BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20250101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260710T163000
DTEND;TZID=Asia/Seoul:20260710T173000
DTSTAMP:20260415T212633
CREATED:20260324T141000Z
LAST-MODIFIED:20260326T130309Z
UID:12471-1783701000-1783704600@dimag.ibs.re.kr
SUMMARY:Ting-Wei Chao\, Entropy method and mixture bound
DESCRIPTION:The entropy method has been used in many recent works in extremal combinatorics. With the help of Shannon entropy\, significant progress has been made on several classical problems\, such as the union-closed conjecture and the Sidorenko conjecture. In our recent work\, we use the entropy method to give new proofs of the Kruskal–Katona theorem and Turán’s theorem\, as well as some of their generalizations. The new ingredient in our approach is a method for upper bounding the sum of $2^{\mathbb{H}(X_i)}$  for random variables $X_1\,\cdots\,X_k$ whose supports do not overlap too much. We call this method the mixture bound\, and it can be viewed as an entropic version of double counting. In this talk\, I will introduce the mixture bound and show some examples of how it can be applied on colorful versions of the Kruskal–Katona theorem. Base on joint work with Maya Sankar and Hung-Hsun Hans Yu.
URL:https://dimag.ibs.re.kr/event/2026-07-10/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
END:VCALENDAR