# Sang-hyun Kim (김상현), On rational 2×2 matrices without relations

## September 7 Tuesday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

For a rational number $q= s/r$, we consider the two 2×2 matrices $A=\begin{pmatrix}1&0\\1&1\end{pmatrix}$ and  $B_q=\begin{pmatrix}1&q\\0&1\end{pmatrix}$. It is a long-standing conjecture (traced at least back to Rimhak Ree) that A and B(q) admit a nontrivial group relation if $|q|<4$; the converse is classical. For the special case $s≤27$ and $s\neq 24$, we prove this conjecture. We give a lower bound estimate of the natural density for all the other values of s. (Joint with Thomas Koberda)

## Details

Date:
September 7 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:
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Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
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기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209