Calculating the residues for rational integrals in complex variables is a classical problem in mathematics. It is directly related to questions on algebraic cycles, their cohomology classes, and the Abel–Jacobi map. In this talk I will present joint work with Michael Hopkins in which we use topological cohomology theories to shed some new light on the Abel–Jacobi map.

When Korea achieved its independence in 1945 there were less than 10 bachelors in Mathematics in Korea. In 1960’s GDP per capita of Korea was less than 70 dollars, almost same as poor countries in Africa. We present a leisurely talk on the development of Korean Mathematics since 1945, especially on the behind stories how we could succeed in hosting ICM 2014 in Seoul.

Also, a comparison between the research trends of South and North Korean Mathematics is provided, based on our analysis of the statistics of almost all the articles published by both Korean mathematicians from 2001 to 2010.

Belief propagation (BP) is a popular message-passing algorithm for computing a maximum-a-posteriori assignment in a graphical model. It has been shown that BP can solve a few classes of Linear Programming (LP) formulations to combinatorial optimization problems including maximum weight matching and shortest path. However, it has been not clear what extent these results can be generalized to. In this talk, I first present a generic criteria that BP converges to the optimal solution of given LP, and show that it is satisfied in LP formulations associated to many classical combinatorial optimization problems including maximum weight perfect matching, shortest path, network flow, traveling salesman, cycle packing and vertex cover. Using the criteria, we also construct the exact distributed algorithm, called Blossom-BP, solving the maximum weight matching problem over arbitrary graphs. In essence, Blossom-BP offers a distributed version of the celebrated Blossom algorithm (Edmonds '1965) jumping at once over many sub-steps of the Blossom-V (most recent implementation of the Blossom algorithm due to Kolmogorov, 2011). Finally, I report the empirical performance of BP for solving large-scale combinatorial optimization problems. This talk is based on a series of joint works with Sungsoo Ahn (KAIST), Michael Chertkov (LANL), Inho Cho (KAIST), Dongsu Han (KAIST) and Sejun Park (KAIST).

Although biological processes are undeniably complex, there are underlying mathematical principles that govern the operation of many of these. In this talk, I will show how the combination of chemical reactions with positive feedback coupled with diffusion underlies that operation of many systems, including signaling networks, pattern forming developmental processes, and measurement-based decisions. I will also show how mathematical modeling and analysis leads to an improved understanding of emergent and collective behaviors in cell biology.