These are notes/slides for some of the talks I gave. The talks, Littlewood Richardson Number and Cyclic Sieving Phenomenon, reflect my current research interest.

## Angel Wins (SASMS, fall 2007)

A proof of the angel problem posed by Conway. The problem was open for more than 20 years, but 4 independent proofs cropped up in the year 2007. I present the simplest proof by András Máthé. This is the first talk I gave as an undergraduate.

*Intended audience: first year undergraduates* angel_wins.ppt | |

File Size: | 294 kb |

File Type: | ppt |

## Vinogradov's Three Primes Theorem (May 2008)

This theorem, a weak version of the Weak Goldbach Conjecture, states that any sufficiently big odd number can be written as the sum of three primes.

*Intended audience: graduate**students in the field* threeprimes.pdf | |

File Size: | 112 kb |

File Type: |

## Szemerédi's theorem for 4 term AP (July 2008)

A Ramsey type result that says a subset of natural numbers with positive density contains a non-trivial 4 term arithmetic sequence. I have some horribly huge blocks of equations. I didn't really know better in my second year.

*Intended audience: graduate students in the field* szemeredi.pdf | |

File Size: | 167 kb |

File Type: |

## Packing Squares in Squares (SASMS, fall 2008)

A survey of the current state of a specific packing problem.

*Intended audience: first year undergraduates* packing.ppt | |

File Size: | 476 kb |

File Type: | ppt |

## Picard Group of Algebraic Curves (July 2009)

For an algebraic curve, its Picard group can be realized as line bundles with tensor product, divisor classes with addition, or a first cohomology group. I show proof of this and some simple examples.

*Intended audience: graduate**students in the field* picard.pdf | |

File Size: | 241 kb |

File Type: |

## Mathematics of Paper Folding (SASMS, winter 2010)

I talk about the theory of flat folding, how circle packing problem affected paper folding, and real life applications of paper folding.

*Intended audience: first year undergraduates* paperfolding.odp | |

File Size: | 1945 kb |

File Type: | odp |

## Nontransitivity in Tournaments (CUMC, July 2010)

I present a simple proof that relates the number non-transitive triples in a tournament with the in-degrees of the vertices. I also show how "draws" should be handled. This result comes from a research I did in high school.

*Intended audience: first year undergraduates* nontrans.pdf | |

File Size: | 323 kb |

File Type: |

## Littlewood Richardson Number (August 2010)

A quick introduction to LR Number. I show how it arises in symmetric function theory and its combinatorial interpretation (LR tableaux). I briefly mention the problem I've been working on.

*Intended audience: upper year undergraduates who are not familiar with the field* lr_number2.pdf | |

File Size: | 341 kb |

File Type: |

## Cyclic Sieving Phenomenon (February 2011)

An introduction to CSP. I show how CSP can be shown using representation theory.

*Intended audience: graduate students who are not familiar with the field* csp_talk.pdf | |

File Size: | 451 kb |

File Type: |

## Music and Math (SASMS, summer 2011)

Explains why we use 12 tone system in music using diophantine approximation. I couldn't play any sound/music because my laptop speaker was too weak. T.T Midi/mp3 files are not included so the sound/music will not play for you too.

*Intended audience: first year undergraduates* m_and_m.odp | |

File Size: | 3218 kb |

File Type: | odp |