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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20261006T163000
DTEND;TZID=Asia/Seoul:20261006T173000
DTSTAMP:20260821T005558Z
CREATED:20260821T005539Z
LAST-MODIFIED:20260821T005558Z
UID:13133-1791304200-1791307800@dimag.ibs.re.kr
SUMMARY:Daniel McGinnis\, Multi-generic initial ideals\, regularity\, and the optimal colorful fractional Helly theorem for $d$-Leray complexes
DESCRIPTION:A celebrated result of Bayer and Stillman from 1987 states that for a homogeneous ideal $I$ of a polynomial ring $S$\, the regularities of $S/I$ and $S/\textrm{GIN}(I)$ are the same under the reverse lexicographic monomial ordering\, where $\textrm{GIN}(I)$ is the generic initial ideal. If $R$ is a polynomial ring whose variables are subdivided into disjoint blocks of variables $X_1\,\dots\,X_c$\, there is a natural multi-grading on $R$\, and one can analogously define a multi-graded version of the generic initial ideal for any multi-homogeneous ideal $I$ of $R$. However\, the full strength of the Bayer-Stillman Theorem fails in the multi-graded setting; there are multi-homogeneous ideals $I$ such that the regularities are not preserved after passing to the multi-graded generic initial ideal no matter the choice of monomial ordering. \nWe prove lower bounds on the regularity of $R/I$ in terms of almost regular sequences of the multi-graded generic initial ideal of $I$ restricted to each block of variables. Again\, we use the reverse lexicographic monomial ordering\, but interestingly\, the lower bound result requires a particular choice of ordering on the variables. \nAs an application\, we prove the optimal fractional Helly theorem for $d$-Leray simplicial complexes\, a problem stemming from the work of Kim in 2017.
URL:https://dimag.ibs.re.kr/event/2026-10-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20261013T163000
DTEND;TZID=Asia/Seoul:20261013T173000
DTSTAMP:20260819T090026Z
CREATED:20260811T214705Z
LAST-MODIFIED:20260819T090026Z
UID:13078-1791909000-1791912600@dimag.ibs.re.kr
SUMMARY:Julien Codsi\, Recent progress in the tree-⍺ world
DESCRIPTION:Treewidth is a graph parameter commonly used to quantify how “close” a graph is to a tree. Although it is a cornerstone of structural graph theory and algorithm design\, it is nearly useless for algorithmic purposes in many dense graph classes. In this talk\, we discuss the tree-independence number\, a more versatile graph parameter that replaces the standard width measure with the stability number. We will present recent results aimed at characterizing the graph classes in which this parameter enables sub-exponential time algorithms for problems that are\, in general\, NP-hard.
URL:https://dimag.ibs.re.kr/event/2026-10-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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