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
35. SOME COMMUTATIVE RINGS DEFINED BY MULTIPLICATION LIKE-CONDITIONS
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
42.  AXIOMS OF CONSTRUCTION FROM QUANTUM BAYESIANISM
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
46.  LEVEL ALGEBRAS-SOME REMARKS
47.  A SYSTEMATIC ANALYSIS OF THE GENERALISATION CONCEPT IN EARLY ALGEBRA FOR YOUNG LEARNERS–SOME IDEAS FOR THE CLASSROOM
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
99.  GEOMETRICAL CONTRIBUTION OF øRäDHARâCâRYA
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
113.  ON GEOMETRIC PROOFS OF THEOREMS ON SUMS OF SQUARES
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
122.  PROJECTIVE CURVES WITH NICE NORMAL BUNDLES AND CONTAINING A PRESCRIBED SUBSET OF A HYPERPLANE
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
130.  TWISTED THOM ISOMORPHISMS IN BALMER-WITT THEORY
131.  A curricular morphology of arithmetic to teach in Schools of Craftsmen Apprentices
132.  Dimensions of Morphological Integration
133.  COMBINATORIC PROPERTIES AND RELATIONS OF WORDS IN CANTOR SEQUENCES
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
149. IMPORTANT ISSUES IN MATHEMATICS TEACHING
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
236.  COMPUTATIONAL SKILLS AMONG PRIMARY SCHOOL STUDENTS WITH RESPECT TO GENDER
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
239.  ELLIPTIC SURFACES AND INTERSECTIONS OF ADELIC R-DIVISORS
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

Research Topics Physics

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