Math Research Topics

By: Prof. Dr. Fazal Rehman Shamil | Last updated: February 3, 2024

Mathematical Finance – Research Topics

  1. Government Fighting Pandemic, Stock Market Return, and COVID-19 Virus Outbreak
  2. Analysis of commercial land leasing of the district governments of Beijing in China
  3. Stochastic dominance efficient sets and stochastic spanning
  4. A Unified Entropic Pricing Framework of Option: Using Cressie-Read Family of Divergences
  5. A Multilevel Study of the Impact of District-Level Characteristics on Texas Student Growth Trajectories on a High-Stakes Math Exam
  6. The demand for AI skills in the labor market
  7. How Does the Market React to Corporate Philanthropic Behavior?—evidence from the COVID-19 Pandemic Shock
  8. Mathematics learning opportunities in preschool: Where does the classroom library fit in?
  9. Non-life insurance ratemaking techniques
  10. The Role of Business Capabilities in Supporting Organization Agility and Performance During the COVID-19 Pandemic: An Empirical Study in Indonesia
  11. Board interlocks and stock liquidity: New evidence from an emerging market

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Numerical Analysis – Research Topics

  1. Protecting the Historic Buildings of Mexico: The Barrel Vault of San Agustin Church in Morelia
  2. A Numerical Algorithm to Reconstruct the Missing Points from the Membrane Wings of a Bat via the Computerized Motion Capture System
  3. Contrast Enhancement Algorithm Using Definite Integration Mathematical Method Trapezoidal Rule
  4. Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error …
  5. Estimations of Vertical Rail Bending Moments from Numerical Track Deflection Measurements Using Wavelet Analysis and Radial Basis Function Neural Networks
  6. Numerical investigation of nanoparticles shape impacts on thermal energy transfer and flow features of nanofluid impingement jets
  7. Numerical Investigation of High-Frequency Wave-Leak Interaction in Water-Filled Pipes
  8. Irreversibility investigation of Casson fluid flow in an inclined channel subject to a Darcy-Forchheimer porous medium: a numerical study
  9. Experimental and numerical failure analysis of horizontal axis water turbine carbon fiber-reinforced composite blade
  10. Numerical simulation and analysis of fracture etching morphology during acid fracturing of dolomite reservoirs

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Mathematical Biology – Research Topics

  1. Representation of solutions for linear fractional systems with pure delay and multiple delays
  2. Review of fractional epidemic models
  3. Mathematical analysis of crime dynamics in and out of prisons
  4. A Tutorial on the Mathematical Model of Single Cell Variational Inference
  5. Economic Dynamics with Memory: Fractional Calculus Approach
  6. International Conference «Marchuk Scientific Readings 2020»(MSR-2020), dedicated to the 95th anniversary of the birthday of Academician Guri I. Marchuk
  7. Living Systems: The Epistemic Relation to Reality
  8. Data Integration Using Advances in Machine Learning in Drug Discovery and Molecular Biology
  9. Expanded NK cells from umbilical cord blood and adult peripheral blood combined with daratumumab are effective against tumor cells from multiple myeloma patients
  10. A random multiplicative model of Piéron’s law and choice reaction times

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Symplectic geometry – Research Topics

  1. Shift operators and connections on equivariant symplectic cohomology
  2. The relation between Feynman diagrams and Kontsevich graphs in non-commutative star products
  3. Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
  4. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints
  5. On the invariance of Welschinger invariants
  6. Holomorphic anomaly equation for
  7. A lift of the Seiberg–Witten equations to Kaluza–Klein five-manifolds
  8. Equivariant cohomology for differentiable stacks
  9. Billiard tables with rotational symmetry
  10. T-duality and T-folds for point particles

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Random Graphs – Research Topics

  1. A cycle-based formulation for the Distance Geometry Problem
  2. Two-type annihilating systems on complete and star graphs
  3. Minimizing the number of complete bipartite graphs in a -saturated graph
  4. Persistence of hubs in growing random networks
  5. Network dismantling: From vertex separator to edge separator using explosive percolation
  6. Failure and Communication in a Synchronized Multi-drone System
  7. Frozen 1-RSB structure of the symmetric Ising perceptron
  8. Two Problems in Extremal Combinatorics

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Fluidic shaping – Research Topics

  1. Area-optimal simple polygonalizations: The CG challenge 2019
  2. Monitoring leaf phenology in moist tropical forests by applying a superpixel-based deep learning method to time-series images of tree canopies
  3. Computing coordinated motion plans for robot swarms: The cg: shop challenge 2021
  4.  Connectivity constrains quantum codes
  5. Performance of PV integrated dynamic overhangs applied to US homes
  6. Quantifying potential dynamic façade energy savings in early design using constrained optimization
  7. Discrete conformal equivalence of polyhedral surfaces
  8. … extreme learning machine model coupled with K-means clustering and firefly algorithm for estimating monthly reference evapotranspiration in parallel computation
  9.  Pre-surgical prediction of ischemic mitral regurgitation recurrence using in vivo mitral valve leaflet strains
  10. Feasibility study of urban flood mapping using traffic signs for route optimization

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Computational Geometry – Research Topics

  1. Fluidic shaping of optical components
  2. Pointwise Fabrication and Fluidic Shaping of Carbon Nanotube Field Emitters
  3. Fluidic-based virtual aerosurface shaping
  4.  Thermal modulation of fluidic lenses in microgravity
  5. Fabrication of diffractive optical elements by programmable thermocapillary shaping of thin liquid films
  6. Programmable thermocapillary shaping of thin liquid films
  7. Stochasticity, succession, and environmental perturbations in a fluidic ecosystem
  8. Shaping acoustic fields as a toolset for microfluidic manipulations in diagnostic technologies
  9. Liquid crystal microfluidics for tunable flow shaping
  10. Opto-fluidic velocimetry using liquid crystal microfluidics

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Quantitative Biology – Research Topics

  1. Mathematica: a system for doing mathematics by computer
  2. Conservation priorities in a biodiversity hotspot: analysis of narrow endemic plant species in New Caledonia
  3. How does mathematics anxiety impair mathematical abilities? Investigating the link between math anxiety, working memory, and number processing
  4. Genetic architecture of mandible shape in mice: effects of quantitative trait loci analyzed by geometric morphometrics
  5. Integration of cadherin adhesion and the cytoskeleton at adherens junctions
  6. Quantitative analyses of empirical fitness landscapes
  7. Monte Carlo strategies in scientific computing
  8. Control theory for humans: Quantitative approaches to modeling performance
  9. Quantitative methods and biogeographic analysis
  10. An Introduction to Mathematical Biology

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Generalized complex geometry – Research Topics

  1. Generalized Ricci Flow
  2.  A study on dual-generalized complex and hyperbolic-generalized complex Numbers
  3. Generalization across multiple mathematical domains: Relating, forming, and extending
  4. Generalized finite difference method for electroelastic analysis of three-dimensional piezoelectric structures
  5. Fractal structure and generalization properties of stochastic optimization algorithms
  6.  New spaces in mathematics: Formal and conceptual reflections
  7. On the topology of warped product pointwise semi-slant submanifolds with positive curvature
  8. Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms
  9. Generalized Gibbs’ Phase Rule
  10. A generalized finite difference method for solving Stokes interface problems

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Graphs clustering – Research Topics

  1. Test of understanding graphs in kinematics: Item objectives confirmed by clustering eye movement transitions
  2. Symbol alphabets from plabic graphs III: N= 9
  3.  Supercritical percolation on nonamenable graphs: Isoperimetry, analyticity, and exponential decay of the cluster size distribution
  4. A novel method of spectral clustering in attributed networks by constructing parameter-free affinity matrix
  5. The PACE 2021 parameterized algorithms and computational experiments challenge: Cluster Editing
  6. Symbol alphabets from plabic graphs II: rational letters
  7. Automatic analysis of attack graphs for risk mitigation and prioritization on large-scale and complex networks in Industry 4.0
  8. Figures of graph partitioning by counting, sequence and layer matrices
  9.  Combining clickstream analyses and graph-modeled data clustering for identifying common response processes
  10. Lexical Sense Labeling and Sentiment Potential Analysis Using Corpus-Based Dependency Graph

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Graphs Limits – Research Topics

  1. GAMES: A Gentle Approach to Math, Excel, and Stats (Course 2)
  2. Scaling limits for the Gibbs states on distance-regular graphs with classical parameters
  3. Common graphs with arbitrary connectivity and chromatic number
  4. Graph Indices for Cartesian Product of-sum of Connected Graphs
  5. Hydrodynamic limits of non-Markovian interacting particle systems on sparse graphs
  6. Local limits of spatial inhomogeneous random graphs
  7. Inverse limits with set-valued functions having graphs that are arcs
  8. Mean-field limits of phase oscillator networks and their symmetries
  9. On breadth-first constructions of scaling limits of random graphs and random unicellular maps
  10. Inverse Limits with Markov-Type Functions

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Research Topics on Hydrodynamic quantum analogs

  1. Real surreal trajectories in pilot-wave hydrodynamics
  2. A Hydrodynamic Quantum Analogue: Walking Droplets
  3. Fluid Dynamicists Need to Add Quantum Mechanics into their Toolbox
  4. A hydrodynamic analog of superradiant emission
  5. Hydrodynamic superradiance in wave-mediated cooperative tunneling
  6. Gravitational edge modes, coadjoint orbits, and hydrodynamics
  7. Walking droplets as a damped-driven system
  8. Hydrodynamic derivation of the Gross–Pitaevskii equation in general Riemannian metric
  9. A Minimal Orbital Quantization Model and Quantum Hall Effect Analog in Pilot-Wave Hydrodynamics
  10. Probing quantum effects with classical stochastic analogs

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Research Topics on Interfacial Phenomena

  1. Polyphenolic antioxidants in lipid emulsions: Partitioning effects and interfacial phenomena
  2. Mathematical modeling on transient multiphase flow and slag entrainment in continuously casting mold with double-ruler EMBr through LES+ VOF+ DPM method
  3. Plasmon and plexciton driven interfacial catalytic reactions
  4. Quantitative determination of lithium depletion during rapid cycling in sulfide-based all-solid-state batteries
  5.  Mathematical analysis and its experimental comparisons for the accumulative roll bonding (ARB) process with different superimposed layers
  6. Mathematical modeling of novel porous transport layer architectures for proton exchange membrane electrolysis cells
  7. Mechanical and durable properties of chopped basalt fiber reinforced recycled aggregate concrete and the mathematical modeling
  8. Mathematical modelling of food hydrolysis during in vitro digestion: From single nutrient to complex foods in static and dynamic conditions
  9. Lamb wave scattering analysis for interface damage detection between a surface-mounted block and elastic plate
  10. Computational fluid dynamics (CFD) simulation of inclusion motion under interfacial tension in a flash welding process.

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Research Topics on Large deviations

  1. Large deviations principle for 2D Navier-Stokes equations with space-time localized noise
  2. Large deviations of currents in diffusions with reflective boundaries
  3. Sanov-type large deviations and conditional limit theorems for high-dimensional Orlicz balls
  4. Dynamical Large Deviations for Homogeneous Systems with Long Range Interactions and the Balescu–Guernsey–Lenard Equation
  5. Asymptotically-preserving large deviations principles by stochastic symplectic methods for a linear stochastic oscillator
  6. Decision Theory and large deviations for dynamical hypotheses tests: The Neyman-Pearson Lemma, Min-Max and Bayesian tests
  7. Entropic optimal transport: Geometry and large deviations
  8. Multifractal analysis and large deviations of homological growth rates for hyperbolic surfaces
  9. Finite time large deviations via matrix product states
  10. Large deviations for the greedy exploration process on configuration models

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Research Topics on Partial differential equations, Nonlinear analysis

  1. Boundary Hölder regularity for a class of fully nonlinear elliptic partial differential equations
  2. Novel analysis of the fractional-order system of non-linear partial differential equations with the exponential-decay kernel
  3.  Reducing computational efforts in linear and nonlinear analysis of peridynamic models under impact loads
  4.  THIRD ORDER ITERATIVE METHOD FOR SOLVING NON-LINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION IN FINANCIAL APPLICATION
  5. A reduced order method for nonlinear parameterized partial differential equations using dynamic mode decomposition coupled with k-nearest-neighbors regression
  6. Nonlinear analysis of the ballast influence on the train-bridge resonance of a simply supported railway bridge
  7. Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations
  8.  The effect of a new two-point nonlocal condition on the eigenvalue problem of the difference scheme for an elliptic partial differential equation
  9. A novel method to impose boundary conditions for higher-order partial differential equations
  10. Efficient Approaches for Solving Systems of Nonlinear Time-Fractional Partial Differential Equations

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Research Topics on Medical imaging

  1. Introduction to the mathematics of medical imaging
  2. Active contour and segmentation models using geometric PDE’s for medical imaging
  3. Math, magnets, and medicine: Enabling personalized oncology
  4.  Webb’s physics of medical imaging
  5.  The Radon transform and medical imaging
  6. Towards new functional nanostructures for medical imaging
  7. Fluid–structure interaction in blood flows on geometries based on medical imaging
  8. Kyoto prizes in math and medical imaging.
  9. Relevance of accurate Monte Carlo modeling in nuclear medical imaging
  10. Compressive sensing in medical imaging

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Research Topics on Learning Theory

  1. A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level
  2. The math is not the territory: navigating the free energy principle
  3. A Qualitative Descriptive Study of Teachers’ Implemented Instructional Strategies and Perceived Effectiveness for Foundational Math Literacy Elements
  4. Mastery Learning and Specs Grading in Discrete Math
  5. The Magic Is in the Margins: UDL Math
  6. Development of an Android-Based for Math E-Module by using Adobe Flash Professional CS6 for Grade X Students of Senior High School
  7. Teacher capacity to adopt and use student-centered instruction in secondary math classrooms
  8. A self-regulated learner framework for students with learning disabilities and math anxiety
  9. Balance Board Math:“Being the graph” through the sense of balance for embodied self-regulation and learning
  10. A study of enjoyment of mathematics lessons and career aspirations of upper secondary students under Math-Science and Math-English programs

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Research Topics on Symplectic Geometry

  1. Symplectic geometry of Cartan–Hartogs domains
  2. Symplectic   topology and algebraic families
  3. Symplectic geometry and necessary conditions for optimality
  4. When Symplectic   topology meets Banach space geometry
  5. Flexible embeddings in contact and Symplectic geometry
  6. Symplectic geometry and the motion of a particle in a magnetic field
  7. New construction of authentication codes with arbitration from pseudo-Symplectic geometry over finite fields
  8. A survey on Symplectic   and multi-Symplectic  algorithm

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Research Topics on Stochastic processes

  1. Stochastic processes with applications
  2.  Adventures in stochastic processes
  3. Detection of stochastic processes
  4.  Basics of applied stochastic processes
  5.  Stochastic processes and applications
  6.  Elements of applied stochastic processes
  7.  An introduction to stochastic processes with applications to biology
  8.  Applied probability and stochastic processes
  9.  Essentials of stochastic processes
  10.  Stochastic processes in physics and chemistry

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Research Topics on Numerical Analysis

  1. Evidence for two Numerical  systems that are similar in humans and guppies
  2.  Numerical notation: A comparative history
  3. Asymmetric numeral systems : entropy coding combining speed of Huffman coding with compression rate of arithmetic coding
  4. Numerical  system for infrared scanners and application to the subsurface control of materials by photothermal radiometry
  5.  Quantities, amounts, and the Numerical core system
  6.  Dynamical systems and Numerical analysis
  7. Development of optimum process design system by Numerical simulation
  8. Numerical representations in primates.
  9.  Numerals: Comparative-etymological Analyses of Numeral Systems and Their Implications: Saharan, Nubian, Egyptian, Berber, Kartvelian, Uralic, Altaic …
  10. Numerical analysis of dynamical systems

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More Math Research Topics

Percolation Metamaterials Medical Imaging
H-principles Applied And Computational Geometry Algebraic k-theory
Phase transition Large deviation interfacial phenomena
Computational Geometry Generalized complex geometry Graphs clustering
Graphs Limits Hydrodynamic quantum Interfacial Phenomena
Nonlinear partial differential equations Large deviations  Partial differential equations, Nonlinear analysis 
Learning Theory Random Graphs Random Graphs 2

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