- Date: 4 Aug. (Thu.)
- Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
- Time: 16:00-17:50
- Speaker 1: Jyoti Rani (IISER Mohali)
- Time:16:00-16:50
- Title: A Study of the Joint q-Numerical Range and the A-q-Numerical Range of Operators
- Abstract:
In this talk, we will discuss the concept of the numerical range and its extensions to different operator-theoretic frameworks. We begin with the notion of q-numerical range in multivariable operator theory, namely the joint q-numerical range. In this setting, we will discuss some equivalent conditions for the convexity of the joint q-numerical range, its relation to the joint C-numerical range, and its connections with the joint point spectrum and the joint approximate point spectrum. We will also go through a few key bounds for the joint q-numerical radius.
In the second part of the talk, we will consider the concept of the q-numerical range of a bounded linear operator in the framework of semi-Hilbertian spaces. Here, we will explore the convexity and compactness properties of the q-numerical range and present an equivalent condition for the equality case in an inequality for the q-numerical radius in semi-Hilbertian spaces. We will also examine several geometric properties of the A-q-numerical range, including spectral inclusion results and a circular disk union formula. Additionally, we will introduce the notion of an A-nilpotent operator. Furthermore, we will discuss several refined inequalities for the q-numerical radius via Orlicz functions.
In the second part of the talk, we will consider the concept of the q-numerical range of a bounded linear operator in the framework of semi-Hilbertian spaces. Here, we will explore the convexity and compactness properties of the q-numerical range and present an equivalent condition for the equality case in an inequality for the q-numerical radius in semi-Hilbertian spaces. We will also examine several geometric properties of the A-q-numerical range, including spectral inclusion results and a circular disk union formula. Additionally, we will introduce the notion of an A-nilpotent operator. Furthermore, we will discuss several refined inequalities for the q-numerical radius via Orlicz functions.
- Speaker 2: Anshu (University of Ulsan)
- Time:17:00-17:50
- Title: Quantum Wasserstein distance on quantum permutation group
- Abstract:
In this talk, we will discuss the categorical definition of a quantum permutation group. Then we will describe the quantum Wasserstein distances on the trace space of the quantum permutation groups. We will also show how the Wasserstein distance recovers the Hamming distance in the classical case.
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