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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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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:20230101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240604T163000
DTEND;TZID=Asia/Seoul:20240604T173000
DTSTAMP:20260417T234352
CREATED:20240327T044132Z
LAST-MODIFIED:20240707T071933Z
UID:8429-1717518600-1717522200@dimag.ibs.re.kr
SUMMARY:Jane Tan\, Semi-strong colourings of hypergraphs
DESCRIPTION:A vertex colouring of a hypergraph is $c$-strong if every edge $e$ sees at least $\min\{c\, |e|\}$ distinct colours. Let $\chi(t\,c)$ denote the least number of colours needed so that every $t$-intersecting hypergraph has a $c$-strong colouring. In 2012\, Blais\, Weinstein and Yoshida introduced this parameter and initiated study on when $\chi(t\,c)$ is finite: they showed that $\chi(t\,c)$ is finite whenever $t \geq c$ and unbounded when $t\leq c-2$. The boundary case $\chi(c-1\, c)$ has remained elusive for some time: $\chi(1\,2)$ is known to be finite by an easy classical result\, and $\chi(2\,3)$ was shown to be finite by Chung and independently by Colucci and Gyárfás in 2013. In this talk\, we present some recent work with Kevin Hendrey\, Freddie Illingworth and Nina Kamčev in which we fill in this gap by showing that $\chi(c-1\, c)$ is finite in general.
URL:https://dimag.ibs.re.kr/event/2024-06-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240611T163000
DTEND;TZID=Asia/Seoul:20240611T173000
DTSTAMP:20260417T234352
CREATED:20240220T031718Z
LAST-MODIFIED:20240705T154023Z
UID:8279-1718123400-1718127000@dimag.ibs.re.kr
SUMMARY:Maria Chudnovsky\, Anticomplete subgraphs of large treewidth
DESCRIPTION:We will discuss recent progress on the topic of induced subgraphs and tree-decompositions. In particular this talk with focus on the proof of a conjecture of Hajebi that asserts that (if we exclude a few obvious counterexamples) for every integer t\, every graph with large enough treewidth contains two anticomplete induced subgraphs each of treewidth at least t. This is joint work with Sepher Hajebi and Sophie Spirkl.
URL:https://dimag.ibs.re.kr/event/2024-06-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240618T163000
DTEND;TZID=Asia/Seoul:20240618T173000
DTSTAMP:20260417T234352
CREATED:20240330T144427Z
LAST-MODIFIED:20240707T071910Z
UID:8450-1718728200-1718731800@dimag.ibs.re.kr
SUMMARY:Semin Yoo (유세민)\, Paley-like quasi-random graphs arising from polynomials
DESCRIPTION:We provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs defined by polynomials over finite fields\, such as Paley graphs\, Paley sum graphs\, and graphs associated with Diophantine tuples and their generalizations from number theory. As an application\, we provide new lower bounds on the clique number and independence number of general quasi-random graphs. In particular\, we give a sufficient condition for the clique number of quasi-random graphs of order $n$ to be at least $(1-o(1))\log_{3.008}n$. Such a condition applies to many classical quasi-random graphs\, including Paley graphs and Paley sum graphs\, as well as some new Paley-like graphs we construct. If time permits\, we also discuss some problems of diophantine tuples arising from number theory\, which is our original motivation. \nThis is joint work with Seoyoung Kim and Chi Hoi Yip.
URL:https://dimag.ibs.re.kr/event/2024-06-18/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20240628T163000
DTEND;TZID=Asia/Seoul:20240628T173000
DTSTAMP:20260417T234352
CREATED:20240620T045259Z
LAST-MODIFIED:20240705T151013Z
UID:8775-1719592200-1719595800@dimag.ibs.re.kr
SUMMARY:Wonwoo Kang (강원우)\, Skein relations for punctured surfaces
DESCRIPTION:Since the introduction of cluster algebras by Fomin and Zelevinsky in 2002\, there has been significant interest in cluster algebras of surface type. These algebras are particularly noteworthy due to their ability to construct various combinatorial structures like snake graphs\, T-paths\, and posets\, which are useful for proving key structural properties such as positivity or the existence of bases. In this talk\, we will begin by presenting a cluster expansion formula that integrates the work of Musiker\, Schiffler\, and Williams with contributions from Wilson\, utilizing poset representatives for arcs on triangulated surfaces. Using these posets and the expansion formula as tools\, we will demonstrate skein relations\, which resolve intersections or incompatibilities between arcs. Topologically\, a skein relation replaces intersecting arcs or arcs with self-intersections with two sets of arcs that avoid the intersection differently. Additionally\, we will show that all skein relations on punctured surfaces include a term that is not divisible by any coefficient variable. Consequently\, we will see that the bangles and bracelets form spanning sets and exhibit linear independence. This work is done in collaboration with Esther Banaian and Elizabeth Kelley.
URL:https://dimag.ibs.re.kr/event/2024-06-28/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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