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1 2016 Course Description of Undergraduate Seminars ( )
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9 1. () [1] [1] [2] [3] [3] [1] [1] [2] M. P. Do Carmo, Riemannian Geometry, Birkhäuser, [3] O Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, A ( ) itoken@math.nagoya-u.ac.jp : , II 3
10 1. ( ) 2. 3.,., 3.,,,.,.,,.,,.,,,,.,,.,,,,. 4.,.,,,., ,,. 6.,. 3,.,.,,.,,,. 7. [1] [2] () [3] Miles Reid Undergraduate Algebraic Geometry London Mathematical society 8. A ( ) y-ito@math.nagoya-u.ac.jp, 16:30 17:30 ( ),. 4
11 1. ( ) ,,., (S 1 ) n, R n,., Dym-McKean, Howe., R n GL n (R).,., Fulton-Harris.,,,.,,,,.,,. 4.,,,. 5.,,. 6.,. 3,. 7. [1] Dym, McKean, Fourier Series and Integrals [2] Fulton, Harris, Representation Theory-A First Course, Springer [3] Howe, On the role of the Heisenberg group in harmonic analysis (Project Euclid. Google Howe, role, Heisenberg..,, ( ) uzawa@math.nagoya-u.ac.jp. 5
12 1. ( ) 2. 3.,,,.,.,, ( ).,,.,.. [1][2], Morse( )...,.,.,,.,,.,,. 4..,,.. 5.., ,. 3,. 7. [1], [2], 8. A ( ) ohta@math.nagoya-u.ac.jp ,
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14 1. () , Cafe David 7. [1] J. Schultens, Introduction to 3-manifolds, Grad. Stud. Math. 151, Amer. Math. Soc., A ( ) tomomi@math.nagoya-u.ac.jp :00 15:00 (14 8
15 1. ( ) [1] ( ) gyoja@math.nagoya-u.ac.jp
16 1. ( ) 2. 3.,. C. E. Shannon A Mathematical Theory of Communication (1948 ) [1]. Neumann EDSAC (1949 ),.,.,,., , 2,.,. 5.,, 3, 3. II ( ). 6.,, (Lebesgue ).., 4 I, II ( ). 7. [1] C. E. Shannon W. Weaver, ( ),,, [2] C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, The University of Illinois Press, (), ( ) kubo@math.nagoya-u.ac.jp 13:30 14:30,. 10
17 1. () 2. 3.,,,,,.,,,,,,.,,. 4.,, [1].. 5.,. 3, 3. 6.,.,,. 7. [1] J.H., J.,,, 1995, (=Rational points on elliptic curves, Undergraduate Texts in Mathematics, Springer, 2010) 8. A ( ) (16:00-17:30) 11
18 1. ( ) 2. 3., , 1 2 X n + a 1 X n a n 1 X + a n (a 1,..., a n Z, n 1).,, Galois,, ζ L [2], 2, 2, [1]...., [1].,,., [2] 2010, [3]. [5],. [1], ,,, ,, 3 ( ).,., [1]., 2012, 2014,, [2] [1]. 5.,,. 6.,,,..,. 7. [1] [2] [3] ( ) [4] ( ) [5] ) 8. A ( ) hiroshis@math.nagoya-u.ac.jp 16:30 17:30, 16:00 17:00,. 12
19 1. () 2. 3.,.,,..,,,,,,,,,., [4],., [4] [5]. Cohen Macaulay Gorenstein. [4, 5], [3] ( 1 ) [1]., Krull., [4, 5], [2]. 4.., [1] M. F. Atiyah; I. G. MacDonald, Introduction to Commutative Algebra, Westview Press, [2] W. Bruns; J. Herzog, Cohen Macaulay rings, Cambridge University Press, [3],,, [4],,, [5] H. Matsumura, Commutative ring theory, Second edition, Cambridge University Press, A ( ) takahashi@math.nagoya-u.ac.jp 16:30 17:
20 1. ( ) 2. 3.,.,,.,,,,.,,.,.,,,.,,.,, ,.,,. 5.. I. 6.,.,., I. 7. [1],,, ( ) naito@math.nagoya-u.ac.jp 15:00 16:00 14
21 1. () (),,,.,,,.,.,,.,.,, [5],.,,.,,,, ,,. 5.,,. 6..,,,. 7. [1] [ ], [2] J. E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag. [3], [4] W. Fulton, J. Harris Representation theory, Springer-Verlag [5]. 8. A ( ) hayashi@math.nagoya-u.ac.jp. 15
22 1. ( ) 2. ( ) 3.,,.,,,,,, Fourier.,,,, Fourier,.,,, Poisson-Laplace,, Sobolev,, Fourier.,,.,,,.,. 4.,,.. 5., I ( ), ( ). 6.,,,,,, Lebesgue, Fourier,,,. 7. [1], ( ),,, [2],,, [3] L.C. Evans, Partial Differential Equations, AMS, [4],,, [5], ( ),,, [6],, ( ),,, [7] L. Grafakos, Classical Fourier Analysis, Springer, ( ) hishida@math.nagoya-u.ac.jp 12:00 13:00 16
23 1. ( ) ( ),., [1]., [2]., [3]..,,. 4..,,.,. 5.. (. ) [1] ( ) [2] [3]. 8. A ( ) furusho@math.nagoya-u.ac.jp 27 12:00 13:00 17
24 1. ( ) 2. 3.,.,,,. L.,.,,,.,.,,.,. 4.,,, [1]. 5.,,. 6.,,.,.,,. 7. [1] COE 23, Math-for-Industry,, [2] Minking Eie, Topics in Number Theory, World Scientific, [3],,, ( ) kohjimat@math.nagoya-u.ac.jp. 18
25 1. () , 1. C n n C n,,,,,,,,,,,,, 2. 1/2,,,,,,,, I., II., III., IV., V., VI.,.. 4.,. 5.,,,. 6.,,. 7. [1] 1-3 [2] A ( ) minami@math.nagoya-u.ac.jp 12:00-13:00,. 19
26 1. () [1] [2] [3] Milnor 20 [4] 1 11 [5] 1 2 ) [1] [2] [3] J. Milnor, Topology from the Differentiable Viewpoint, Princeton Univ. Press [4] J. Milnor and J. Stasheff, Characteristic Classes, Princeton University Press. [5] Bott-Tu, Differential Forms in Algebraic Topology, GTM 82, Springer-Verlag ( ) moriyosi@math.nagoya-u.ac.jp 20
27 1. () ,,,,.,,., van der Waerden [1],.,,,.,,.,,. 4.,.,,,,.,. 5. III. 6.,,.,,,.,,. 7. [1] B.L. van der Waerden, Group Theory and Quantum Mechanics, Springer, [2] H. Weyl, The Theory of Groups and Quantum Mechanics, Dover, [3] J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press. [4] [5] Roman Zwicky, Symmetries of Quantum Mechanics rzwicky2/soqm/romansoqm 2015.pdf [6] P. Woit, Quantum Theory, Groups and Representations woit/qm/qmbook.pdf Weyl von Neumann.. [4],. 8. A ( ) 21
28 1. ( ) [1] 4. 5., 6. [1] [1] [2] 7. [1],,, [2],,, A ( ) noby@math.nagoya-u.ac.jp 13:45 14:45 22
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