The aims of our research group on Operator Inequalities, Optimization, and Computational Topology and Applications are as follows:

1. Advance Mathematical Knowledge:
   To contribute to the development of theoretical frameworks and methodologies in operator inequalities, optimization techniques, and computational topology.

2. Solve Real-World Problems:
   To apply mathematical principles to address practical challenges in science, engineering, and data analysis, bridging the gap between theory and application.

3. Foster Collaborative Research:
   To create a vibrant community of scholars, fostering collaboration within the group and with national and international research institutions.

4. Support Student Development:
   To mentor and engage undergraduate and graduate students, equipping them with hands-on research experience and empowering them to excel in their academic and professional careers.

5. Promote Interdisciplinary Applications:
   To explore the integration of our research with other disciplines, such as computer science, physics, and engineering, to maximize its impact across diverse fields.

6. Publish High-Impact Work:
   To produce innovative and high-quality research papers that address fundamental questions and offer meaningful contributions to the global mathematical community.

7. Enhance Mathematical Awareness:
   To promote the significance and beauty of mathematics in solving complex problems, inspiring future generations of researchers and practitioners.

These goals guide our efforts to advance both the academic understanding and practical applications of these mathematical disciplines.​