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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20230101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241105T163000
DTEND;TZID=Asia/Seoul:20241105T173000
DTSTAMP:20260415T201844
CREATED:20240718T042813Z
LAST-MODIFIED:20241022T011746Z
UID:9550-1730824200-1730827800@dimag.ibs.re.kr
SUMMARY:Michał Pilipczuk\, Monadic stability and monadic dependence
DESCRIPTION:We will give an overview of the recent attempts of building a structure theory for graphs centered around First-Order transductions: a notion of containment inspired by finite model theory. Particularly\, we will speak about the notions of monadic dependence and monadic stability\, their combinatorial characterizations\, and the developments on the algorithmic front.
URL:https://dimag.ibs.re.kr/event/2024-11-05/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241111T110000
DTEND;TZID=Asia/Seoul:20241111T173000
DTSTAMP:20260415T201844
CREATED:20241101T055140Z
LAST-MODIFIED:20241111T080120Z
UID:10031-1731322800-1731346200@dimag.ibs.re.kr
SUMMARY:IBS-DIMAG Workshop on Topology and Combinatorics
DESCRIPTION:The IBS-DIMAG Workshop on Topology and Combinatorics will be held on November 11\, 2024 at Room B332\, Institute for Basic Science (IBS)\, Daejeon\, South Korea. \nInvited Speakers (tentative)\n\nKarim Adiprasito (Jussieu Institute of Mathematics)\nMinho Cho조민호 (IBS Extremal Combinatorics and Probability Group)\nNiloufar Fuladi (INRIA Center of Université de Lorraine)\nMinki Kim김민기 (GIST)\nDohyeon Lee이도현 (KAIST & IBS Discrete Mathematics Group)\nGeunho Lim임근호 (Jussieu Institute of Mathematics)\nSemin Yoo유세민 (IBS Discrete Mathematics Group)\n\nTentative Schedule\n\n11:00-11:30 Karim Adiprasito\, The Charney Davis conjecture and Boolean decompositions\n12:00-14:00 Lunch Break\n14:00-14:30 Niloufar Fuladi\, Universal families of arcs and curves on surfaces\n14:30-15:00 Semin Yoo유세민\, The Charney-Davis conjecture and its related complexes (survey)\n15:00-15:30 Geunho Lim임근호\, Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds\n15:30-16:00 Break\n16:00-16:30 Minki Kim김민기\, Some extensions of the colorful Helly theorem\n16:30-17:00 Minho Cho조민호\, Fractional Helly theorems via weak saturation\n17:00-17:30 Dohyeon Lee이도현\, Betti number of clique complex of H-free graphs (survey)\n18:00-20:00 Banquet\n\nOrganizer\n\nSemin Yoo유세민\, IBS Discrete Mathematics Group\n\nAbstracts\nKarim Adiprasito\, The Charney Davis conjecture and Boolean decompositions\nI will present a novel approach to the Charney Davis conjecture by introducing anticommutative Lefschetz properties\, and studying them on the Danzer complex of flag spheres. \nSemin Yoo\, The Charney-Davis conjecture and its related complexes (survey)\nThe Charney-Davis conjecture lies in the intersection between topology and combinatorics. The conjecture is a special case of the Hopf-Chern-Thurston conjecture for all nonpositively curved\, piecewise Euclidean manifolds which are cellulated by regular Euclidean cubes. In 2001\, Davis and Okun solved the conjecture for a 4-dimensional case\, and some other partial results are also known. However\, the conjecture is still open so far. \nIn this talk\, I will describe five statements that solve the Charney-Davis conjecture and explain some complexes to achieve this goal. \nNiloufar Fuladi\, Universal families of arcs and curves on surfaces\nIn this talk I introduce a family of curves that realize all pants decomposition of a surface: a family of simple closed curves Γ on a surface realizes all types of pants decompositions if for any pants decomposition of the surface\, there exists a homeomorphism sending it to a subset of the curves in Γ. The study of such universal families of curves is motivated by questions on graph embeddings\, joint crossing numbers and finding an elusive center of moduli space. I will discuss the case of surfaces without punctures\, where we establish an exponential upper bound and a superlinear lower bound on the minimum size of the family of curves with this universal property. I also talk about a similar concept of universality for triangulations of polygons\, where we provide bounds which are tight up to logarithmic factors. In this talk\, I will explain the background and context and no prior knowledge in topology or surfaces is needed. \nThis is joint work with Arnaud de Mesmay and Hugo Parlier. \nGeunho Lim\, Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds\nUsing L^2 cohomology\, Cheeger and Gromov define the L^2 rho-invariant on manifolds with arbitrary fundamental groups\, as a generalization of the Atiyah-Singer rho-invariant. There are many interesting applications in geometry\, topology\, and combinatorics. In this talk\, we show linear bounds on the rho-invariants in terms of simplicial complexity of manifolds by using hyperbolization methods. As applications\, we give new concrete examples in the complexity theory of high-dimensional (homotopy) lens spaces. This is a joint work with Shmuel Weinberger. \nMinki Kim\, Some extensions of the colorful Helly theorem\nGiven $k > d$ finite families of convex sets in $\mathbb{R}^d$\, if every colorful $(d+1)$-tuple is intersecting\, then the union of $k-d$ color classes is intersecting. This is known as the colorful Helly theorem. Based on recent joint work with Alan Lew\, I will present some extensions of the colorful Helly theorem and their applications. \nMinho Cho\, Fractional Helly theorems via weak saturation\nTwo celebrated extensions of the classical Helly’s theorem are the fractional Helly theorem and the colorful Helly theorem. Bulavka\, Goodarzi\, and Tancer recently established the optimal bound for the unified generalization of the fractional and the colorful Helly theorems using a colored extension of the exterior algebra. In this talk\, we introduce a combinatorial reduction of both the fractional Helly theorem and its colorful version to a classical problem in extremal combinatorics known as weak saturation. No such results connecting the fractional Helly theorem and weak saturation are known in the long history of literature. These reductions\, along with basic linear algebraic arguments for the reduced weak saturation problems\, let us give new short proofs of the optimal bounds for both the fractional Helly theorem and its colorful version without using exterior algebra. \nThis is joint work with Debsoumya Chakraborti\, Jinha Kim\, and Minki Kim. \nDohyeon Lee\, Betti number of clique complex of H-free graphs (survey)\nThe clique complex of a graph is a simplicial complex whose faces correspond to cliques of the given graph. In this talk\, we investigate extremal properties of the Betti numbers of clique complexes. While general simplicial complexes with n vertices can have a total Betti number approximately $2^n$\, Adamaszek showed that Betti number of clique complex is bounded by around $1.32^n$. Furthermore\, if the underlying graph has an independence number at most two\, the bound tightens to $1.25^n$. Adiprasito\, Nevo\, and Tancer established additional bounds on the total Betti number for clique complexes of (induced) H-free graphs for various graph H\, along with constructions of graphs with large total Betti number. In another direction\, Zhang and Wu demonstrated that for ternary graphs (whose with no induced cycles of length 3n)\, the Betti number of the independence complex (the clique complex of the complement of a graph) is at most one. Indeed\, Jinha Kim showed that these independence complexes are either contractible or homotopy spheres.
URL:https://dimag.ibs.re.kr/event/2024-11-11/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Workshops and Conferences
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241112T163000
DTEND;TZID=Asia/Seoul:20241112T173000
DTSTAMP:20260415T201844
CREATED:20240831T051640Z
LAST-MODIFIED:20240917T095446Z
UID:9815-1731429000-1731432600@dimag.ibs.re.kr
SUMMARY:Karim Adiprasito\, Ehrhart theory revisited: Algebraic aspects\, unimodality and more
DESCRIPTION:Ehrhart theory is the study of lattice polytopes\, specifically aimed at understanding how many lattice points are inside dilates of a given lattice polytope\, and the study has a wide range of connections ranging from coloring graphs to mirror symmetry and representation theory. Recently\, we introduced new algebraic tools to understand this theory\, and resolve some classical conjectures. I will explain the combinatorial underpinnings behind two of the key techniques: Parseval identities for semigroup algebras\, and the character algebra of a semigroup.
URL:https://dimag.ibs.re.kr/event/2024-11-12/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241126T163000
DTEND;TZID=Asia/Seoul:20241126T173000
DTSTAMP:20260415T201844
CREATED:20241018T131301Z
LAST-MODIFIED:20241018T132054Z
UID:9992-1732638600-1732642200@dimag.ibs.re.kr
SUMMARY:Eng Keat Hng\, Graphon branching processes and fractional isomorphism
DESCRIPTION:In 2005\, Bollobás\, Janson and Riordan introduced and extensively studied a general model of inhomogeneous random graphs parametrised by graphons. In particular\, they studied the emergence of a giant component in these inhomogeneous random graphs by relating them to a broad collection of inhomogeneous Galton-Watson branching processes. \nFractional isomorphism of finite graphs is an important and well-studied concept at the intersection of graph theory and combinatorial optimisation. It has many different characterizations that involve a range of very different and seemingly unrelated properties of graphs. Recently\, Grebík and Rocha developed a theory of fractional isomorphism for graphons. \nIn our work\, we characterise inhomogeneous random graphs that yield the same inhomogeneous Galton-Watson branching process (and hence have a similar component structure). \nThis is joint work with Jan Hladký and Anna Margarethe Limbach.
URL:https://dimag.ibs.re.kr/event/2024-11-26/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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