Chern Medal Award 2018 Masaki Kashiwara

International Mathematical Union

26 Apr 201903:55

Summary

TLDRBorn in 1947, the speaker's journey in mathematics began with a love for algebraic analysis and representation theory. As a special assigned professor at a university, their work spans 50 years, with significant contributions to manifolds, including theorems and formulas bearing their name. The speaker emphasizes the importance of discerning the essential from the trivial in research and the growing intersection of mathematics with other fields like physics and computer science, fostering new theories and understanding.

Takeaways

🎓 The speaker was born in 1947, two years after the Second World War, in Europe but Tokyo is mentioned, indicating a possible correction or emphasis on their connection to Tokyo.
🌾 The speaker's father worked in agriculture and their mother was a housewife, providing insight into their family background.
📚 The speaker has a deep-rooted passion for mathematics, which began at a very young age and has continued throughout their life.
📘 They have an extensive collection of notebooks, which they have not counted but estimate to be in the hundreds, indicating a significant amount of work and dedication to mathematics.
🔍 The speaker's mathematical journey started when they saw 'photo makiato', which might be a reference to a pivotal moment or person in their mathematical development.
🏫 The speaker is a special assigned professor at a Research Institute for Mathematical Sciences at a university, showing their high level of academic achievement and contribution.
📈 They have studied algebraic analysis and representation theory, as well as symplectic geometry, demonstrating a broad and deep expertise in various mathematical fields.
📝 One of their most important works is a book on manifolds with complex structures, which includes several theorems or formulas named after them.
🏆 The speaker is known for their work on crystal bases and an index theorem, among other contributions, highlighting their influence in the field of mathematics.
🤝 The speaker emphasizes the importance of the interaction between mathematics and other disciplines, such as physics and computer science, which is becoming increasingly strong.
🔬 They are actively involved in making progress by developing new theories or gaining new understandings in the intersection of mathematics with other fields.

Q & A

In what year was the speaker born?
-The speaker was born in 1947.
What was the speaker's father's occupation?
-The speaker's father worked in agriculture.
What was the speaker's mother's role?
-The speaker's mother was a housewife.
Where was the speaker born, and what is significant about the timing?
-The speaker was born in Europe, two years after the Second World War.
What is the speaker's current position at the university?
-The speaker is a special assigned professor at the Research Institute for Mathematical Sciences at the University.
What was the speaker's initial interest in mathematics?
-The speaker loved mathematics from a very young age and enjoyed writing on sheets of paper.
How many notebooks did the speaker mention having?
-The speaker mentioned having several hundreds of notebooks but did not count the exact number.
What sparked the speaker's interest in algebraic analysis?
-The speaker's interest in algebraic analysis started when they saw 'photo makiato' (possibly a misheard or misspoken term).
What is the speaker's area of expertise in mathematics?
-The speaker's area of expertise includes algebraic analysis, representation theory, and symplectic geometry.
What is the most important book the speaker has written?
-The most important book the speaker wrote is on manifolds with something unclear (likely a misheard term), which includes several theorems or formulas named after them.
What are some of the theorems or formulas named after the speaker?
-The speaker mentioned 'casual crystal bases' and an 'index theorem' as examples of theorems or formulas named after them.
What does the speaker find important in mathematical research?
-The speaker finds it important to discern what is important and what is not in mathematical research.
What challenges does the speaker face in their research?
-The speaker faces challenges in dividing their time between mathematics and its interactions with other fields such as physics, computer science, and photonics.
How does the speaker perceive the development of mathematics?
-The speaker perceives the development of mathematics as becoming increasingly intertwined with other fields, leading to new theories and understanding.

Outlines

00:00

📚 Early Life and Academic Interests

The speaker, born in 1947, two years post-WWII, grew up in Europe with a father engaged in agriculture and a housewife mother. Despite being born in Tokyo, the speaker's passion for mathematics was ignited at a young age, leading to an extensive collection of notebooks filled with mathematical expressions. The speaker's academic journey began with algebraic analysis and representation theory, eventually branching into symplectic geometry.

📘 Mathematical Contributions and Publications

The speaker is a distinguished professor at a Research Institute for Mathematical Sciences, with a focus on manifolds and secure theorems. They have authored a significant book on the subject and are known for several theorems and formulas that bear their name, such as the casual crystal bases and the index theorem. The speaker emphasizes the importance of discerning what is significant in mathematical research.

🔬 Interdisciplinary Research Challenges

The speaker discusses the increasing intersection between mathematics and other fields, such as physics and computer science, which presents new challenges and opportunities. They highlight the difficulty of the past 50 years in research, particularly in understanding the interaction between mathematics and other disciplines, and the continuous emergence of new theories and insights.

Mindmap

Keywords

💡Second World War

The Second World War, also known as World War II, was a global conflict that lasted from 1939 to 1945. It involved many of the world's nations, including all of the great powers, organized into two opposing military alliances. The war is a significant historical event that provides context for the speaker's birth year, as it shaped the post-war world in which they grew up.

💡Agriculture

Agriculture refers to the practice of cultivating plants and livestock to produce food, fiber, and other products. In the script, it is mentioned that the speaker's father worked in agriculture, indicating the family's livelihood and possibly the rural setting of the speaker's early life.

💡Housewife

A housewife is a term traditionally used to describe a woman whose primary occupation is managing a household and caring for her family. The speaker mentions their mother as a housewife, which provides insight into her role and the family dynamics during the speaker's upbringing.

💡Europe

Europe is a continent that comprises the western part of Eurasia and is bordered by the Arctic Ocean to the north and the Atlantic Ocean to the west. The speaker was born in Europe, yet mentions Tokyo, which could imply a connection or move to Asia, specifically Japan, at some point in their life.

💡Tokyo

Tokyo is the capital city of Japan and one of the 47 prefectures of the country. It is the center of the Greater Tokyo Area and the most populous metropolitan area in the world. The mention of Tokyo in the script suggests that the speaker has a connection to Japan, possibly through work or education.

💡Special Assigned Professor

A special assigned professor is an academic position that may come with specific responsibilities or recognition of expertise in a particular field. The speaker holds this title at a research institute, indicating their high level of professional achievement and specialization in their field.

💡Mathematics

Mathematics is an area of study that deals with the properties and relationships of numbers, quantities, shapes, and patterns. The speaker's love for mathematics from a young age is a central theme of the video, highlighting their passion and dedication to the field.

💡Algebraic Analysis

Algebraic analysis is a branch of mathematics that combines algebra and analysis, often involving the study of functions and equations. The speaker mentions studying algebraic analysis, which is part of their academic background and expertise.

💡Representation Theory

Representation theory is a mathematical discipline that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. It is one of the areas the speaker has studied, indicating their broad and deep knowledge in mathematics.

💡Manifolds

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. The speaker mentions writing an important book on manifolds, which suggests their contribution to the field of differential geometry or topology.

💡Casual Crystal Bases

Casual here likely refers to 'categorical'水晶基, which is a concept in the field of algebraic geometry and representation theory. The speaker's interest in categorical crystal bases indicates their work in advanced mathematical structures and their applications.

💡Index Theorem

An index theorem in mathematics is a result that relates the analytical index of an elliptic differential operator to its topological index. The speaker mentions achieving an index theorem, which is a significant contribution to the field of differential geometry and topology.

💡Research

Research in the context of the script refers to the systematic investigation and study of materials and sources to establish facts and reach new conclusions. The speaker discusses the challenges and importance of research in mathematics, emphasizing the process of discovery and understanding.

💡Interaction

In the script, interaction refers to the relationship and mutual influence between mathematics and other fields such as physics or computer science. The speaker highlights the growing connection between these disciplines, indicating the interdisciplinary nature of their work.

Highlights

Born in 1947, two years after the Second World War.

Father worked in agriculture, mother was a housewife.

Born in Europe yet mentions Tokyo, suggesting a connection or move.

Special assigned professor at the Research Institute for Mathematical Sciences, University.

Early love for mathematics evident from a young age.

Lost count of the number of notebooks filled with mathematical expressions.

Inspired by a photo to study algebraic analysis and representation theory.

50 years of study in microlocal analysis.

Contributions to practical geometry.

Authored a significant book on manifolds with complete security.

Several theorems or formulas named after the professor.

Interest in crystal bases and the Atiyah-Singer index theorem.

Emphasis on finding what is important in mathematical research.

Challenges in dividing and working with other fields like physics and computer science.

Interaction between mathematics and other fields becoming increasingly strong.

Progress in making new theories or understandings in mathematics.