The moduli space of decorated twisted G-local systems on a marked surface, originally introduced by Fock--Goncharov, is known to have a natural cluster K_2 structure. In particular, we have a canonically defined cluster algebra A and an upper cluster algebra U inside its field of rational functions. In order to investigate the structure of the function ring of that moduli space, we introduce the Wilson lines valued in the simply-connected group G, which are “framed versions” of those studied by myself and Hironori Oya. We see that the function ring of the moduli space is generated by the matrix coefficients of Wilson iines, and some of them are cluster monomials. As an application, we prove that both A and U coincide with the function ring. Time permitting, I will also mention some relations to the skein theory. This talk is based on a joint work with Hironori Oya and Linhui Shen.
Zeroth order pseudodifferential operators on torus are studied as microlocal model of internal waves. These operators can have embedded eigenvalues. After 0th order analytic perturbations, the embedded eigenvalues become resonances and we prove a series expansion of the resonances. As results of the expansion, we obtain the Fermi golden rule for 0th order operators and we answer the question about the generic absence of embedded eigenvalues of 0th order operators asked by Colin de Verdiere.
Laughter, reunion with old friends, performances, warm vibes....That’s what the end of 2021 is for!
For more than 2000 years, every leap in human understanding of the universe and the laws of the universe depends on a better measurement of the distance of more distant celestial bodies. This lecture will review the human method of ranging celestial bodies for 2000 years, and take you from the Earth Moon system to the era of galactic cosmology.
The standard model of particle physics is a comprehensive theory to describe the basic laws of the micro world, and the non-zero mass of neutrinos is the only experimental phenomenon beyond the standard model. Clarifying the mass origin of neutrinos is a major problem to be solved in contemporary physics. With the theme of neutrino mass, the lecture reviewed the hypothesis and discovery of neut...
From Newton's law of universal gravitation to Einstein's general theory of relativity is a qualitative leap in human understanding of the essence of gravitation. Over the past 100 years, various experimental observations, recent direct observations of gravitational waves and photos of black holes have verified the general theory of relativity, but the essence of gravity is still a major topic o...
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