Outreach

Mini-Workshop on Matrix Analysis and Applications
 
This meeting aims to foster research and collaboration among mathematicians working in various aspects of linear and multilinear algebra, matrix analysis, quantum information, and quantum computing. The inaugural meeting, held at the University of North Florida, led to several research publications by its participants. We aspire to establish this gathering as a regular tradition for researchers with shared interests in matrix analysis and quantum information.

Confirmed participants:

Sergey Belyi, Troy University, USA, sbelyi@troy.edu
Malgorzata Czerwinska, University of North Florida, USA, m.czerwinska@unf.edu
Sejong Kim, Chungbuk National University, Korea, skim@chungbuk.ac.kr
Trung Hoa Dinh, Troy University, USA, thdinh@troy.edu
Raluca Dumitru, University of North Florida, USA, 
raluca.dumitru@unf.edu
Jose Franco, University of North Florida, USA, 
jose.franco@unf.edu
Huajun Huang, Auburn University, USA, huanghu@auburn.edu
Suman Kumar, Troy University, USA, skumar@troy.edu
Hiroyuki Osaka, Ritsumeikan University, Japan, osaka@se.ritsumei.ac.jp
 

For inquiries about the location and accommodation, please contact Dr. Hoa Dinh at thdinh@troy.edu.

Tentative schedule for March 15th:
8:30am-9:30am: Hiroyuki Osaka, Detecting entanglement witnesses and its application to the entanglement cost for zero-error distributed quantum computation. Abstract:

9:30am-10:30am: Jose Franco, On some questions relating to the near order. Abstract: In this talk, we will discuss some new questions regarding the near order. Some of these relate to the Furuta inequality and characterizations of the chaotic order.

10:30am-11:30am: Huajun Huang, Recent progress in the orders of the Bures-Wasserstein mean and the Alpha Procrustes mean. Abstract: In this talk, we will present the progress on the exploration of the order relations in the Bures-Wasserstein mean and the Alpha Procrustes mean. A few updated results and discussions will be posted. 

11:30am-1pm: Lunch time. We will have lunch at the university dinning hall.

1:30pm-2:30pm: Sejong Kim, New candidates of matrix geometric means. Abstract: There are two important geometric means of positive definite matrices, which are metric and spectral geometric means. In this talk we introduce new candidates substituting those geometric means. We study their properties by comparing with original geometric means in the view point of geodesic, operator inequality and log-majorization. Finally, we discuss with open questions and extension to multi-variable means.

2:30pm-3:30pm: Hoa Dinh, Revisit some relations between the spectral geometric mean and Wasserstein mean. Abstract: In this talk, we introduce a new form of spectral geometric mean, the Wasserstein mean, and explore its applications in studying these objects and related questions.

3:30pm-4:30pm: Sergey Belyi, Canonical L-systems and c-Entropy. Abstract: We introduce and  evaluate c-Entropy and dissipation coefficient  of canonical L-systems based on the multiplication operator. We also consider the coupling of such L-systems and derive explicit formulas for its c-Entropy and dissipation coefficient.

 

The previous workshop at the University of North Florida, November 2024

The list of preprints after the Florida Mini-workshop:

Minh Thanh Duong, Anh Vu Le, Cong Trinh Le, Trung Hoa Dinh. Revisit some relations between the spectral geometric mean and Wasserstein mean. Submitted, 2025.
Trung Hoa Dinh, Jose Franco, Sejong Kim. On alternative means. In preparation.
Trung Hoa Dinh, Ai Nhan Nguyen, Hiroyuki Osaka. On 2-geometric mean and applications. In preparation.
R. Dumitru, J. A. Franco, S. Kim, and M. Czerwinska, A theory of alternative means of matrices, submitted.
R. Dumitru, J. A. Franco, and S. Kim, In-betweenness and Heinz mean inequalities, submitted.