강연영상 7 페이지 > 서울대학교 수리과학부

 







There have been at least two surprising events to geometers in 80-90s that they had to admit physics really helps to solve classical problems in geometry. Donaldson proved the existence of exotic 4-dimensional Euclidean space using gauge theory and Givental counts rational curves in quintic threefolds using Feynman diagram in string theory. These events hugely popularised new mathematical topics such as mirror symmetry and enumerative geometry via moduli spaces. In this talk, we present what happened in this field in a past few decades and something happening right now.

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A feature of log-correlation naturally appears in diverse objects such as random matrices, random discrete geometries and Riemann zeta function. In this talk, I will give an overview on the theory of log-correlated fields and talk about recent progress on it.

 

This talk concerns maximal functions given by averages over some family of geometric objects. I will discuss the boundedness of those maximal functions on the Lebesgue spaces and its role in problems of harmonic analysis.