Hong Liu, Sublinear expander and embeddings sparse graphs


A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdős and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some

Gil Kalai, The Cascade Conjecture and other Helly-type Problems

Zoom ID: 868 7549 9085

For a set $X$ of points $x(1)$, $x(2)$, $\ldots$, $x(n)$ in some real vector space $V$ we denote by $T(X,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$. We let $t(X,r)=1+\dim(T(X,r))$. Radon's theorem asserts that If $t(X,1)< |X|$, then $t(X, 2) >0$. The first

O-joung Kwon (권오정), Graph minor theory and beyond

Room 1501, Bldg. E6-1, KAIST

One of the important work in graph theory is the graph minor theory developed by Robertson and Seymour in 1980-2010. This provides a complete description of the class of graphs that do not contain a fixed graph H as a minor. Later on, several generalizations of H-minor free graphs, which are sparse, have been defined

Xavier Goaoc, Order types and their symmetries

Room 1501, Bldg. E6-1, KAIST

Order types are a combinatorial classification of finite point sets used in discrete and computational geometry. This talk will give an introduction to these objects and their analogue for the projective plane, with an emphasis on their symmetry groups. This is joint work with Emo Welzl.

Dabeen Lee (이다빈), Non-smooth and Hölder-smooth submodular optimization

Room 1501, Bldg. E6-1, KAIST

We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves an guarantee when the function is monotone and Hölder-smooth, meaning that it admits a Hölder-continuous gradient. For functions that are non-differentiable or non-smooth, we propose a variant of the mirror-prox algorithm that

Rob Morris, Ramsey theory: searching for order in chaos

Room 1501, Bldg. E6-1, KAIST

In many different areas of mathematics (such as number theory, discrete geometry, and combinatorics), one is often presented with a large "unstructured" object, and asked to find a smaller "structured" object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that

Maria Chudnovsky, Induced subgraphs and tree decompositions

Room 1501, Bldg. E6-1, KAIST

Tree decompositions are a powerful tool in both structural graph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. Tree decompositions

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