Jeck Lim, Sums of linear transformations

June 2 Thursday @ 10:30 AM - 11:30 AM KST

Zoom ID: 870 0312 9412 (ibsecopro)

Speaker

We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $\mathbb{Z}^d$, $|L_1 A+L_2 A|\geq (|\det(L_1)|^{1/d}+|\det(L_2)|^{1/d})^d |A|- o(|A|).$ This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and $L_2$. As an application, we prove a lower bound for $|A + \lambda \cdot A|$ when $A$ is a finite set of real numbers and $\lambda$ is an algebraic number.
Joint work with David Conlon.

Details

Date:
June 2 Thursday
Time:
10:30 AM - 11:30 AM KST
Event Category:
Event Tags:

Venue

Zoom ID: 870 0312 9412 (ibsecopro)

Organizer

Joonyung Lee (이준경)
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