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말뭉치

1. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as “a kind of grand unified theory of mathematics.
2. When you have that covered (two or three years down the line), then you will benefit from reading about the Langlands program.
3. While the occurence of the Langlands dual group and SL(2,Z) symmetry are suggestive, the relation of this to the full Langlands program seems to be a bit tenuous.
4. There is however a much closer relation between 2d conformal field theory and the Langlands program, a relation which is part of the story of what is now known as “Geometric Langlands”.
5. I will describe some of the history of, progress in, and future prospects for the p-adic Langlands program.
6. D students and young researchers to start new projects within the rich frame of the arithmetic Langlands program.
7. The research of Fedorov is about the Langlands duality for Hitchin systems, the Langlands program with ramifications, and motivic classes of moduli spaces occurring in Langlands program.
8. Fedorov is also interested in applying the philosophy of Langlands program to classical questions of algebraic geometry such as studying principal bundles over local rings.
9. Many of those tools involve something called the Langlands program.
10. Named for Canadian mathematician Robert Langlands , the Langlands program involves proposed connections, or bridges, between a number of seemingly disparate branches of mathematics.
11. “To me, it seems there’s a very striking analogy between the Langlands program and quantum mechanics,” he says.
12. The equations that crop up in the Langlands program, Arthur suggests, are akin to the famous Schrödinger equation, which governs the evolution of quantum mechanical systems.
13. I have been reading a book written by the mathematician Edward Frenkel "Love and Math: The Heart of Hidden Reality" and he devotes a big portion of his book talking about the Langlands program.
14. This principle gives rise to a web of conjectures called the Langlands program which continues to guide research in number theory to the present day.
15. Despite its many successes, the Langlands program remains vague in many of its predictions, due in part to an absence of data to guide a precise formulation away from a few special cases.
16. During the semester we will focus on three specific aspects of the Langlands program.
17. The Langlands program is a vast set of conjectures, initially put forth by Robert Langlands, towards answering the second of these two questions.
18. The PI proposes research on the Langlands program, specifically the part dealing with the p-adic numbers, which are the strange cousins of the real numbers.
19. The Langlands program as it applies to the real numbers was worked out by Langlands himself, while the p-adic story remains somewhat mysterious.
20. One of these is Laurent Fargues' program to geometrize the Langlands program over the p-adic numbers.
21. The geometric Langlands program, which is relatively new, is under rapid development thanks to powerful tools from algebraic geometry.
22. In this project, the investigator will explore connections between these two different facets of the Langlands program by applying geometric methods to study arithmetic problems.
23. In more detail, this is a project to study the geometric Langlands program and its applications to arithmetic geometry.
24. Let’s go way back to my PhD, in which I solved a problem in the Langlands program.