141 Formal Group Names: A Comprehensive Guide to Formal Group Theory and Applications

This comprehensive guide delves into the intricacies of formal group theory and its diverse applications, providing a thorough exploration of 141 formal group names. From the fundamental concepts to advanced applications, this guide serves as a valuable resource for mathematicians, physicists, and researchers seeking a deeper understanding of formal group theory.

1. Formal Groups

1. Formal Group
2. Formal Group Law
3. Formal Group Homomorphism
4. Formal Group Isomorphism
5. Formal Group Endomorphism
6. Formal Group Automorphism
7. Formal Group Scheme
8. Formal Group of Finite Height
9. Formal Group of Infinite Height
10. Formal Group of Dimension 1
11. Formal Group of Dimension 2
12. Formal Group of Dimension 3
13. Formal Group of Dimension 4
14. Formal Group of Dimension 5

    2. Classification of Formal Groups

15. Dieudonné Classification
16. Witt Classification
17. Serre Classification
18. Grothendieck Classification
19. Mumford Classification
20. Deligne Classification
21. Illusie Classification
22. Fontaine Classification
23. Kato Classification
24. Mazur Classification
25. Tate Classification
26. Faltings Classification
27. Chai Classification
28. Kedlaya Classification
29. Liu Classification
30. Yuan Classification

    3. Applications of Formal Groups

31. Iwasawa Theory
32. Galois Cohomology
33. Elliptic Curves
34. Modular Forms
35. Number Theory
36. Algebraic Geometry
37. Topology
38. Physics
39. Quantum Field Theory
40. String Theory
41. Cosmology
42. Black Holes
43. Dark Matter
44. Dark Energy
45. Quantum Gravity
46. Unified Field Theory
47. Grand Unified Theory
48. Theory of Everything

    4. Notable Formal Groups

49. The Additive Formal Group
50. The Multiplicative Formal Group
51. The Lubin-Tate Formal Group
52. The Drinfeld Formal Group
53. The Elliptic Curve Formal Group
54. The Modular Formal Group
55. The Tate Formal Group
56. The Fontaine Formal Group
57. The Kato Formal Group
58. The Mazur Formal Group
59. The Faltings Formal Group
60. The Chai Formal Group
61. The Kedlaya Formal Group
62. The Liu Formal Group
63. The Yuan Formal Group

    5. Historical Development of Formal Group Theory

64. Évariste Galois
65. Niels Henrik Abel
66. Carl Friedrich Gauss
67. Bernhard Riemann
68. Henri Poincaré
69. David Hilbert
70. Emmy Noether
71. Hermann Weyl
72. André Weil
73. Jean-Pierre Serre
74. Alexander Grothendieck
75. Robert Langlands
76. Pierre Deligne
77. Jean-Marc Fontaine
78. Kazuya Kato
79. Barry Mazur
80. Gerd Faltings
81. Ching-Li Chai
82. Kiran Kedlaya
83. Qing Liu
84. Xinyi Yuan

    6. Open Problems in Formal Group Theory

85. The Hodge Conjecture
86. The Riemann Hypothesis
87. The Birch and Swinnerton-Dyer Conjecture
88. The Langlands Program
89. The Fontaine-Mazur Conjecture
90. The Kato Conjecture
91. The Mazur-Tate Conjecture
92. The Faltings Conjecture
93. The Chai Conjecture
94. The Kedlaya Conjecture
95. The Liu Conjecture
96. The Yuan Conjecture

    7. Resources for Further Study

97. Books on Formal Group Theory
98. Articles on Formal Group Theory
99. Conferences on Formal Group Theory
100. Online Resources on Formal Group Theory
101. Software for Formal Group Theory
102. Databases on Formal Group Theory
103. Mailing Lists on Formal Group Theory
104. News Groups on Formal Group Theory
105. Blogs on Formal Group Theory
106. Podcasts on Formal Group Theory
107. Videos on Formal Group Theory

     8. Conclusion

108. The Significance of Formal Group Theory
109. The Future of Formal Group Theory
110. Challenges and Opportunities in Formal Group Theory
111. The Interdisciplinary Nature of Formal Group Theory
112. The Beauty and Elegance of Formal Group Theory

     9. Appendix

113. Glossary of Terms
114. Bibliography
115. Index
116. About the Author
117. Acknowledgments

     10. List of Figures

118. Figure 1: The Lubin-Tate Formal Group
119. Figure 2: The Drinfeld Formal Group
120. Figure 3: The Elliptic Curve Formal Group
121. Figure 4: The Modular Formal Group
122. Figure 5: The Tate Formal Group
123. Figure 6: The Fontaine Formal Group
124. Figure 7: The Kato Formal Group
125. Figure 8: The Mazur Formal Group
126. Figure 9: The Faltings Formal Group
127. Figure 10: The Chai Formal Group
128. Figure 11: The Kedlaya Formal Group
129. Figure 12: The Liu Formal Group
130. Figure 13: The Yuan Formal Group

     11. List of Tables

131. Table 1: Classification of Formal Groups
132. Table 2: Applications of Formal Groups
133. Table 3: Notable Formal Groups
134. Table 4: Historical Development of Formal Group Theory
135. Table 5: Open Problems in Formal Group Theory
136. Table 6: Resources for Further Study
137. Table 7: List of Figures
138. Table 8: List of Tables

     12. Index

139. Index of Names
140. Index of Terms
141. Index of Symbols