## Research Project Ideas on Algebraic k-theory Math

1. HOMOLOGICAL STABILITY MINICOURSE LECTURE 1: THE HOMOLOGY OF SYMMETRIC GROUPS

2. On a deformation theory of finite dimensional modules over repetitive algebras

3. Connectedness in Tropical Combinatorics

4. Galois module structure of the units modulo of cyclic extensions of degree

5. Graph Schemes, Graph Series, and Modularity

6. TODAY, I LEARNED…

7. The singularity and cosingularity categories of for groups with cyclic Sylow -subgroups

8. On the Chow groups of Plücker hypersurfaces in Grassmannians

9. Existential rank and essential dimension of diophantine sets

10. ON TRACIAL Z-STABILITY OF SIMPLE NON-UNITAL C-ALGEBRAS

11. Nuclear dimension of crossed products associated to partial dynamical systems

12. A Class of Polynomial Semirings which are not B-Type Stable

13. The Fermi gerbe of Weyl semimetals

14. A Note on Invariant Basis Number and Types for Strongly Graded Rings

15. Complete curves in the moduli space of polarized K3 surfaces and hyper-K\” ahler manifolds

16. On homology of the $ MSU $ spectrum

17. Sheaves of modules on atomic sites and discrete representations of topological groups

18. Frobenii on Morava -theoretical quantum groups

19. Common physical theory for quantum/classical particles in complex vector space

20. Combinatorics of injective words for Temperley-Lieb algebra

21. Springer motives

22. A dichotomy for simple self-similar graph C⁎-algebras

23. Real motivic and ‐equivariant Mahowald invariants

24. Monopole Floer homology and integral twisted cohomology

25. Absolute Mechanics

26. Ramified class field theory and duality over finite fields

27. Algebraic spectral theory and Serre multiplicity formula

28. Geometry and physics: where are we going?

29. On localization for cubical higher Chow groups

30. Hom-pre-Malcev and Hom-M-Dendriform algebras

31. Albanese Kernel of the Product of Curves Over A p-adic Field

32. Hereditary cotorsion pairs and silting subcategories in extriangulated categories

33. Non-simple Purely Infinite Steinberg Algebras with Applications to Kumjian–Pask Algebras

34. On the distribution of prime divisors in Krull monoid algebras

35. 21st Century planar field emission theory and its role in vacuum breakdown science

36. Non-Trivial, Left-Covariant, Continuously Closed Paths over Lines

37. K-theoretic Hall algebras of quivers with potential as Hopf algebras

38. Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

39. Leavitt path algebras of labelled graphs

40. Supergroup Gauge Theory

41. Hodge numbers are not derived invariants in positive characteristic

42. Finiteness properties of automorphism spaces of manifolds with finite fundamental group

43. Renormalised singular stochastic PDEs

44. The Mahler measure of a three-variable family and an application to the Boyd–Lawton formula

45. Nice group structure on the elementary orbit space of unimodular rows

46. On BiHom-associative dialgebras

47. Overgroups of subsystem subgroups in exceptional groups: inside a sandwich

48. Representation Theory of Quivers and Finite Dimensional Algebras

49. ON THE GORENSTEIN COHOMOLOGICAL DIMENSION OF GROUP EXTENSIONS

50. Ambidexterity and height

51. Donaldson–Thomas invariants of threefold flops

52. Completion of skew completable unimodular rows

53. Higher depth mock theta functions and q-hypergeometric series

54. Structure to polynomial factors in orthogonal calculus

55. Switching Spinless and Spinful Topological Phases with Projective Symmetry

56. Lifting properties of formal triangular matrix rings

57. An operadic approach to substitution in Lie-Butcher series

58. Rohlin Actions of Finite Groups on the Razak–Jacelon Algebra

59. Koszul algebras and quadratic duals in Galois cohomology

60. x1. Vvedenie

61. The R -Matrix of the Quantum Toroidal Algebra U q , t ( gl …

62. Generalized Graph Manifolds, Residually Finiteness, and the Singer Conjecture

63. Strongly Gorenstein-projective Quiver Representations

64. Spherical Tropicalization

65. Gabriel–Zisman Cohomology and Spectral Sequences

66. Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras

67. A characteristic map for the holonomy groupoid of a foliation

68. Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

69. On adjoint Bloch–Kato Selmer groups and adjoint -adic -functions for

70. LIE SOLVABLE LEAVITT PATH ALGEBRAS

71. On graded primitive leavitt path algebras

72. Crystallographic interacting topological phases and equivariant cohomology: to assume or not to assume

73. Rota-Baxter operators on cocommutative Hopf algebras

74. Hodge decomposition of string topology

75. Right-angled Artin groups and enhanced Koszul properties

76. Necessary conditions for the existence of Morita Contexts in the bicategory of Landau-Ginzburg Models

77. Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature

78. On finite dimensionality of Chow groups

79. Euler characteristics of Brill-Noether varieties

80. A proof of the Extended Delta Conjecture

81. Genera Of Integer Representations And The Lyndon-Hochschild-Serre Spectral Sequence

82. The Filtered Circle

83. Paschke duality and assembly maps

84. Vertical Vafa–Witten invariants

85. Topological Lattice Defects by Grupoid Methods and Kasparov’s -Theory

86. On Problems in Arithmetic Representation Theory

87. The second stable homotopy groups of motivic spheres

88. On Lie algebroid over algebraic spaces

89. ‘Real’gerbes and Dirac cones of topological insulators

90. PELUANG MENGHILIRKAN MATEMATIKA MELALUI RISET MATEMATIKA: STUDI KASUS MATEMATIKA KOMPUTASI PADA DESAIN MOTIF BATIK FRAKTAL …

91. A teoria algébrica de formas quadráticas aplicada a uma disputa entre dois orixás

92. Quantifier elimination for quasi-real closed fields

93. Topological Modular Forms and Quantum Field Theory

Algebraic k-theory Research Topics