## Math Club Home

### Upcoming Events

All events take place in the 5th floor lounge of Malott unless otherwise noted. To see posters from talks in the past, click here. To see the gallery of entries from the 2016 bake-off, click here.

Monday, December 3rd; 5:15pm

Presented by Daoji Huang.

A formal proof is a proof in which every logical inference has been checked all the way back to the fundamental axioms of mathematics. Although there is a long way to go for formalization to be practical for working mathematicians, existing theories and technologies of formal verification are already capable of formalizing a large body of modern mathematics. In this talk, I will introduce the building blocks of formal verification, including logical foundations, proof assistants, and expressing mathematics formally in such systems. In particular, I will illustrate the relevant concepts by giving a brief overview of type theories, the Coq proof assistant, and the Flyspeck project that formally verified the 400 years old Kepler’s Conjecture on sphere packing. Furthermore, I will discuss common challenges in formalization endeavors.

Monday, November 26th; 5:15pm

Presented by Professor Bob Connelly.

Put a bunch of circular disks in a container and squeeze the container until they jam. What does the packing look like? What can you say about the density of the packing? When the disks are the same size and the container is a flat torus, the answer is known. If the Radii in ratio 1:2:3, density = 7π/24=0.92015.. sizes are random as with granular materials, for existence, there will be a minimum number of contacts. If the graph of contacts is a triangulation, often the density of the packing is quite large. Evan Solomonides and Maria Yampolskaya will demonstrate a simulation of packings as the container contracts until they jam.

Monday, November 19th; 5:15pm

Presented by Jack Cook.

Using the tools of smooth manifold theory, we propose a generalized framework for olfactory reception, learning, and processing. Inspection of the tangent bundle to a manifold yields vector fields which allow for quantification of changes. We utilize group actions to discover fibre bundles over the manifold and discover various properties related to learning. Under this paradigm, we develop a method for categorization as well as analytical tools to model changes in the category. We end with a quick discussion of searching for data on the manifold in a way that beats nearest neighbour.''

Monday, November 12th; 5:15pm

Presented by Jessie Tan.

The Weil Conjectures are four statements about an analogue of the Zeta function over finite fields. I’m going to talk about the roots of polynomial equations in a “mod p” setting, define the zeta function for a projective variety, and with the new vocabulary I’ll state the Weil Conjectures at the end. Familiarity of finite fields and projective geometry is useful but not required.

Monday, November 5th; 5:15pm

Presented by Seraphina Lee.

Elliptic curves are a special kind of curve that can be given as solutions to equations of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6, with an added point at infinity. I will begin with an introduction to basic definitions, followed by a discussion of their significance, plus what we know (and don't know) about the group structure on their Q- and F_p-points.

Monday, October 29th; 5:15pm

Presented by Kabir Kapoor.

The braid group B_n is the group whose elements are braids running vertically in 3-space (as pictured above), the group operation being concatenation. Braid groups show up all over the place, from knot theory, to operator algebras, to robotics. We will discuss several equivalent ways of thinking about these groups and then present some applications.

Thursday, October 25th; 6pm

Presented by Professor Gabor Domokos.

Professor Domokos, a member of the Hungarian Academy of Sciences,
is known for his work in homogeneous convex monostatic bodies. They
are more commonly known as g\"omb\"ocs. He has donated a g\"omb\"oc to the
Math Department that will be on display in the library - the unveiling is on
10/25 at 2pm. This talk will be rare opportunity to meet the inventor of
the g\"omb\"oc.

Monday, October 22nd; 4pm

Come talk to professors, figure out what classes to take, and hear about study abroad programs for math, the Putnam and Math Modeling Competitions, and other fun math things!

Monday, October 15th; 5:15pm

Presented by Matt Funkhouser.

I’ll be discussing the minimal surface problem, the mathematical treatment of the most fun phenomenon, bubbles. I’ll blow bubbles and use differential equations to show why they are how they are.

Monday, October 1st; 5:15pm

Presented by Alex Black.

In 1911, Toeplitz famously conjectured that any simple closed curve in R^2 encloses a square. Over the summer, I didn't prove this but approached the similar problem of whether any two simple closed curves in R^2 and in R^3 enclose a parallelogram between them. This problem had a surprising connection with a problem I called ring on a string, which essentially asks whether you can pass a ring along a closed string without ever rotating the ring. I will discuss this connection and progress made thus far on both problems.

Monday, September 24th; 5:15pm

Presented by Nathaniel Bannister.

I will give an introduction to Turing Machines, which now serve as the model for computation. Following a proof that the Halting Problem is undecideable, meaning there is no Turing Machine to determine if an arbitrary Turing Machine will halt, I will explore some of the uses Turing Machines have found in mathematics in the more than 80 years since their conception.

Monday, September 17th; 5:15pm

Presented by Ely Sandine.

I will be giving an introduction to fractal analysis on the Sierpinski Gasket (triangle), and discussing recent progress made in Cornell's SPUR program, overseen by Professor Strichartz. I will start by constructing derivatives through analogy with standard calculus. I will then define polynomials with respect to a family of Laplacians, and explain our group's recent observations. The first part of the talk will be quite elegant, and the second part will have interesting graphs and pretty pictures, including a moving one at the end!

Puzzle Session

Thursday, Aug 30th; 6pm-7pm

Come hang out with fellow math enthusiasts and try some puzzles! Pizza is provided.

Origami Session

Thursday, September 6th; 6pm-7pm

Come hang out with fellow math enthusiasts and make origami! Pizza is provided.

Monday, September 10th; 5:15pm

Presented by Isaac Legred.

Popular culture has an interesting way of talking about Quantum Mechanics that has led to many misconceptions arising in public conversation. Physicists trying to explain the intricate mechanics of the universe using kittens have captured the public imagination for years. The purpose of this talk is to try to clarify why physicists keep wanting to put poor animals in boxes with poison, and how this relates to developments in Linear Algebra, Real Analysis, and Representation Theory.

Want to give a talk or suggest an event? Contact Linus Setiabrata (ls823).