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 |