Jinbong Lee (Seoul National University)
Title: Maximal operators given by Fourier multipliers and applications
Abstract: Averages of functions over certain geometric objects such as ball, surfaces, curves have been intensively studied in harmonic analysis. A maximal function related to such averages is one of main objects in studying both quantitative and qualitative behavior of functions. In this talk, the speaker introduces L^p boundedness and pointwise convergence property of maximal operators associated with Fourier multipliers. Brief backgrounds of harmonic analysis will be presented for non-analysis audience. This is joint work with Jinsol Seo.
Sunyo Moon (Hanyang University)
Title: On the Laplacian spectrum of k-symmetric graphs
Abstract: For some positive integer , if the finite cyclic group can act freely on a graph , then we say that is k-symmetric. In 1985, Faria showed that the multiplicity of Laplacian eigenvalue 1 is greater than or equal to the difference between the number of pendant vertices and the number of quasi-pendant vertices. But if a graph has a pendant vertex, then it is at most 1-connected. In this talk, we introduce a class of 2-connected k-symmetric graphs with a Laplacian eigenvalue 1. We also give a class of k-symmetric graphs in which all Laplacian eigenvalues are integers. This talk is based on the joint work with Hyungkee Yoo.
Jihoon Park (Korea University)
Title: Curve graphs, combinatorial HHS theory and Artin groups
Abstract: Curve graph is a graph that first introduced by Harvey in 1978 as an object that reflects the combinatoric, geometric structure of the mapping class groups. By its various deep results for the mapping class groups and the right angled artin groups, generalize the curve graph to given finitely generated groups is one major interest in geometric group theory and especially in HHS theory, due to its hierarchical property. In this talk, we will briefly review the curve graph of various groups and combinatorial HHS theory and its application to the finite type artin groups.
Jooyeon Park (Sookmyung Women’s University)
Title: Laplacian eigenvalue distribution of a graph with given independence number
Abstract: For a graph G, let α(G) be the independence number of G, let L(G) be the Laplacian matrix of G, and let GI be the number of eigenvalues of L(G) in the interval I. Ahanjideh, Akbari, Fakharan and Trevisan proved that α(G) ≤ GI [0,n-α(G)] if G is an n-vertex connected graph. Choi, Moon and Park characterized when the equality α(G)= GI [0,n-α(G)] holds forα(G)=2 and α(G)=n-2. In this talk, we give a characterization for α(G)=3 and α(G)=n-3.
Hyung-Joon Tag (Dongguk University)
Title: Diameter two properties and the Daugavet property in Banach spaces
Abstract: In the theory of Banach spaces, there have been fruitful results concerning specific behaviors of certain operators on a Banach
space in connection to the geometrical structures of the unit ball. Among various properties investigated in this manner, this talk will focus on the Daugavet property with which Banach space satisfies
∥I + T∥ = 1 + ∥T∥.
for every rank-one operator T : X → X and exhibits the big slice phenomenon in Banach spaces, i.e. every slice of the unit ball has diameter
two. We also look at weaker notions than the Daugavet property called the diameter two properties and specific geometrical points on the unit sphere related to the Daugavet property and the diameter two properties, which have been active research topics in the last decade.
Hyungkee Yoo (Ewha Womans Univeersity)
Title: Dimension of quantum knot systems and quantum circuits
Abstract: The quantum knot was established from the work of Kauffman and Lomonaco in 2004. They developed a knot mosaic as a way to describe quantum knots, and from this they defined a quantum knot system. In this lecture, I introduce former results on the dimension of quantum knots and quantum knot systems, and share ideas about quantum algorithms that calculate the dimension of quantum knot systems.