Research Topics Arithmetical algebraic geometry

By Prof. Fazal Rehman Shamil
Last modified on May 30th, 2022

Research Area/ Research Interest: Arithmetical algebraic geometry

Research Paper Topics for: Masters and PhD Thesis and publication

  1. Point-Counting and the Zilber–Pink Conjecture
  2. Algorithmic aspects of arithmetical structures
  3. Fermat and Descartes in Light of Premodern Algebra and Viète
  4. Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction
  5.  Zero-cycle groups on algebraic varieties
  6.  Fractional Thermoentropy Spaces of Topological Quantum Fields
  7. Generalizations of Alladi’s formula for arithmetical semigroups
  8. A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra
  9. On the non-archimedean Monge-Amp\ere equation in mixed characteristic
  10. Arithmetical structures on dominated polynomials
  11. The matrix taxonomy of finitely complete categories
  12. Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize
  13.  Fractional Thermoentropy Spaces of Large Scale Systems
  14. Groebner fan and embedded resolutions of ideals on toric varieties
  15. Curves in projective spaces: questions and remarks
  16. Finiteness theorems for complements of large divisors
  17. New constructions of entanglement-assisted quantum codes
  18. Configurations of eigenpoints
  19. Axiomatizing the existential theory of Fp ((t))
  20. Upper bounds for regularity of radicals of ideals and arithmetic degrees
  21. On the description of identifiable quartics
  22.  Notes of Everything
  23.  Reconstructing curves from their Hodge classes
  24. Noncommutative Riemann hypothesis
  25.  On the Tightness of Semidefinite Relaxations for Rotation Estimation
  26. Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications
  27. The Case for the Irreducibility of Geometry to Algebra
  28. On regularity of symbolic Rees algebras and symbolic powers of vertex cover ideals of graphs
  29. Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on del pezzo surfaces
  30. Analytic Spread and Associated primes of divisorial filtrations
  31. Milnor-Witt cycle modules over an excellent DVR
  32.  Faculty of Mathematics
  33. Projective dimension and Castelnuovo–Mumford regularity of -spread ideals
  34. Using intra‐task flexibility on an intelligent tutoring system to promote arithmetic problem‐solving proficiency
  36. Polarizations of powers of graded maximal ideals
  37. Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds
  38. Confirming Mathematical Conjectures by Analogy
  39. On the sequence
  40. “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects
  41.  “A Senior Wrangler Among Senior Wranglers”: The Mathematical Education of Robert Leslie Ellis
  43.  Hyperbolicity of the moduli of certain Fano threefolds
  44. ACM curves in multiprojective spaces
  45. The Zariski-Riemann Space as a Universal Model for the Birational Geometry of a Function Field
  48. Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic
  49. Nothing Will Come of Everything: Software Towers and Quantum Towers
  50. Low degree Hurwitz stacks in the Grothendieck ring
  51. Totalising partial algebras: Teams and splinters
  52. The effect of using PDEODE teaching strategy supported by the e-learning environment in teaching mathematics for developing the conceptual understanding and …
  53. Didactic situations in project-based learning: The case of numerical patterns and sequences
  54. The Zariski-Riemann Space as a Universal Model for the Birational Geometry of a Function Field
  55. Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification
  56. -Adic interpolation of orbits under rational maps
  57. Local Complete Intersections and Weierstrass Points
  58. Exploring quantitative relationship through area conservation activity
  59. A theorem about maximal Cohen–Macaulay modules
  60. Pragmaticism as a Philosophy of Cognitive Mathematics
  61. On The Axioms Of Common Meadows: Fracterm Calculus, Flattening And Incompleteness
  62. A sum-bracket theorem for simple Lie algebras
  63. Three Arithmetical Exponential Sums
  64. أثر الرياضيات على التطورات المنطقية في القرن التاسع عشر؛ مقال عن الجبر الرمزي عند جورج بيکوک‎
  65. Geometric Properties of Weighted Projective Space Simplices
  66. Adelic geometry on arithmetic surfaces, I: Idelic and adelic interpretation of the Deligne pairing
  67. Homotopy and Arithmetic
  68. Cubic Fourfolds with an Involution
  69. H-instanton bundles on three-dimensional polarized projective varieties
  70. Efficient computation of Cantor’s division polynomials of hyperelliptic curves over finite fields
  71. Geometry of certain Brill–Noether locus on a very general sextic surface and Ulrich bundles
  72. Ulrich bundles on double covers of projective spaces
  73. On surfaces of minimal degree in P5
  74. Algebraic number fields generated by an infinite family of monogenic trinomials
  75. Dynamical and qKZ equations modulo , an example
  76. A cut-by-curves criterion for overconvergent of -isocrystals
  77. On the equations defining some Hilbert schemes
  78.  23 Research in Mathematics Education
  79. Hankel edge ideals of trees and (semi-) Hamiltonian graphs
  80. Derived category and ACM bundles of moduli space of vector bundles on a curve
  81. On the Connection of Structure Sense in Mathematics and Who Sees and Transforms It: Internal Structure, Visual Salience, and Transformative Algebra
  82. Around the support problem for Hilbert class polynomials
  83. Perspectives on the problem-posing activity by prospective teachers: A cross-national study
  84. Gödel’s Incompleteness Theorems
  85. Does Frege Have Aristotle’s Number?
  86. Infinite rank Hermitian Lattices and Loop Groups
  87. Logical Paradox and Unsoundness in Quantum Physics
  88. On linear systems with multiple points on a rational normal curve
  89. Perfectoid Spaces: An Annotated Bibliography
  90. 0-Dimensional Persistent Homology Analysis Implementation in Resource-Scarce Embedded Systems
  91. Calculating Complete Lists of Belyi Pairs
  92. Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus
  93. Varieties of mathematical understanding
  94. Companion varieties for root systems and Fermat arrangements
  95. Faster ILP Algorithms for Problems with Sparse Matrices and Their Applications to Multipacking and Multicover Problems in Graphs and Hypergraphs
  96.  Iterative methods and preconditioners for systems of linear equations
  97. Central elements and the Gaeta topos: An algebraic and functorial overview on coextensive varieties
  98. Sharp bounds on the height of K-semistable toric Fano varieties
  100.  Functional transcendence in mixed Hodge theory
  101. Integral -adic Hodge filtrations in low dimension and ramification
  102. A Prodigy of Universal Genius: Robert Leslie Ellis, 1817-1859
  103. Orientability for Fredholm maps and Spectral Theory
  104.  Equations for GL invariant families of polynomials
  105. Numerical properties of exceptional divisors of birational morphisms of smooth surfaces
  106.  Institute of Mathematics, UMCS
  107. On the dynamical Bogomolov conjecture for families of split rational maps
  108. Fiber cones of rational normal scrolls are Cohen–Macaulay
  109.  Rational normal curves and Hadamard products
  110. Bounds for the degree and Betti sequences along a graded resolution
  111. Binomiality testing and computing sparse polynomials via witness sets
  112. Lattices and hypergraphs associated to square-free monomial ideals
  114. Fundamental properties of complex integrals and series
  115. On algebraic properties of power monoids of numerical monoids
  116.  Brane Physics Solutions for M-Theory
  117. Noticing and Wondering to Rehumanize Mathematics Classrooms
  118. Essential Mathematics for Undergraduates
  119. Representation transformations in transition from empirical to structural generalization
  120. Around the Chevalley–Weil theorem
  121. Objects, Structures, and Logics
  123. SPLP: A Certifiably Globally Optimal Solution to the Relative Pose Estimation Problem Using Points and Line Pairs
  124. The geometry of musical rhythm: what makes a “good” rhythm good?(2nd edn.) by Godfried T. Toussaint, pp. 352,£ 37.15 (paperback), ISBN 978-0-8153-7097-0, CRC …
  125. Syntomic complexes and -adic \’etale Tate twists
  126. Congruences of Galois representations attached to effective -motives over global function fields
  127. On wall-crossing invariance of certain sums of Welschinger numbers
  128.  Methods of Solving Problems In Semiconductor Physics
  129. Betti numbers under small perturbations
  131.  A curricular morphology of arithmetic to teach in Schools of Craftsmen Apprentices
  132.  Dimensions of Morphological Integration
  134. Calibrating Computational Complexity via Definability: The Work of Julia F. Knight
  135. On the Brumer-Stark Conjecture and Refinements
  136. Milliet Dechales as Historian of Mathematics
  137.  The Significance of Plato for a “Disenchanted Aristotelian” Reading of Hegel’s Philosophy of Right–Draft
  138. Corrigendum to “On the construction of weakly Ulrich bundles”[Adv. Math. 381 (2021) 107598]
  139. Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems
  140. Calabi-Yau CFTs and random matrices
  141. John Wallis and the “Rectification” of the Parabola
  142. “Palpable to thinking”: Othello and Gross Conceits
  143.  Effects of augmented reality application integration with computational thinking in geometry topics
  144.  Numbers: Arithmetic and Computation
  145. Hyperbolicity and uniformity of varieties of log general type
  146.  Explanation in Mathematics: Proofs and Practice (forthcoming in Philosophy Compass)
  147. The genus of curves in and not contained in quadrics
  148. Some recent advances in topological Hochschild homology
  150. Dynamics, Adaptation, and Control for Mental Models Analysed from a Self-modeling Network Viewpoint
  151.  The Science of Less-Than-Brute Force: When Satisfiability Solving Meets Symbolic Computation
  152. Effects of digital games on student motivation in mathematics: A meta‐analysis in K‐12
  153.  Metabelian groups and elliptic curves
  154. D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods
  155.  Robert Leslie Ellis: An Almost Perfect Moral Nature
  156.  On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces
  157. Categorical Torelli theorems: results and open problems
  158. Mathematical Analysis at University
  159. Semigroup rings as weakly Krull domains
  160. Moduli of distributions via singular schemes
  161. On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations
  162. From Magnitudes to Geometry and Back: De Zolt’s Postulate
  163.  The New Era in American Mathematics, 1920–1950
  164.  Report on candidates’ work in the Caribbean Advanced Proficiency Examination, May/June 2008: Pure Mathematics (Rest of the Region)
  165.  Enumeration of spanning trees and forests in graphs
  166. I Can See the Ellipsoid from the Inside: Girtonian Responses to Francis Galton’s Survey on Mental Imagery
  167.  Euler: The master of us all
  168. An Invitation to Higher Arity Science
  169.  Technology-Based Collaborative Learning for Developing the Dynamic Concept of the Angle
  170. Comparative Study of Mathematics Education in the Philippines and Japan
  171.  Wittgenstein Games
  172. Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and its Application in MCGDM Problems
  173. Calabi-Yau CFTs and random matrices
  174. Model theory of adeles I
  175. Universal algebraic methods for non-classical logics
  176. Balanced Curves and Minimal Rational Connectedness on Fano Hypersurfaces
  177. Sangaku in Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid
  178. Verifying Switched System Stability With Logic
  179. Facets of symmetric edge polytopes for graphs with few edges
  180. Investigation of Mathematical-Pedagogical Knowledge among Prospective Teachers in the Early Childhood Program at the College for Arabic Speakers
  181.  Berkeley and Mathematics
  182. A Review of Majorana fermions and the laws of form
  183. On the classification of non-big Ulrich vector bundles on quadrics and fourfolds
  184. Degree of rational maps and specialization
  185. Geometria e aritmética: um encaixe imperfeito
  186. Relationships between hyperelliptic functions of genus 2 and elliptic functions
  187. Using Didactic Models to Design Adaptive Pathways to Meet Students’ Learning Needs in an Online Learning Environment
  188. Teacher Degree Students Attitudes Towards STEM Activities in two Spanish Universities
  189. Computing Riemann-Roch polynomials and classifying hyper-K\” ahler fourfolds
  190.  Writing and choosing problems for a popular high school mathematics competition
  191. Topological invariants for words of linear factor complexity
  192. Applications of tensor networks in quantum chemistry and polynomial regression
  193. The K\” ahler different of a 0-dimensional scheme
  194. Confluent complement: an algorithm for the intersection of face ideals
  195. Requiem for Plato: The Sociology of Mathematics
  196. A Characterization for the Validity of the Hermite–Hadamard Inequality on a Simplex
  197.  Integration with Complex Numbers: A Primer on Complex Analysis
  198.  The canonical module of GT-varieties and the normal bundle of RL-varieties
  199. On a workflow for efficient computation of the permeability of tight sandstones
  200. The last chapter of the Disquisitiones of Gauss
  201. Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments
  202. Common valuations of division polynomials
  203.  Εικασία Fermat, Η μοντέρνα προσέγγιση
  204.  Critical Condition Identification and Simulation of a Continuous Synergetic Growth Model Based on Dynamic Software GeoGebra
  205.  Normal log canonical del Pezzo surfaces of rank one and type (IIb)
  206. Marked Godeaux surfaces with special bicanonical fibers
  207. Study of Linear Differential-Algebraic Equations of Higher-Order and Characteristics of Matrix Polynomials
  208. Lifting Elements in Coherent Quantales
  209. Degree based Topological indices of Subdivision Graph
  210. Extensions of absolute values on two subfields
  211. Automorphisms on algebraic varieties: K3 surfaces, hyperkähler manifolds, and applications on Ulrich bundles
  212. Schemes Supported on the Singular Locus of a Hyperplane Arrangement in ℙn
  213. Plancherel Measures of Reductive Adelic Groups and Von Neumann Dimensions
  214. Turing and the Epistemological Value of the General Concept of Formal System
  215.  Integral points of Shimura varieties: an” all or nothing” principle
  216. Data-driven geometric scale detection via Delaunay interpolation
  217.  Originator of Calabi-Yau space and other theorems Harvard Mathematics Dept.
  218. Teacher Development Structured Around Reasoning About Functions
  219. Conceptual Frameworks on the Relationship Between Physics–Mathematics in the Newton Principia Geneva Edition (1822)
  220.  Intuition in Mathematics: from Racism to Pluralism
  221. On absolutely profinitely solitary lattices in higher rank Lie groups
  222. Modules whose finiteness dimensions coincide with their cohomological dimensions
  223. On the Early Collections of the Works of Ġiyāṯ al-Dīn Jamšīd al-Kāšī
  224. Pre-service mathematics teachers’ problem-formulation processes: Development of the revised active learning framework
  225. Moduli spaces and Modular forms
  226. Can we dream of a 1-adic Langlands correspondence?
  227.  The Empowering Paradox of “1= 2.” Mark Z. Danielewski’s Arithmopoetics
  228. On product-one sequences over dihedral groups
  229. Embedding Semantic Anchors to Guide Topic Models on Short Text Corpora
  230. Applications of linear algebra to cryptography
  231. Codimension one distributions of degree 2 on the three-dimensional projective space
  232. Women’s participation in mathematics in Scotland, 1730–1850
  233. Neutrosophic cubic Maclaurin symmetric mean aggregation operators with applications in multi‐criteria decision‐making
  234. Executive functions, math anxiety and math performance in middle school students
  235. Training Mental Rotation Skills by building houses to improve Spatial Ability
  237. A Classification of Artificial Intelligence Systems for Mathematics Education
  238. Dimensions on Lattice Ordered Abelian Groups and Model Theory of Modules over Pr\” ufer Domains
  240. On Eigenvalues and Energy of Geometric–Arithmetic Matrix of Graphs
  241. The aperiodic Domino problem in higher dimension
  242. Powers of monomial ideals with characteristic-dependent Betti numbers
  243. Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
  244. Determinantal representations and the image of the principal minor map
  245.  The KSBA compactification of the moduli space of D 1 , 6 -polarized Enriques surfaces
  246.  The Impact of International Assessments on Mathematics Teacher Development in the Kingdom of Saudi Arabia (KSA).
  247. -Categorical Perverse -adic Differential Equations over Stacks
  248. A relation between a vertex-degree-based topological index and its energy
  249. Generalized Dold sequences on partially-ordered sets
  250. Hypercomputation
  251.  ABC, GA, AG HDR Indices of Certain Chemical Drugs
  252.  K3 curves with index k > 1
  253. The Real Numbers
Prof.Fazal Rehman Shamil (Available for Professional Discussions)
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