On December 30, 2020, Paul Seymour from Princeton University was the speaker of the Virtual Discrete Math Colloquium. He presented his recent breakthrough on the Erdős-Hajnal conjecture with Maria Chudnovsky, Alex Scott, and Sophie Spirkl, which in particular proves that the Erdős-Hajnal conjecture holds for the cycle of length 5. The title of his talk was “The Erdős-Hajnal conjecture is true for excluding a five-cycle“.

## Jinha Kim explained the recent result on the Kalai-Meshulam conjecture by Zhang and Wu at the Discrete Math Seminar

On December 22, 2020, at the Discrete Math Seminar, Jinha Kim (김진하) from the IBS Discrete Mathematics Group presented the proof of the Kalai-Meshulam conjecture by Zhang and Wu, proving that for a graph G, the total Betti number of the independence complex of every induced subgraph of G is at most 1 if and only if G has no induced cycle of length 0 mod 3. The title of her talk was “On a conjecture by Kalai and Meshulam – the Betti number of the independence complex of ternary graphs“.

## Jaiung Jun (전재웅) gave an online talk introducing multi-complexes at the Virtual Discrete Math Colloquium

On December 17, 2020, Jaiung Jun (전재웅) from SUNY New Paltz presented an online talk introducing multi-complexes and their Hopf algebra at the Virtual Discrete Math Colloquium. The title of his talk was “On the Hopf algebra of multi-complexes“.

(The photo above was taken last year in his other seminar talk.)

## Karl Heuer gave an online talk focusing on even circuits in oriented matroids at the Virtual Discrete Math Colloquium

On December 9, 2020, Karl Heuer from Technische Universität Berlin gave an online talk on the problem of detecting even directed circuits in a regular oriented matroid and related classes of oriented matroids at the Virtual Discrete Math Colloquium. The title of his talk was “Even Circuits in Oriented Matroids“.

## Hong Liu presented his result with R. Montgomery on the resolution the odd cycle problem of Erdős and Hajnal at the Discrete Math Seminar

On December 8, 2020, Hong Liu from University of Warwick presented a talk on his recent work with Richard Montgomery, answering the odd cycle problem of Erdős and Hajnal (1981). The title of his talk is “A solution to Erdős and Hajnal’s odd cycle problem“.

## Deniz Sarikaya presented results on necessary conditions for locally finite graphs to have a Hamiltonian cycle at the Virtual Discrete Math Colloquium

On December 3, 2020, Deniz Sarikaya from Universität Hamburg gave an online talk about necessary conditions for locally finite graphs to have a Hamiltonian cycle in terms of their forbidden induced subgraphs. The title of his talk was “What means Hamiltonicity for infinite graphs and how to force it via forbidden induced subgraphs“.

## Joonkyung Lee (이준경) gave online talks on the Ramsey multiplicity and common graphs at the Discrete Math Seminar

On November 30 and December 2, 2020, Joonkyung Lee (이준경) from University College London gave two online talks on the Ramsey multiplicity and common graphs at the Discrete Math Seminar organized by Jaehoon Kim at KAIST. The titles of his talks are “On Ramsey multiplicity” and “On common graphs“.

(The photo above was taken earlier in his other seminar talk.)

## Debsoumya Chakraborti gave a talk on finding a rainbow matching in an edge-colored graph at the Discrete Math Seminar

On December 1, 2020, Debsoumya Chakraborti from the IBS Discrete Mathematics Group presented his theorem with Po-Shen Loh about the existence of a rainbow matching of size q in a simple graph whose edges are colored properly by 2q+o(q) colors. The title of his talk was “Rainbow matchings in edge-colored simple graphs“.