Kyeongsik Nam (남경식), Random walks on percolation
In general, random walks on fractal graphs are expected to exhibit anomalous behaviors, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach …
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Seminars and Colloquiums
Events
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Room B332 IBS (기초과학연구원)
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Colin Geniet, Permutations, patterns, and twin-width
Room B332 IBS (기초과학연구원)This talk will first introduce combinatorics on permutations and patterns, presenting the basic notions and some fundamental results: the Marcus-Tardos theorem which bounds the density of matrices avoiding a given …
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Felix Christian Clemen, Triangles in the Plane
Room B332 IBS (기초과학연구원)A classical problem in combinatorial geometry, posed by Erdős in 1946, asks to determine the maximum number of unit segments in a set of $n$ points in the plane. Since …
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Michał Pilipczuk, Monadic stability and monadic dependence
Room B332 IBS (기초과학연구원)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, …
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Karim Adiprasito, Ehrhart theory revisited: Algebraic aspects, unimodality and more
Room B332 IBS (기초과학연구원)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 …
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Eng Keat Hng, Graphon branching processes and fractional isomorphism
Room B332 IBS (기초과학연구원)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 …
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Yulai Ma, Pairwise disjoint perfect matchings in regular graphs
Room B332 IBS (기초과학연구원)An $r$-graph is an $r$-regular graph in which every odd set of vertices is connected to its complement by at least $r$ edges. A central question regarding $r$-graphs is determining …
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Jun Gao (高峻), Phase transition of degenerate Turán problems in p-norms
Room B332 IBS (기초과학연구원)For a positive real number $p$, the $p$-norm $\|G\|_p$ of a graph $G$ is the sum of the $p$-th powers of all vertex degrees. We study the maximum $p$-norm $\mathrm{ex}_{p}(n,F)$ …
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Joonkyung Lee (이준경), Counting homomorphisms in antiferromagnetic graphs via Lorentzian polynomials
Room B332 IBS (기초과학연구원)An edge-weighted graph $G$, possibly with loops, is said to be antiferromagnetic if it has nonnegative weights and at most one positive eigenvalue, counting multiplicities. The number of graph homomorphisms …
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Zixiang Xu (徐子翔), Multilinear polynomial methods and stability results on set systems
Room B332 IBS (기초과학연구원)In 1966, Kleitman established that if \( |A \triangle B| \leq d \) for any \( A, B \in \mathcal{F} \), then \( |\mathcal{F}| \leq \sum_{i=0}^{k} \binom{n}{i} \) for \( …