On November 7th, from 5 to 8:50PM, in LIT125, UMS will be hosting our second Undergraduate Talk Extravaganza! The event will consist of eight short undergraduate talks, and a break for pizza. The schedule for the event, including the talks and their abstracts, are listed below.
5:00 – 5:20: Raymond Ying, with “Proving Compactness Theorem via Tychnoff’s Theorem”
> Abstract: The Compactness Theorem relates the satisfiability of a (potentially infinite) set of sentences with the satisfiability of just finite subset of sentences. This is a classic theorem of first order logic and we will show how this can be proven without invoking high level logical techniques, but instead as an application of Tychonoff’s Theorem from topology.
5:25 – 5:45: Jihu Ryu, with “From Cards to Codes: the Power of De Brujin Sequences “
> Abstract: I will demonstrate a simple card trick using the principles of de Brujin sequence. Subsequently, I will explore the key properties of de Brujin sequence. Finally, I will discuss its applicability and illustrate their relevance to various fields.
5:50 – 6:10: Penelope Beall, with “A few $q$-analogs”
> Abstract: A $q$-analog is something which returns the thing it is an analog of when $q$ is sent to $1$. We will visit a few $q$-analogs in areas such as $q$-combinatorics and $q$-calculus.
6:15 – 6:35: Ramsey Makan, with “The Search for Mersenne Primes”
> Abstract: In October of this year, a new largest prime number was discovered by a member of the Great Internet Mersenne Prime Search (GIMPS). The prime, a Mersenne prime in particular, is over 41 million digits long and broke the record held for nearly six years by a prime almost 25 million digits long. I will be defining Mersenne primes and discussing how the new number was discovered, the applications of primes to cryptography, the connection between Mersenne primes and perfect numbers, and how the future of prime discovery has changed forever.
6:40 – 7:10: Break for pizza!
7:15 – 7:35: Andersen Wall, with “A Common Mathematical Language: Category Theory”
> Abstract: Category theory provides a unifying framework for various fields of mathematics by considering the underlying structure of these fields. In this talk, we will explore how category theory can be used to connect various areas of mathematics, from set theory to topology. The talk will highlight key concepts including functors and natural transformations.
7:40 – 8:00: Austin Lam, with “Radiation and Particle Accelerators”
> Abstract: We rigorously examine the general cause of electromagnetic radiation. If time permits, we will discuss the science of particle accelerators.
8:05 – 8:25: Julian Carvajal, with “Rotations and an introduction to lie theory”
> Abstract: This talk introduces the orthogonal group O(n) and the special orthogonal group SO(n), which describes rotations in n-dimensional space and serves as a key example of a Lie group. We will explore the Lie algebra of SO(n) and discuss why understanding Lie groups and algebras is essential for studying continuous symmetries like rotation in both mathematics and physics.
8:30 – 8:50: Nicholas Kozenieski, with “Field Theory and Instabilities”
> Abstract: We learn in classical mechanics that extremals of the action functional give the Euler-Lagrange equations of motion when the Lagrangian function is assumed to depend on at most the first order derivatives of configuration space coordinates. Where did this assumption come from, and what is its usefulness? Here we will talk briefly about Ostrogradski instabilities and their profound implications on classical and quantum field theories.