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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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DTSTART:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210602T170000
DTEND;TZID=Asia/Seoul:20210602T180000
DTSTAMP:20260420T060013
CREATED:20210506T022454Z
LAST-MODIFIED:20240705T184206Z
UID:4042-1622653200-1622656800@dimag.ibs.re.kr
SUMMARY:Adam Zsolt Wagner\, Constructions in combinatorics via neural networks
DESCRIPTION:Recently\, significant progress has been made in the area of machine learning algorithms\, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular\, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go\, purely through self-play. In this talk\, I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the “game” of trying to find a counterexample to a mathematical conjecture\, and show some examples where this approach was successful.
URL:https://dimag.ibs.re.kr/event/2021-06-02/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210616T170000
DTEND;TZID=Asia/Seoul:20210616T180000
DTSTAMP:20260420T060013
CREATED:20210428T010009Z
LAST-MODIFIED:20240705T184215Z
UID:4020-1623862800-1623866400@dimag.ibs.re.kr
SUMMARY:Alan Lew\, Representability and boxicity of simplicial complexes
DESCRIPTION:An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology\, Roberts defined the boxicity of a graph G to be the minimal k such that G can be written as the intersection of k interval graphs. \nA natural higher-dimensional generalization of interval graphs is the class d-representable complexes. These are simplicial complexes that carry the information on the intersection patterns of a family of convex sets in $mathbb R^d$. We define the d-boxicity of a simplicial complex X to be the minimal k such that X can be written as the intersection of k d-representable complexes. \nA classical result of Roberts\, later rediscovered by Witsenhausen\, asserts that the boxicity of a graph with n vertices is at most n/2. Our main result is the following high dimensional extension of Roberts’ theorem: Let X be a simplicial complex on n vertices with minimal non-faces of dimension at most d. Then\, the d-boxicity of X is at most $frac{1}{d+1}binom{n}{d}$. \nExamples based on Steiner systems show that our result is sharp. The proofs combine geometric and topological ideas.
URL:https://dimag.ibs.re.kr/event/2021-06-16/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210630T170000
DTEND;TZID=Asia/Seoul:20210630T180000
DTSTAMP:20260420T060013
CREATED:20210617T062135Z
LAST-MODIFIED:20240707T081259Z
UID:4277-1625072400-1625076000@dimag.ibs.re.kr
SUMMARY:Florian Gut and Attila Joó\, Large vertex-flames in uncountable digraphs
DESCRIPTION:The local connectivity  $ \kappa_D(r\,v) $ from $ r $ to $ v $ is defined to be the maximal number of internally disjoint $r\rightarrow v $ paths in $ D $. A spanning subdigraph $ L $ of $ D $ with $  \kappa_L(r\,v)=\kappa_D(r\,v) $ for every $ v\in V-r $ must have at least $ \sum_{v\in V-r}\kappa_D(r\,v) $ edges. It was shown by Lovász that\, maybe surprisingly\, this lower bound is sharp for every finite digraph. The optimality of an $ L $ can be captured by the following characterization: For every $ v\in V-r $ there is a system $ \mathcal{P}_v $ of internally disjoint $ r\rightarrow v $ paths in $ L $ covering all the ingoing edges of $ v $ in $ L $ such that one can choose from  each $ P\in \mathcal{P}_v $ either an edge or an internal vertex in such a way that the resulting set meets every $ r\rightarrow v $ path of $ D $. We prove that every digraph of size at most $ \aleph_1 $  admits such a spanning subdigraph $ L $. The question if this remains true for larger digraphs remains open.
URL:https://dimag.ibs.re.kr/event/2021-06-30/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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