## The IMI Colloquium Report in October 11, 2023

January 22, 2024

Title: **Introduction of mathematical applications in optical / precision instrument industry**

Speaker: **Yuuya Takayama, Yuki Hayashi** (Mathematical Sciences Research Laboratory, Advanced Technology Research & Development Division, Nikon Corporation)

Place: IMI Auditorium(W1-D-413) and Live streaming with zoom

Attendance: 37 (Students: 18; Staffs: 6; Other: 13)

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At this colloquium, two people from Nikon Corporation gave lectures. First, Dr. Takayama told us that his majore had been in differential geometry and gauge theory until his doctoral course, that he had learned from his supervisor “formulating mathematically what is known in physics”, that the presept plays an important role in his current work, and that today’s lecture will also introduce practical /industrial examples related to this presept. He also told us the role of mathematics in “manufacturing” from his experiences in both mathematics and industry. Moreover, As an example from research on the mathematics behind manufacturing, he introduced the understanding of machine learning through graph theory, algebraic frequency analysis and its application, and the use of projective spaces in image analysis. Finally, Dr. Hayashi introduced reinforcement learnings and domain adaptations in robot learging, and introduced deep learning model compression techniques as examples of mathematics related to product developments. We find examples of how mathematical knowledges play various important roles as the common foundation in manufacturing, and we also find useful knowledges for discovering new research topics in mathematics.