What topics do you want to cover this semester? What activities do we want to plan? This meeting will mainly be a meet and greet with fellow club memebers so we can discuss out plans for the rest of the semester.
What topics do you want to cover this semester? What activities do we want to plan? This meeting will mainly be a meet and greet with fellow club memebers so we can discuss out plans for the rest of the semester.
In 2011, Dan Shechtman was awarded the Nobel Prize in Chemistry for his discovery of quasicrystals, novel materials with properties somewhere between the regularity of crystals and the disorder of random structures. In parallel with this scientific breakthrough, mathematicians have developed tools for understanding aperiodic order, such as Fibonacci substitutions and Penrose tilings. We will survey these mathematical models of quasicrystals, relying on linear algebra and graph theory. Eigenvalues play a central role, giving insight into how these exotic materials could behave. These problems can be subtle and surprising, opening opportunities for a wide range of mathematical contributions. We will describe our collaborative approach, which integrates numerical computation as a key tool in mathematical discovery, providing a bridge between pure and applied mathematics.
The field of Number theory is very diverse, as it has been studied for thousands of years. One of its newer subfields is known as Iwasawa/Tate Theory, first established in the 1950s by Kenkichi Iwasawa. This field was developed thanks to the discovery of p-adic numbers as well as Class Field Theory in the earlier parts of the century. In this talk we will give a brief introduction to Iwasawa Theory, and its relationship to traditional Number Theory. As well, we will discuss the history of the field and how it has changed since its inception.
The Riemann zeta function has enchanted mathematicians for over 150 years, and is the focus of one of the Clay Millenium Prize problems. In this talk, we will discuss some surprising geometry that arises from certain values of the zeta function, the genesis of which can be understood from solving some closely related linear ODEs. Emphasis will be placed on concrete computations that can be understood by students who have completed Calc II and ODEs.