a subgroup of its algebraic cousin, the algebraic torus. This object naturally acts on vector spaces via symmetric transformations that split into independent multiplicative directions, analogous to the nontrivial loops around a torus. We can better understand how the algebraic torus preserves the underlying symmetries of a vector space by representing it as a linear algebraic (matrix) group, making it a valuable tool and a transparent bridge between geometric intuition and algebraic structure. Some background in linear algebra will be helpful.

11:45am - 11:55am

James T Needham

Why Monads Exist (and why you should care)

A monad is an algebra in the monoidal category of endofunctors. That probably isn't very helpful. However, monads can still be appreciated without unpacking all the category theory in their formal definition. To this end, I will introduce monads through their purpose: allowing us to compose functions that would not make sense to compose otherwise. I will also touch on how monads are important to functional programming, the main context where they appear out in the wild.

Session 2:

Room: PMA 9.166 

3:30pm - 3:40pm

Ren Watson

Arrow's Impossibility Theorem and Voting Theory

Is it possible to design a fair democratic voting system? In 1950, mathematical economist Kenneth Arrow proved that, utilizing several simple axioms about fair voting systems, no ranked-choice voting system that converts voter preferences into a candidate ranking satisfies all of the fairness axioms. In addition to having important implications for social choice theory, Arrow's Impossibility Theorem has an elegant set-theoretic proof that makes it mathematically as well as socially interesting. In this talk, we discuss the axiomatic framework and proof of this theorem as well as its implications to voting theory.

3:45pm - 3:55pm

Chuck Martin

Who really did it first?

We'll explore mathematical concepts and ideas named after one individual despite being discovered by another. We will begin with well-known examples before diving into some of the more obscure instances of mathematical misattribution.

Room: PMA 10.176

3:30pm - 3:40pm

Sonya Shah

Connect the Dots from Math to Bio

This talk will involve a discussion of RNA, the lesser-known sibling to DNA. RNA is important in cells because it carries genetic information that is translated to make proteins. RNA viruses are unique in the fact that they use enzymes to reverse transcribe RNA into DNA and then insert it into the host cell to be replicated, infecting the cell. We are going to utilize some mathematical concepts that undergraduates would understand, such as elementary graph theory and linear algebra to analyze RNA diagrams. In particular, we are going to learn how to calculate the algebraic connectivity for a diagram, and how that relates to classifying RNA structures.

3:45pm - 3:55pm

Ben Bertram

Protein folding meets spherical trigonometry: Viewing protein backbones from a different angle

Protein folding is often described through local bond angles, but this talk offers a new geometric perspective. Each segment of the protein backbone can be mapped onto a sphere, where backbone angle pairs form spherical triangles. This provides a new way to understand how adjacent angles relate and constrain one another. Viewing these relationships on a curved surface makes complex 3D structures more intuitive to visualize. This perspective could help reveal patterns in folding and improve how we work with protein structure.

ETHICAL CONDUCT AGREEMENT

One of the main goals of Math For All is to create a welcoming environment for all participants. We wish for every participant to feel welcome, included, and safe at our conference.  For that reason, we ask you to be mindful of your words and actions when communicating with others. We all have a bias and make mistakes. With an open mind and a willingness to apologize, we can create a safe space for everybody. 

Harassment or discrimination of any kind based on race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, and gender expression will not be permitted.

Hate speech is not permitted at the conference. We want to clarify that hate speech does not include the criticism of institutions or governments, but rather that of individuals or groups of individuals, and that we welcome conversations that stimulate a growth mind set.   

If there is a situation during the conference that makes you feel unwelcome, we ask you to please talk to one of the organizers so we can help you as best as we can. 

Questions, Comments, Concerns? Please reach out to us!

ORGANIZERS: Amira Sefidi, Ana Artero Calvo, Sam Ward

FACULTY ADVISORS: Lisa Piccirillo

CONTACT: mathforallaustin [at] gmail [dot] com

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