Diophantine Equations and Elliptic Cuves

This Wednesday 10/5 from 5:30-6:30 in LGRT 1634 LGRT 1528 (the actuarial fair will be in 1634 from 4-7 PM – be sure to check that out as well) Holley Friedlander will present “An introduction to Diophantine equations and elliptic curves.” Come listen and enjoy free pizza and soda!

Abstract:
We will consider rational solutions to polynomial equations of the form F(x,y)=0 with integer coefficients. These types of equations were first studied by Greek mathematician Diophantus of Alexandria in the 3rd century. Since then, many interesting applications of Diophantine equations have been discovered. Two natural questions one can ask about these types of equations are: is there a rational solution? and if so, are there infinitely many rational solutions? We will completely answer these questions when the degree of F is 1 or 2. The case degree of F equal to 3 is more delicate and will lead us to the definition of an elliptic curve. The talk will focus on specific examples that emphasize how algebra, number theory, and geometry all play a role in the study of Diophantine equations.

Polygons and Cluster Algebras of Finite Type

This week Jennifer Koonz will be speaking on “Polygons and Cluster Algebras of Finite Type.” Come enjoy pizza and a great talk this Wednesday, 5:30-6:30 in LGRT 1634. Hope to see you there!

Abstract: This will be an expository talk inspired by a graduate summer
school I attended at the Mathematical Sciences Research Institute in
Berkeley, CA. Cluster algebras are combinatorial objects which were
introduced in 2002 by Sergey Fomin and Andrei Zelevinsky. Although the
definition of a cluster algebra is rather involved, finite cluster algebras
can be described pictorially using triangulations of polygons. In this talk,
I will define cluster algebras, give some computational examples of cluster
algebras, and use those examples to illustrate the bijection between the
clusters of a cluster algebra and triangulations of a polygon.

The Lady in the Lake

Our first meeting of the semester is this Wednesday 9/21 from 5:30-6:30 in LGRT 1634. Nico Aiello will give a talk – “The Lady in the Lake”. As usual we will have pizza and soda with the talk. Hope to see you there!

Chases and Escapes: Virtue or Vertigo for the Lady in the Lake?

The ideas of pursuit and evasion pervade much of human existence and
as a result have always been a huge part of human entertainment – it
has been said that half of all fictional writing boils down to a
single conflict between the hunter and the hunted. But more than just
recreational, the study of chases and escapes is also mathematically
interesting and has applications to computer science, surveillance,
traffic control, and military strategy. After learning some
fundamental concepts from game theory, we will discuss the classic
pursuit-evasion problem, The Lady in the Lake, in which a woman finds
herself in a rowboat in the middle of a circular lake while a pursuer
waits for her along the shore. If the pursuer runs at four times the
woman’s rowing speed, can the woman reach a spot on the shore before
her purser does? We will uncover the woman’s optimal escape strategy
in order to answer this question and much further, find the minimum
speed relative to her pursuer’s that the woman must row to evade
capture.

Malthusian Law and the CIA World Factbook

This week (4/6) Professor Jenia Tevelev will give a talk “Malthusian Law and the CIA World Factbook.” The Malthusian law is a dire prediction that the world’s population will double every 50 years or so. Quite surprisingly, this has very interesting consequences for the statistics of various data accumulated in the CIA World Factbook. Come join us for pizza and math from 6-7 PM in LGRT 1634!

Linking of Knots

Hi All,

You’re probably familiar with those oh so frustrating linking puzzles where you have to decouple some twisted up pieces of metal. Jason McGibbon will be talking to us about these puzzles and how they relate to the linking of knots tomorrow (Wednesday) 6-7pm in LGRT 1634. Come join us for pizza, soda, and math!

PS: If you are attending the Henry Jacobs Math Competition, you should still come to Math Club! You can leave a little bit early, and it’s in the same building.

Billiards and Chaos!

This week Luke Mohr will give a talk “Dynamical Billiards and Chaos” OR “Will the Bouncing DVD Logo Ever Hit the Corner?” Come join us Wednesday for a fun talk and pizza from 6-7 in LGRT 1634!

Abstract:
Most of us have seen it. Many DVD players’ screen savers feature a logo bouncing endlessly back and forth about the four sides of your television. The question that has kept me awake on countless nights is: will that logo ever bounce exactly into a corner? I will begin my talk by trying to answer this question, and use this topic as a starting point to introduce the concept of dynamical billiards. Mathematically, a billiard is a system in which a particle bounces within some boundary (or “table”) such that its angle of incidence is equal to its angle of reflection (again, think of this bouncing dvd logo or a cue ball bouncing endlessly within a pool table). I will discuss the different shapes of tables which have been studied and what it means for a table to be chaotic.

Games Night!

Hi all,

This weeks meeting will be a games night! We have Set and Go, but if you have any good games to play, please bring them along. We will be meeting at our usual time and place (LGRT 1634 6-7 PM) Come by for pizza and games!

Movie Night Tonight (2/16)!

Tonight at 6PM in LGRT 1634 we will feature the Horizon documentary “Fermat’s Last Theorem”. The movie tells the exciting story of Andrew Wiles’ proof of one of the most famous mathematical problems in history. This movie is a must see for anyone interested in math! As usual we will have pizza and soda. Come hang out with your fellow math enthusiasts!

Description:
Simon Singh and John Lynch’s film tells the enthralling and emotional story of Andrew Wiles. A quiet English mathematician, he was drawn into maths by Fermat’s puzzle, but at Cambridge in the ’70s, FLT was considered a joke, so he set it aside. Then, in 1986, an extraordinary idea linked this irritating problem with one of the most profound ideas of modern mathematics: the Taniyama-Shimura Conjecture, named after a young Japanese mathematician who tragically committed suicide.

The link meant that if Taniyama was true then so must be FLT. When he heard, Wiles went after his childhood dream again. “I knew that the course of my life was changing.” For seven years, he worked in his attic study at Princeton, telling no one but his family. “My wife has only known me while I was working on Fermat”, says Andrew.

In June 1993 he reached his goal. At a three-day lecture at Cambridge, he outlined a proof of Taniyama — and with it Fermat’s Last Theorem. Wiles’ retiring life-style was shattered. Mathematics hit the front pages of the world’s press. Then disaster struck. His colleague, Dr Nick Katz, made a tiny request for clarification. It turned into a gaping hole in the proof. As Andrew struggled to repair the damage, pressure mounted for him to release the manuscript — to give up his dream. So Andrew Wiles retired back to his attic. He shut out everything, but Fermat.

A year later, at the point of defeat, he had a revelation. “It was the most important moment in my working life. Nothing I ever do again will be the same.” The very flaw was the key to a strategy he had abandoned years before. In an instant Fermat was proved; a life’s ambition achieved; the greatest puzzle of maths was no more.

Modeling the Atmosphere of Jupiter

UPDATE: Due to a scheduling conflict, this first meeting will start at 5:30 instead of 6!
UPDATE: Due to the snow, this meeting has been pushed back until the 9th. See you then!

This coming Wednesday (the 2nd 9th) we will have our first Math Club meeting. Professor Bruce Turkington will be speaking about his own research in modeling the atmosphere of Jupiter. It’s going to be a fascinating talk, so come help us kick off the semester right; join us Wednesday night, 6-7 5:30-6:30 PM in LGRT 1634. And of course, there will be pizza and soda! See the abstract below for some more details about the talk, and a reference (for those of you want to know more)

ABSTRACT:      All pictures of the giant planet, Jupiter, taken by telescopes or satellites show colorful patterns of stripes and spots. These persistent structures are the results of strong winds in the visible layer of the atmosphere.    In this talk I will try to indicate how to construct a mathematical model of that layer of atmosphere, and how the model explains the existence and location of the Great Red Spot.

Reference: B. Turkington, A. Majda, K. Haven and M. DiBattista, Statistical equilibrium predictions of the jets and spots on Jupiter. Proc. Nat. Acad. Sci. 98, 12346-12350, 2001