2015 Course Description of Graduate Seminars ( )
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- ゆきひら こうい
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1 2015 Course Description of Graduate Seminars ( )
2 ( ) 17: ( ) 17: ( ) 3 2 ( ) 4 A A. ( ) 2 (1) 1 2 (2) (3) 2 (4) 1 5 (5) (2), (3) (6),,.
3 ( 1) Jacques Garrigue ( 1) ( 2) Lars Hesselholt ( 1) i
4
5 1. ( ) [1]. [2] [3] [4]. [5], [6].,,, [7]., [8],.,,,. [1],, [2], [3] L. Ryder, Quantum Field Theory, (2nd ed.) Cambridge Univ. Press [4],, [5],, [6] K. Becker, M. Becker and M. Schwarz, String Theory and M-theory: A Modern Introduction, Cambridge Univ. Press 2007 [7] S. Katz, Enumerative Geometry and String Theory, AMS 2006 [8] V. Kac and A. Raina, Bombay Lectures on Highest weight representations of infinite dimensional Lie algebras, World Scientific [9],, [10],,, [11],, I, [12], I, [13],,, [14],, [15],, [16],,,, [17] S. Weinberg, Gravitation and Cosmology, John Wiley & Sons 1972 [18],,, ( ) awata@math.nagoya-u.ac.jp 2:45 3:45 1
6 1. ( ) ,.,,,.,.,.,.,. [1] [2],,.,. [3] [4],.,,.,. [1],,,, [2] G. B. Folland, Harmonic analysis in phase space, Annals of Mathematics Studies 122, Princeton University Press, [3] J. Faraut, S. Kaneyuki, A. Korányi, Q.-K. Lu, R. Guy, Analysis and geometry on complex homogeneous domains, Progress in Mathematics 185, Birkhäuser, [4] R. S. Doran, C. C. Moore, R. J. Zimmer (editors), Group representations, Ergodic theory, and Mathematics Physics, Contemporary mathematics 449, American Mathematical Society, ( ) hideyuki@math.nagoya-u.ac.jp 12:00 13: Cafe David ( 1 2 ),. . 2
7 1. ( ) ] [1] [2] [3], [4] Part II, [3] [1] [5] [6] [7] [8] [9] 3 [1] [2] R. C. Penner, Decorated Teichmüller Theory, European Mathematical Society, [3] M. Bekka and M. Mayer, Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces, Cambridge University Press, [4] B. Farb and D. Margalit, A Primer of Mapping Class Groups, Princeton University Press, [5] [6] V. V. Prasolov and A. B. Sossinsky, Knots, Links, Braids and 3-Manifolds, American Mathematical Society, [7] D. Rolfsen, Knots and Links, American Mathematical Society, [8] [9] A ( ) itoken@math.nagoya-u.ac.jp 12:00 13:30 (Cafe David) 3
8 1. ( ) , [1],,, [2],,, [3] J.P. [4] W.Fulton, Introduction to Toric Varieties, Princeton University Press. [5] D.A. Cox, J.B.Little & H.K.Schenck, Toric Varieties (Graduate Studies in Mathematics), [6] A.Craw & M.Reid, How to calculate A-Hilb C 3, Semin. Confr. vol.6 Soc. Math. France, 2002, [7] S.Cautis, A.Craw & T.Logvinenko, Derived Reid s recipe for abelian subgroups of SL3(C), arxiv: [8] T.Bridgeland, A.King and M.Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14(2001), A ( ) y-ito@math.nagoya-u.ac.jp 13:30 14:30 4
9 1. ( ) ,, Auslander- Reiten,. Auslander [1],.,.. (quiver) (Gabriel) Cohen-Macaulay (Auslander-Reiten),.,,.., [4].,, [5], Cohen-Macaulay [6], [7],.,.,, [2,3]. [1] I. Reiten, S. O. Smalo, O. Solberg: Selected works of Maurice Auslander. Part 1,2, American Mathematical Society, Providence, RI, [2], :,, [3] :,, [4] I. Assem, D. Simson, A. Skowronski: Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory. London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge, [5] D. Happel: Triangulated categories in the representation theory of finite-dimensional algebras. London Mathematical Society Lecture Note Series, 119. Cambridge University Press, Cambridge, [6] Y. Yoshino: Cohen-Macaulay modules over Cohen-Macaulay rings. London Mathematical Society Lecture Note Series, 146. Cambridge University Press, Cambridge, [7] B. Keller: Cluster algebras, quiver representations and triangulated categories, arxiv: ( ) iyama@math.nagoya-u.ac.jp 5
10 1. ( ) 2.,, ,,.,, Fulton, Harris Representation Theory: a first course Springer, Persi Diaconis Group Representations in Probability and Statistics MacKay Information Theory, Inference, and Learning Algorithms. 2 3,, 3, [1],, [2] Fulton, Harris, Representation Theory: A First Course, Springer [3] Persi Diaconis, Group Representations in Probability and Statistics, Inst of Mathematical Statistic, [4] David J.C. MacKay, Inference theory, Inference, and Learning Algorithms, Cambridge University Press, 2003 [5], :,, 2008 [6], : R & WinBUGS,, 2008, pdf, ( ) uzawa@math.nagoya-u.ac.jp 12:00 13:00. 12/24 12:30 14:00, 12/25 12:00 13:00, 1/9 12:00 13:00, 1/10 13:00 14:00 6
11 1. ( ) 2. 3.,,..,,,,,,.,. Differential analysis on complex manifolds (third edition) R.O. Wells, Jr. GTM, ( ) ( ) ohsawa@math.nagoya-u.ac.jp 16:00 17:00 7
12 1. ( ) Floer M1M2 [1] furuta/advice.pdf [2], [3], [4] 5 3 [1] M. Audin and M. Damian, Morse theory and Floer homology, Springer. [2] Y. Manin, Frobenius Manifolds, Quantum Cohomology and Moduli Spaces, A.M.S. [3] H. Hofer and E. Zehnder, Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser. [4],,. A ( ) ohta@math.nagoya-u.ac.jp 12:00 13:
13 1. ( ) ,.,.,,,,,.,,.,.,. M2.,.,,,.,,, 2006 A ( ) ohira@math.nagoya-u.ac.jp 16:30 18:00 9
14 1. ( ) Young [4], [5], [6] 3 [1] [1] R. P. Stanley, Enumerative Combinatorics I, 2nd Edition, Cambridge Univ. Press, [2] R. P. Stanley, Enumerative Combinatorics II, Cambridge Univ. Press, [3] M. Aigner, A Course in Enumeration, Springer, [4] D. M. Bressoud, Proofs and Confirmations : The Story of the Alternating Sign Matrix Conjecture, Cambridge Univ. Press, [5], 1995 [6] 2012 [7] P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, [8] G. E. Andrews, The Theory of Partitions, Cambridge Univ. Press, [9] New Perspectives in Algebraic Combinatorics, edited by L. J. Billera, A. Björner, C. Greene, R. Simion, and R. P. Stanley, Cambridge Univ. Press, A ( ) okada@math.nagoya-u.ac.jp 12:00 13:
15 1. ( ) ,,.,, Klein-Gordon, Schrödinger, ( ), Einstein ( ), KdV ( ), Benjamin-Ono ( ), KP ( ), Zakharov ( Langmuir ), Maxwell-Schrödinger ( ), Landau-Lifschitz ( ).,,,,,.,,,.,,. 1, 2. 1 [1], [2], [3] 1,.,,. [1] 18, (2013). [2] H. Bahouri, J.-Y. Chemin, R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften 343, Springer (2011). [3] L. Grafakos, Classical Fourier Analysis, 2nd Ed., Graduate Text in Math. 249, Springer, [4] L. C. Evans, Partial Differential Equations, 2nd Ed., GSM 19, Amer. Math. Soc. (2010). [5] T. Tao, Nonlinear Dispersive Equations, Local and Global Analysis, CBMS 106, Amer. Math. Soc. (2006). [6] S. Alinhac, Geometric Analysis of Hyperbolic Differential Equations: An Introduction, London Math. Soc. Lecture Note Ser. 374, Cambridge Univ. Press (2010) ( ) jkato@math.nagoya-u.ac.jp 12:00 13:30, 2. 11
16 1. Jacques Garrigue ( ) [1] [2] 1 [1] Jean Gallier, Logic for computer science. Wiley, Online edition: jean/gbooks/logic.html [2] John Harrison, Handbook of practical logic and automated reasoning. Cambridge University Press, [3],,, ( ) garrigue@math.nagoya-u.ac.jp 12:00 13:
17 1. ( ) [1] [2] [3] M2 [1],,, [2],,, [3],,, A ( ) kanno@math.nagoya-u.ac.jp 12:00 13:00 Cafe David 12 25, ,7,8 13
18 1. ( ) KdV., (1) KdV (2) (3) (4) (5) (6) C, C++, Fortran, [1],, [2],, [3], [4],, [5],,,, ( ) kimura@math.nagoya-u.ac.jp. 14
19 1. ( ) [1] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer. [2] J. -P. Serre, ( ) gyoja@math.nagoya-u.ac.jp 15
20 1. ( ) ,,.,,,. (,.), 1948 C. E. Shanon A Mathematical Theory of Communication., ( ) D. Huffman ( ) Huffuman. 1960,, 1977, 1978 J. Ziv A. Lempel LZ77/LZ78..,,. (Huffman, )., ( ). [2], 2..,.., 2. (.) [1] Claude E. Shannon and Warren Weaver, The Mathematical Theory of Communication, Univ. of Illinois Press, ( ( ),,, 2009.) [2] Te Sun Han and Kingo Kobayashi, Mathematics of Information and Coding, Trans. of Math. Mono. 203, AMS Providence, [3] Thomas M. Cover and Joy. A. Thomas, Elements of Information Theory 2nd ed., Wiley Interscience, ( ( ),,, 2012.) ( ) kubo@math.nagoya-u.ac.jp 12:30 13:30 ( ) 16
21 1. ( ) [1] [2] [3] Donaldson-Tian-Yau 2012 Chen-Donaldson-Sun Tian Hamilton-Tian Partial C Chen-Wang Potentrial Donaldson-Tian-Yau Berman [1] Monge-Ampère [2] Perelman Kähler-Ricci flow [3] Donalsdon-Tian-Yau [1] V. Guedj (Ed.), Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics, Springer Lecture Notes in Mathematics 2038 (2012). [2] S. Boucksom, P. Eyssidieux, V. Guedj (Eds.), An Introduction to the Kähler-Ricci Flow, (2012). (Online ) [3] D. D ly, Complex Analytic and Differential Geometry, (2012). (Online ) ( ) ryoichi@math.nagoya-u.ac.jp 17
22 1. ( ) [3] Beauville [1] [2] 2 3 [2] [1] A. Beauville, Complex Algebraic Surfaces, London Mathematical Society. [2] [3] K. Kodaira A ( ) kondo@math.nagoya-u.ac.jp 16:30 17:30 18
23 1. ( ) ,,,,,,.,,, [3], [1],,,. [4]. 2 3,. [1],,, [2], [3], [3], [4], [5].,. 3..,,. [1] Mumford-Oda, chapter 1-6, chapter 7-, internet, office, Café David CD, (, CD Café David ). [2] George R. Kempf, Algebraic varieties, Cambridge Universiry Press, London Mathematical Society lecture note series 172. [3] D. Mumford, The Red book of varieties and schemes, Lecture Notes in mathematics 1358, Springer verlag (, D. ;,, ( ; 19 ). [4] D. Mumford, Algebraic geometry I : complex projective varieties, Springer-Verlag, Grundlehren der mathematischen Wissenschaften 221. [5] I. R. Shafarevich, Basic Algebraic Geomtery, vol. 1, 2 Springer verlag. A ( ) saito@math.nagoya-u.ac.jp Café David. A
24 1. ( ) ,,.,.,,.. Einstein, (, ), Einstein. (,,, ), ( 4 ).,,.,,,. [1] R. M. Wald, General Relativity, Chicago Univ. Press. [2] S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press. [3], [4],, [5], SGC, A ( ) shiromizu@math.nagoya-u.ac.jp 12:00 13:
25 1. ( ) [1] 2006 [2] G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press 1995 [3] L. Grafakos, Classical Fourier Analysis, Springer 2008 [4] L. C. Evans, Partial Differential Equations, 2nd Ed., American Mathematical Society ( ) sugimoto@math.nagoya-u.ac.jp 11:00 12:00, 21
26 1. ( ) , , 1 X n + a 1 X n a n 1 X + a n (a 1,..., a n Z, n 1).,.,,.,,,, 2009,, KANT/KASH PARI/GP,,,,. 2014, [1], ,,. 1 2, , , , 11., , [1] ( ), 1.5 3,, 2,.,.,.,,.,,. [1], I,, [2], II,, [3] J.,,, A ( ) hiroshis@math.nagoya-u.ac.jp 16:00 17:00 ( 16:00 17:00,. ) 22
27 1. ( ) 2. 3., Noether Cohen Macaulay, Cohen Macaulay Cohen Macaulay., [1, 5], [2, 3, 4, 7]..,.,.., [6] IV 4. [1] W. Bruns; J. Herzog, Cohen Macaulay rings, Revised edition, Cambridge University Press, [2] L. W. Christensen, Gorenstein dimensions, Springer Verlag, [3] E. G. Evans; P. Griffith, Syzygies, Cambridge University Press, [4] G. J. Leuschke; R. Wiegand, Cohen-Macaulay representations, American Mathematical Society, [5] H. Matsumura, Commutative ring theory, Second edition, Cambridge University Press, [6],,, [7] Y. Yoshino, Cohen Macaulay modules over Cohen Macaulay rings, Cambridge University Press, A ( ) takahashi@math.nagoya-u.ac.jp 16:30 17:30 23
28 1. ( ) 2. 3.,, Titchmarsh: The theory of the Riemann-zeta function, mean value theorem 2 [1] Chapter I Chapter IV,, 3 [1] E. C. Titchmarsh, The theory of the Riemann-zeta function, Clarendon Press, Oxford. [2] Karatsuba, Voronin, The Riemann-zeta function, ( ) tangawa@math.nagoya-u.ac.jp 12:00 13:00 : 24
29 1. ( ) ,,.,.. 1, ( 0 )? 2,?,? 3,,? 4,? 1 [1]. Fourier,. Part I., Part II.,, 2000 Schrödinger [2],.., , [1] Part I Part II ( ). ( ). Part I,. [3] [4]. [1] Rafael Iório and Valeria de Magalhães Iorio, Fourier Analysis and Partial Differential Equations (Cambridge Studies in Advanced Mathematics), Cambridge Univ. Press. [2] T. Cazenave, Semilinear Schrödinger equations, Amer. Math. Soc. [3],,. [4],, ( ) tsugawa@math.nagoya-u.ac.jp 12:00 13:30( ). ( ) . 25
30 1. ( ) ,,...,.,,,.,,,,.,,,., 1 2, 1, 2,,,,., 1,., 2 3.,,,,.,, [1], [2], [3].,, [5].,, [6].,, [4].,,,,.,. [1] S. Krantz, A Panorama of Harmonic Analysis, The Mathematical Association of America. [2] T. Hytönen, Weighted Norm Inequalities, 52pp., Lecture Note available on Web. [3] H. Tanabe, Functional Analytic Methods for Partial Differential Eqautions, CRC Press. [4] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer. [5] M. Giaquinta, L. Martinazzi, An introduction to the regularity theory for elliptic system, harmonic maps and minimal graphs, Edizioni Della Normale. [6] A. McIntosh, Operator Theory - Spectra and Functional Calculi, 77pp., Lecture Note available on Web. A ( ) yutaka.terasawa@gmail.com, yutaka@math.nagoya-u.ac.jp 14:00 15:00 at my office (A-457), 12:00 13:00 at Cafe David.,. 26
31 1. ( ) ,.,,,,,.,,,.,,., 1.5,.,.,,.,.,. [1] T.Sunada, Topological Crystallography, Springer, [2],,, [3] E.Hairer, C.Lubich, G.Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, 2004 [4] A.N.Langville, C.D.Mayer, Google s PageRank and Beyond, The science of search engine rankings, Princeton University Press, [5] R.Séroul, Programming for Mathematicians, Springer, [6] D.Marsh, Applied Geometry of Computer Graphics and CAD, second edition, Springer, ( ) naito@math.nagoya-u.ac.jp 14:00 15:00. 27
32 1. ( ) ,.,,,,.,., ( ) nagao@math.nagoya-u.ac.jp 12:00-13:00 12:00-13:00 28
33 1. ( ) (cluster algebra). Fomin-Zelevinsky [1]. arxiv(preprint ). S. Fomin and A. Zelevinsky, Cluster algebras I: Foundations, J. Amer. Math. Soc. 15 (2002) S. Fomin and A. Zelevinsky, Y-systems and generalized associahedra, Ann. Math. 158 (2003), S. Fomin and A. Zelevinsky, Cluster algebras II: Finite type classification, Invent. Math. 154 (2003) A. Berenstein, S. Fomin and A. Zelevinsky, Cluster algebras III: Upper bounds, Duke Math. J. 126 (2005) S. Fomin and A. Zelevinsky, Cluster algebras IV: Coefficients, Compos. Math. 143 (2007) ,,. Coxeter Weyl. M, [2]. [1] M. Gekhtman, M. Shapiro, A. Vainshtein, Cluster algebras and Poisson geometry, Amer. Math. Soc, [2] H. E. Humphreys, Reflection groups and Coveter groups, Cambridge studies in advanced mathematics, Cambridge Univ. Press, ( ) nakanisi@math.nagoya-u.ac.jp 12:00-13:00. 29
34 1. ( ) 2. 3.,...,., 2,,,,., (, ), [5],., ([1, 3]),,., [5, 4]... (,, ) [2, 6] (, ) [2, 7] ( ) [8, 9],,.,... [1] J. W. Cannon, W. J.Floyd, R. Kenyon, W. R. Parry, Hyperbolic geometry, Flavors of Geometry, MSRI Publ. 31, [2] R. Benedetti and C. Petronio, Lectures on hyperbolic geometry, Universitext, Springer, [3],,, [4] S. Wolpert, Families of Riemann surfaces and Weil-Petersson geometry, [5] J. Dorfmeister, J. Inoguchi and S. Kobayashi, Constant mean curvature surfaces in hyperbolic 3-space via loop groups, J. Reine Angew. Math. 686 (2014), [6] W. Thurston, The geometry and topology of 3-manifold, Lecture note at Princeton Univ., 1978/79. [7] G. Besson, Calabi-Weil infinitesimal rigidity, Sémin. Congr. 18, , Soc. Math. France, Paris, [8],,, [9] J. W. Cannon, Geometric Group Theory, in Handbook of Geometric Topology, Elsevier, 2002, A ( ) nayatani@math.nagoya-u.ac.jp 12:00 13:00, 2 ( ).,. 30
35 1. ( ) ,.,,. ( ),,,,,,.,,., ( ),.,,,. 2.,.,, [2], [3],. [1].,,,. 45 1,.,,.,,,. 3. [1] 11. [1], [2] J. Hong and S.-J. Kang, Introduction to Quantum Groups and Crystal Bases, Amer. Math. Soc., [3], Mathematical Society A ( ) hayashi@math.nagoya-u.ac.jp 16:30 17:30., . 31
36 1. ( ) [1] Michael A. Nielsen, and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2000) [2] M. Hayashi, Quantum Information: An Introduction, Springer-Verlag, 2006 [3] M. Ohya and D. Petz, Quantum Entropy and its Use, Springer-Verlag, TMP-series (1993). [4],, (2012) (, Introduction to Quantum Information Science, Graduate Texts in Physics, Springer, (2014)) [5] (2014). [6] A ( ) masahito@math.nagoya-u.ac.jp 15:00-17:00, 32
37 1. ( ) (1) 2 (2) (3) (4) Navier-Stokes /,. 2 (1)(2)(3) (4), 1 (1)(2)(3), (4) (1) (2),(3).,., 2.,,.,.,. Sobolev.,.,,,, Lebesgue, Fourier,. [1] L. C. Evans, Partial Differential Equations, Amer. Math. Soc., [2] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, [3] -,,, [4] -,,, [5] H. Sohr, The Navier-Stokes Equations, An Elementary Functional Analytic Approach, Birkhäuser, [6] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Second Edition, Springer, [7] P. G. Lemarie-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman and Hall/CRC, ( ) hishida@math.nagoya-u.ac.jp 16:30 17:
38 1. ( ) 2. Algebraic Graph Theory 3.,. ( girth 5 r-regular Moore graph r {2, 3, 7, 57},.) [3], ( ). ( [2].),,. 3,. [3] Ch.1 7, [3], Ch.8,..,.. 1 ( 3 ),.,, [1, 2].. [1] J.A. Bondy and U.S.R. Murty, Graph Theory, Springer. [2] G. Chartrand, L. Lesniak, and P. Zhang, Graphs and Digraphs, CRC Press. [3] C. Godsil and G. Royle, Algebraic Graph Theory, Springer ( ) futaba@math.nagoya-u.ac.jp 12:00 13:00 ( ),,.,. 34
39 1. ( ) ,,.. [1] [2].. [3],.,, [4]. [5]., [6] Vassiliev..,, [7],...,. 1,.,.,.,.,.. [8],,. [1] Quantum groups and knot invariants, C.Kassel, M.Rosso, V.Turaev, Panoramas et Synthèses, 5. Société Mathématique de France, [2] Quantum invariants. A study of knots, 3-manifolds, and their sets, T.Ohtsuki, Series on Knots and Everything, 29. World Scientific Publishing Co., Inc., River Edge, NJ, [3],,. [4] Lectures on quantum groups, P.Etingof, O.Schiffmann, International Press. [5] Déformation, quantification, théorie de Lie, A.Cattaneo, B.Keller, C.Torossian, A.Bruguières, Panoramas et Synthèses, 20. [6] Introduction to Vassiliev knot invariants, S.Chmutov, S.Duzhin, J.Mostovoy, Cambridge University Press, Cambridge, [7] Topics in Galois theory, J.P.Serre, Research Notes in Mathematics, 1. [8]. A ( ) furusho@math.nagoya-u.ac.jp 26 12:00-13:00 35
40 1. ( ) 2. L 3., L,, L, L, L...,, L,,. 3 4.,. L,,, L,...,. [1] T.M.Apostol, Introduction to Analytic Number Theory, Springer. [2],,,, ( ) kohjimat@math.nagoya-u.ac.jp 12:00 13:
41 1. ( ) ,.,,,,,.,,.,,,,...,, [1], I II III,, [2],,, A ( ) minami@math.nagoya-u.ac.jp 12:00-13:00.,. 37
42 1. ( ) 2. K (Characteristic class) K - (Atiyah-Singer) K Atiyah-Singer 1) - (Stiefel-Whitney) (Chern) (Pontrjagin) 2) K [4] [1] J. Milnor, Characteristic classes, Princeton University Press. [2] [3] Bott-Tu, Differential Forms in Algebraic Topology, GTM 82, Springer-Verlag, [4] Wegge-Olsen, K-theory and C -algebras, Oxford University Press [5] J. Dupont, Curvature and characteristic classes, LNM Vol. 640, Springer-Verlag. [6] P. Shanahan, The Atiyah-Singer Index Theorem, LNM Vol. 638, Springer-Verlag. [7] J. Roe, Elliptic operators, topology and asymptotic methods. Longman ( ) moriyosi@math.nagoya-u.ac.jp 11:30 12:30 38
43 1. ( ) 2. 3.,,.,,.,.,,,., [1], 1.,,,,., TeX,.,.,.,.,, [Reed-Simon], [Rudin].,. [1] V.S. Varadarajan, Geometry of Quantum Theory, Springer, [2] Stanley P. Gudder, Quantum Probability, Academic Press, [3] M. Reed and B. Simon, Functional Analysis, Vol. 1, Academic Press, [4] W. Rudin, Functional Analysis, MacGraw-Hill, [5],,, A ( ) yamagami@math.nagoya-u.ac.jp ( ) 39
44 1. ( ) 2. Brown 3. 3 [1,2] Brown [4], [3]) ( ) [5] [1] * Möters, P.; Peres, Y. Brownian Motion Cambridge University Press (2010). [2] * Revuz, D.; Yor, M. : Continuous Martingales and Brownian Motion, 3rd ed. Springer Verlag, Berlin, (1998). [3] * Yoshida, N.: A short course in probability ( noby/pdf/prob all.pdf) [4] : (2006) [5] : (2012) A ( ) noby@math.nagoya-u.ac.jp 14:30 15:30 40
2016 Course Description of Undergraduate Seminars (2015 12 16 ) 2016 12 16 ( ) 13:00 15:00 12 16 ( ) 1 21 ( ) 1 13 ( ) 17:00 1 14 ( ) 12:00 1 21 ( ) 15:00 1 27 ( ) 13:00 14:00 2 1 ( ) 17:00 2 3 ( ) 12
2014 Course Description of Graduate Seminars ( )
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