**Research Area/ Research Interest: Arithmetical algebraic geometry**

**Research Paper Topics for:** Masters and PhD Thesis and publication

- Point-Counting and the Zilber–Pink Conjecture
- Algorithmic aspects of arithmetical structures
- Fermat and Descartes in Light of Premodern Algebra and Viète
- Mathematics embodied: Merleau-Ponty on geometry and algebra as fields of motor enaction
- Zero-cycle groups on algebraic varieties
- Fractional Thermoentropy Spaces of Topological Quantum Fields
- Generalizations of Alladi’s formula for arithmetical semigroups
- A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra
- On the non-archimedean Monge-Amp\ere equation in mixed characteristic
- Arithmetical structures on dominated polynomials
- The matrix taxonomy of finitely complete categories
- Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize
- Fractional Thermoentropy Spaces of Large Scale Systems
- Groebner fan and embedded resolutions of ideals on toric varieties
- Curves in projective spaces: questions and remarks
- Finiteness theorems for complements of large divisors
- New constructions of entanglement-assisted quantum codes
- Configurations of eigenpoints
- Axiomatizing the existential theory of Fp ((t))
- Upper bounds for regularity of radicals of ideals and arithmetic degrees
- On the description of identifiable quartics
- Notes of Everything
- Reconstructing curves from their Hodge classes
- Noncommutative Riemann hypothesis
- On the Tightness of Semidefinite Relaxations for Rotation Estimation
- Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications
- The Case for the Irreducibility of Geometry to Algebra
- On regularity of symbolic Rees algebras and symbolic powers of vertex cover ideals of graphs
- Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on del pezzo surfaces
- Analytic Spread and Associated primes of divisorial filtrations
- Milnor-Witt cycle modules over an excellent DVR
- Faculty of Mathematics
- Projective dimension and Castelnuovo–Mumford regularity of -spread ideals
- Using intra‐task flexibility on an intelligent tutoring system to promote arithmetic problem‐solving proficiency
- SOME COMMUTATIVE RINGS DEFINED BY MULTIPLICATION LIKE-CONDITIONS
- Polarizations of powers of graded maximal ideals
- Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds
- Confirming Mathematical Conjectures by Analogy
- On the sequence
- “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects
- “A Senior Wrangler Among Senior Wranglers”: The Mathematical Education of Robert Leslie Ellis
- AXIOMS OF CONSTRUCTION FROM QUANTUM BAYESIANISM
- Hyperbolicity of the moduli of certain Fano threefolds
- ACM curves in multiprojective spaces
- The Zariski-Riemann Space as a Universal Model for the Birational Geometry of a Function Field
- LEVEL ALGEBRAS-SOME REMARKS
- A SYSTEMATIC ANALYSIS OF THE GENERALISATION CONCEPT IN EARLY ALGEBRA FOR YOUNG LEARNERS–SOME IDEAS FOR THE CLASSROOM
- Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic
- Nothing Will Come of Everything: Software Towers and Quantum Towers
- Low degree Hurwitz stacks in the Grothendieck ring
- Totalising partial algebras: Teams and splinters
- The effect of using PDEODE teaching strategy supported by the e-learning environment in teaching mathematics for developing the conceptual understanding and …
- Didactic situations in project-based learning: The case of numerical patterns and sequences
- The Zariski-Riemann Space as a Universal Model for the Birational Geometry of a Function Field
- Solving Arithmetic Word Problems Using Natural Language Processing and Rule-Based Classification
- -Adic interpolation of orbits under rational maps
- Local Complete Intersections and Weierstrass Points
- Exploring quantitative relationship through area conservation activity
- A theorem about maximal Cohen–Macaulay modules
- Pragmaticism as a Philosophy of Cognitive Mathematics
- On The Axioms Of Common Meadows: Fracterm Calculus, Flattening And Incompleteness
- A sum-bracket theorem for simple Lie algebras
- Three Arithmetical Exponential Sums
- أثر الرياضيات على التطورات المنطقية في القرن التاسع عشر؛ مقال عن الجبر الرمزي عند جورج بيکوک
- Geometric Properties of Weighted Projective Space Simplices
- Adelic geometry on arithmetic surfaces, I: Idelic and adelic interpretation of the Deligne pairing
- Homotopy and Arithmetic
- Cubic Fourfolds with an Involution
- H-instanton bundles on three-dimensional polarized projective varieties
- Efficient computation of Cantor’s division polynomials of hyperelliptic curves over finite fields
- Geometry of certain Brill–Noether locus on a very general sextic surface and Ulrich bundles
- Ulrich bundles on double covers of projective spaces
- On surfaces of minimal degree in P5
- Algebraic number fields generated by an infinite family of monogenic trinomials
- Dynamical and qKZ equations modulo , an example
- A cut-by-curves criterion for overconvergent of -isocrystals
- On the equations defining some Hilbert schemes
- 23 Research in Mathematics Education
- Hankel edge ideals of trees and (semi-) Hamiltonian graphs
- Derived category and ACM bundles of moduli space of vector bundles on a curve
- On the Connection of Structure Sense in Mathematics and Who Sees and Transforms It: Internal Structure, Visual Salience, and Transformative Algebra
- Around the support problem for Hilbert class polynomials
- Perspectives on the problem-posing activity by prospective teachers: A cross-national study
- Gödel’s Incompleteness Theorems
- Does Frege Have Aristotle’s Number?
- Infinite rank Hermitian Lattices and Loop Groups
- Logical Paradox and Unsoundness in Quantum Physics
- On linear systems with multiple points on a rational normal curve
- Perfectoid Spaces: An Annotated Bibliography
- 0-Dimensional Persistent Homology Analysis Implementation in Resource-Scarce Embedded Systems
- Calculating Complete Lists of Belyi Pairs
- Hyperbolic Geometrically Uniform Codes and Ungerboeck Partitioning on the Double Torus
- Varieties of mathematical understanding
- Companion varieties for root systems and Fermat arrangements
- Faster ILP Algorithms for Problems with Sparse Matrices and Their Applications to Multipacking and Multicover Problems in Graphs and Hypergraphs
- Iterative methods and preconditioners for systems of linear equations
- Central elements and the Gaeta topos: An algebraic and functorial overview on coextensive varieties
- Sharp bounds on the height of K-semistable toric Fano varieties
- GEOMETRICAL CONTRIBUTION OF øRäDHARâCâRYA
- Functional transcendence in mixed Hodge theory
- Integral -adic Hodge filtrations in low dimension and ramification
- A Prodigy of Universal Genius: Robert Leslie Ellis, 1817-1859
- Orientability for Fredholm maps and Spectral Theory
- Equations for GL invariant families of polynomials
- Numerical properties of exceptional divisors of birational morphisms of smooth surfaces
- Institute of Mathematics, UMCS
- On the dynamical Bogomolov conjecture for families of split rational maps
- Fiber cones of rational normal scrolls are Cohen–Macaulay
- Rational normal curves and Hadamard products
- Bounds for the degree and Betti sequences along a graded resolution
- Binomiality testing and computing sparse polynomials via witness sets
- Lattices and hypergraphs associated to square-free monomial ideals
- ON GEOMETRIC PROOFS OF THEOREMS ON SUMS OF SQUARES
- Fundamental properties of complex integrals and series
- On algebraic properties of power monoids of numerical monoids
- Brane Physics Solutions for M-Theory
- Noticing and Wondering to Rehumanize Mathematics Classrooms
- Essential Mathematics for Undergraduates
- Representation transformations in transition from empirical to structural generalization
- Around the Chevalley–Weil theorem
- Objects, Structures, and Logics
- PROJECTIVE CURVES WITH NICE NORMAL BUNDLES AND CONTAINING A PRESCRIBED SUBSET OF A HYPERPLANE
- SPLP: A Certifiably Globally Optimal Solution to the Relative Pose Estimation Problem Using Points and Line Pairs
- 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 …
- Syntomic complexes and -adic \’etale Tate twists
- Congruences of Galois representations attached to effective -motives over global function fields
- On wall-crossing invariance of certain sums of Welschinger numbers
- Methods of Solving Problems In Semiconductor Physics
- Betti numbers under small perturbations
- TWISTED THOM ISOMORPHISMS IN BALMER-WITT THEORY
- A curricular morphology of arithmetic to teach in Schools of Craftsmen Apprentices
- Dimensions of Morphological Integration
- COMBINATORIC PROPERTIES AND RELATIONS OF WORDS IN CANTOR SEQUENCES
- Calibrating Computational Complexity via Definability: The Work of Julia F. Knight
- On the Brumer-Stark Conjecture and Refinements
- Milliet Dechales as Historian of Mathematics
- The Significance of Plato for a “Disenchanted Aristotelian” Reading of Hegel’s Philosophy of Right–Draft
- Corrigendum to “On the construction of weakly Ulrich bundles”[Adv. Math. 381 (2021) 107598]
- Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems
- Calabi-Yau CFTs and random matrices
- John Wallis and the “Rectification” of the Parabola
- “Palpable to thinking”: Othello and Gross Conceits
- Effects of augmented reality application integration with computational thinking in geometry topics
- Numbers: Arithmetic and Computation
- Hyperbolicity and uniformity of varieties of log general type
- Explanation in Mathematics: Proofs and Practice (forthcoming in Philosophy Compass)
- The genus of curves in and not contained in quadrics
- Some recent advances in topological Hochschild homology
- IMPORTANT ISSUES IN MATHEMATICS TEACHING
- Dynamics, Adaptation, and Control for Mental Models Analysed from a Self-modeling Network Viewpoint
- The Science of Less-Than-Brute Force: When Satisfiability Solving Meets Symbolic Computation
- Effects of digital games on student motivation in mathematics: A meta‐analysis in K‐12
- Metabelian groups and elliptic curves
- D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods
- Robert Leslie Ellis: An Almost Perfect Moral Nature
- On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces
- Categorical Torelli theorems: results and open problems
- Mathematical Analysis at University
- Semigroup rings as weakly Krull domains
- Moduli of distributions via singular schemes
- On the geometry of K3 surfaces with finite automorphism group and no elliptic fibrations
- From Magnitudes to Geometry and Back: De Zolt’s Postulate
- The New Era in American Mathematics, 1920–1950
- Report on candidates’ work in the Caribbean Advanced Proficiency Examination, May/June 2008: Pure Mathematics (Rest of the Region)
- Enumeration of spanning trees and forests in graphs
- I Can See the Ellipsoid from the Inside: Girtonian Responses to Francis Galton’s Survey on Mental Imagery
- Euler: The master of us all
- An Invitation to Higher Arity Science
- Technology-Based Collaborative Learning for Developing the Dynamic Concept of the Angle
- Comparative Study of Mathematics Education in the Philippines and Japan
- Wittgenstein Games
- Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and its Application in MCGDM Problems
- Calabi-Yau CFTs and random matrices
- Model theory of adeles I
- Universal algebraic methods for non-classical logics
- Balanced Curves and Minimal Rational Connectedness on Fano Hypersurfaces
- Sangaku in Multiple Geometries: Examining Japanese Temple Geometry Beyond Euclid
- Verifying Switched System Stability With Logic
- Facets of symmetric edge polytopes for graphs with few edges
- Investigation of Mathematical-Pedagogical Knowledge among Prospective Teachers in the Early Childhood Program at the College for Arabic Speakers
- Berkeley and Mathematics
- A Review of Majorana fermions and the laws of form
- On the classification of non-big Ulrich vector bundles on quadrics and fourfolds
- Degree of rational maps and specialization
- Geometria e aritmética: um encaixe imperfeito
- Relationships between hyperelliptic functions of genus 2 and elliptic functions
- Using Didactic Models to Design Adaptive Pathways to Meet Students’ Learning Needs in an Online Learning Environment
- Teacher Degree Students Attitudes Towards STEM Activities in two Spanish Universities
- Computing Riemann-Roch polynomials and classifying hyper-K\” ahler fourfolds
- Writing and choosing problems for a popular high school mathematics competition
- Topological invariants for words of linear factor complexity
- Applications of tensor networks in quantum chemistry and polynomial regression
- The K\” ahler different of a 0-dimensional scheme
- Confluent complement: an algorithm for the intersection of face ideals
- Requiem for Plato: The Sociology of Mathematics
- A Characterization for the Validity of the Hermite–Hadamard Inequality on a Simplex
- Integration with Complex Numbers: A Primer on Complex Analysis
- The canonical module of GT-varieties and the normal bundle of RL-varieties
- On a workflow for efficient computation of the permeability of tight sandstones
- The last chapter of the Disquisitiones of Gauss
- Middle school students’ reasoning with regards to parallelism and perpendicularity of line segments
- Common valuations of division polynomials
- Εικασία Fermat, Η μοντέρνα προσέγγιση
- Critical Condition Identification and Simulation of a Continuous Synergetic Growth Model Based on Dynamic Software GeoGebra
- Normal log canonical del Pezzo surfaces of rank one and type (IIb)
- Marked Godeaux surfaces with special bicanonical fibers
- Study of Linear Differential-Algebraic Equations of Higher-Order and Characteristics of Matrix Polynomials
- Lifting Elements in Coherent Quantales
- Degree based Topological indices of Subdivision Graph
- Extensions of absolute values on two subfields
- Automorphisms on algebraic varieties: K3 surfaces, hyperkähler manifolds, and applications on Ulrich bundles
- Schemes Supported on the Singular Locus of a Hyperplane Arrangement in ℙn
- Plancherel Measures of Reductive Adelic Groups and Von Neumann Dimensions
- Turing and the Epistemological Value of the General Concept of Formal System
- Integral points of Shimura varieties: an” all or nothing” principle
- Data-driven geometric scale detection via Delaunay interpolation
- Originator of Calabi-Yau space and other theorems Harvard Mathematics Dept.
- Teacher Development Structured Around Reasoning About Functions
- Conceptual Frameworks on the Relationship Between Physics–Mathematics in the Newton Principia Geneva Edition (1822)
- Intuition in Mathematics: from Racism to Pluralism
- On absolutely profinitely solitary lattices in higher rank Lie groups
- Modules whose finiteness dimensions coincide with their cohomological dimensions
- On the Early Collections of the Works of Ġiyāṯ al-Dīn Jamšīd al-Kāšī
- Pre-service mathematics teachers’ problem-formulation processes: Development of the revised active learning framework
- Moduli spaces and Modular forms
- Can we dream of a 1-adic Langlands correspondence?
- The Empowering Paradox of “1= 2.” Mark Z. Danielewski’s Arithmopoetics
- On product-one sequences over dihedral groups
- Embedding Semantic Anchors to Guide Topic Models on Short Text Corpora
- Applications of linear algebra to cryptography
- Codimension one distributions of degree 2 on the three-dimensional projective space
- Women’s participation in mathematics in Scotland, 1730–1850
- Neutrosophic cubic Maclaurin symmetric mean aggregation operators with applications in multi‐criteria decision‐making
- Executive functions, math anxiety and math performance in middle school students
- Training Mental Rotation Skills by building houses to improve Spatial Ability
- COMPUTATIONAL SKILLS AMONG PRIMARY SCHOOL STUDENTS WITH RESPECT TO GENDER
- A Classification of Artificial Intelligence Systems for Mathematics Education
- Dimensions on Lattice Ordered Abelian Groups and Model Theory of Modules over Pr\” ufer Domains
- ELLIPTIC SURFACES AND INTERSECTIONS OF ADELIC R-DIVISORS
- On Eigenvalues and Energy of Geometric–Arithmetic Matrix of Graphs
- The aperiodic Domino problem in higher dimension
- Powers of monomial ideals with characteristic-dependent Betti numbers
- Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
- Determinantal representations and the image of the principal minor map
- The KSBA compactification of the moduli space of D 1 , 6 -polarized Enriques surfaces
- The Impact of International Assessments on Mathematics Teacher Development in the Kingdom of Saudi Arabia (KSA).
- -Categorical Perverse -adic Differential Equations over Stacks
- A relation between a vertex-degree-based topological index and its energy
- Generalized Dold sequences on partially-ordered sets
- Hypercomputation
- ABC, GA, AG HDR Indices of Certain Chemical Drugs
- K3 curves with index k > 1
- The Real Numbers

# Research Topics Physics

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