9:30 - 11:30 Poo-Sung Park

12:30 - 14:30 Sang June Lee

14:30 - 16:30 Ji Young Kim

16:30 -18:30 Chong Gyu Lee

Poo-Sung Park

Surreal numbers and LADDER gam

Ladder is a new Nim-like game. Given several sequences of numbers, the player $L$ erases increasing subsequences and the player $R$ erases decreasing subsequnces. The last mover wins the game. We analyze this game with the combinatorial game theory.

Sang June Lee

AKPSS theorem and Infinite Sidon sets of integers

AsetSofnaturalnumbersisaSidonsetifallthesumss1+s2 withs1,s2 ∈Sands1 ≤s2 are distinct. Let constants α > 0 and 0 < δ < 1 be fixed, and let pm = min{1, αm−1+δ } for all positive integers m. Generate a random set R ⊂ N by adding m to R with probability pm, independently for each m. We investigate how dense a Sidon set S contained in R can be. Our results show that the answer is qualitatively very different in at least three ranges of δ. We prove quite accurate results for the range 0 < δ ≤ 2/3, but only obtain partial results for the range 2/3 < δ ≤ 1.
This is joint work with Y. Kohayakawa, C. G. Moreira and V. Rödl.

Ji Young Kim

Sums of nonvanishing integral squares

In 1911, Dubois determined all positive integers that are represented by sums of k nonvanishing squares for any $k \geq 4$. In this talk, we extend the Dubouis' results to real quadratic fields $\mathbb{Q}\sqrt{m}$ and we will show that for each positive integer $k \geq 5$, there exists a bound $\mathcalC(m, k)$ such that every totally positive integer in the real quadratic field $\mathbb{Q}\sqrt{m}$ whose norm exceeds $\mathcalC(m, k)$ can be expressed as a sum of k nonvanishing integral squares in $\mathbb{Q}\sqrt{m}$.

Chong-Gyu Lee

Geometric parametrization of quadratic polynomial maps of topological degree 2.

In previous work, we parametrize planar Henon maps with information at fixed points. In this talk, we introduce the critical pods, which will provide enough information to parametrize quadratic polynomial maps of topological degree 2.