Upcoming and Recent Events

Click on an event title to see the associated poster. To see a full list of upcoming and past events, please visit the events page. If you have any questions please see the contact page. Finally, if you are interested in nostalgia and/or some cool gifs you can visit a previous version of this site here.

• Math Club Talk

  Nathaniel Bannister

  2021-4-29

  What's an anagram for Banach-Tarski? Banach-Tarski Banach-Tarski! The Banach Tarski theorem is a result from 1924 asserting that, given any two subsets A and B of R^n with n>=3 which are bounded with nonempy interior, there is a way to decompose A into finitely many pieces which, through a combination of rotations, reflections and translations, can be reassembled to make B. Some particularly surprising examples include when A is a ball and B is two balls or B is a larger ball. We will outline a proof of this result and outline some recent results showing that, under certain conditions, the pieces can be made somewhat "nice," including decomposing a square into finitely many Borel pieces and translating them to make a circle.

• Math Club Talk

  Clarice Pertel

  2021-4-8

  L.E.J. Brouwer’s intuitionism was a controversial departure from classical mathematics and has been embraced by physicists and computer scientists, but not by classical mathematicians. In the Nuprl proof development system, much research has been done using intuitionistic mathematics. I will discuss Brouwer’s free choice sequences, as well as introduce homotopy theory and type theory. Finally, I will discuss how Vladimir Voevodsky’s univalence axiom provides an interesting lens with which to reimagine the foundations of mathematics.

• Kieval Lecture!

  Professor Dylan Thurston

  2021-4-1

  Dylan Thurston will be delivering this year's annual Kieval Lecture! The talk will be at 4:00pm on Zoom. More information is available here.

• Math Club Talk

  Tik Chan

  2021-3-25

  The theory of singular integral operators is one of the great achievements in analysis of the past century. Beginning in the 1950s, Alberto Calderón and Antoni Zygmund began developing what is now known as Calderón-Zygmund theory, which is now one of the cornerstones of harmonic analysis, in order to understand these objects. Since then, singular integrals and the methods developed from their study have become powerful tools throughout analysis, even finding some applications in the sciences. In this talk, we will introduce the concept of singular integral operators in harmonic analysis with a focus on the Hilbert transform. In particular, the emphasis will be on the methods used to study these objects and the big picture ideas behind the proofs rather than the specific results or technical details. Knowledge of basic analysis is assumed and familiarity with Lp spaces will be helpful (but not required as we will review all the necessary properties).

• Math Club Talk

  Ely Sandine

  2021-2-22

  In this talk we'll compute the Fourier transform of log |x| using linear algebra. We'll start by showing how to derive the important properties of the Fourier transform without resorting to integration by parts and then go from there. Some familiarity with log is assumed, although in principle not required. There will be pictures.

• Math Club Talk

  Daniela Rodriguez-Chavez

  2020-10-26

  It is hypothesized that as a result of the buildup of greenhouse gases in the atmosphere, as early as within the next few centuries a sixth mass extinction will occur. Because the oceans absorb 30% of carbon (a greenhouse gas) emissions released into the atmosphere, they are key components in understanding both past and future climate events. In this talk, we will examine an oceanic carbon cycle model, and the implications of the results regarding a potential mass extinction.

• Math Club Talk

  Andrew Graven

  2020-10-12

  Poincar\'e's Last Geometric Theorem states that if $T:A\rightarrow A$ is any any area-preserving homeomorphism of the annulus $A$ which ``twists'' the inner and outer boundaries of $A$ in opposite directions, then $T$ has at least two fixed points. Poincar\'e was originally interested in this result because it implies the existence of periodic orbits in the three body problem. He proved several special cases of the theorem via intuitive geometric arguments, however later complete proofs lost much of this geometric flavor. We extend Poincar\'e's argument to the general case of the theorem, while maintaining strong emphasis on his original geometric constructions. Joint work with Professor John Hubbard.

• Math Club Talk

  Nikita Borisov

  2020-03-18

  Given a ring $R$, a map $\delta:R\rightarrow R$ is a derivation if it is additive and satisfies the Leibniz rule ($\delta(ab)=\delta(a)b+a\delta(b)$ for all $a,b\in R$). It is well known that the set of derivations on a ring, denoted $\text{Der}(R)$, form a Lie ring (i.e. $\text{Der}(R)$ is closed under addition and lie brackets $[\delta_1,\delta_2]=\delta_1\circ\delta_2-\delta_2\circ\delta_1$), but are typically not closed under composition. Take for instance the formal derivative on polynomials of $x$; the double derivative doesn't satisfy the Leibniz rule. We would like to study the cases when they are closed under composition (i.e. $\Der(R)$ forms a ring) with a particular focus on finite rings.