Research Programs

Faculty-Mentored Research Catalog

Spanning Mathematics, Computer Science, Biology & Medicine, Architecture, and Economics — each project is guided 1-on-1 by mentors from MIT, Harvard, Stanford, CMU, and other leading universities.

13Programs
7Disciplines
1v1Mentorship
13 Programs
MATHEMATICSMIT Mentor12 Weeks

Introduction to Algebraic Topology: From Polygons to Surfaces

Starting from foundational topological concepts, explore manifolds, group theory, and the fundamental group, progressing to core algebraic topology tools such as the Seifert–van Kampen theorem, and culminating in a 5-page expository paper and presentation on a chosen topic.

~5-Page Expository PaperFinal PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules · Advanced Track Available
  1. Sessions 1–2 | Topological Foundations & Surfaces: Open sets, continuous maps, homeomorphisms; examples of surfaces and proving sets are manifolds
  2. Sessions 3–4 | Euler Characteristic, Quotient Spaces & Surface Classification: RP², S², T², and identifying surfaces from polygon gluings via orientation and Euler characteristic
  3. Sessions 5–6 | Group Theory & Structure: Groups, free products, cosets, homomorphisms, quotient groups, and classification of finitely generated abelian groups
  4. Sessions 7–8 | The Fundamental Group: Homotopy of paths and computing fundamental groups of manifolds and gluing spaces
  5. Sessions 9–10 | Van Kampen Theorem & Applications: Degree of maps, retractions, fundamental group of wedges of circles, and induced homomorphisms
  6. Sessions 11–12 | Independent Topic & Presentation: Deep dive into a chosen topic, short oral presentation, and a ~5-page expository paper

Advanced Directions (tailored by mentor): Preparation for entry-level mathematical research problems in algebraic topology and manifolds

Level & Fit: High school, undergraduate, and prospective graduate students interested in pure mathematicsInquire →
MATHEMATICSMIT Mentor12 Weeks

Geometric Analysis & Partial Differential Equations

Begin with Laplace and heat equations alongside differential geometry of curves and surfaces (Gauss–Bonnet theorem and minimal surfaces), then closely read the classic Gage–Hamilton paper on curve shortening flow under mentor supervision, reconstructing omitted proofs or extending a result.

Research Paper / ReportFinal PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules · Advanced Track Available
  1. Weeks 1–2 | Laplace Equation & Harmonic Functions: Maximum principles, fundamental solutions, derivative estimates, and Liouville’s theorem
  2. Weeks 2–3 | Heat Equation & Parabolic Methods: Parabolic maximum principles, heat kernel, and a priori estimates
  3. Weeks 4–7 | Differential Geometry of Curves & Surfaces: Curvature, torsion, Theorema Egregium, and the Gauss–Bonnet theorem
  4. Week 8 | Minimal Surfaces (Plateau Problem): First and second variation formulas, stability, and Bernstein’s problem
  5. Weeks 9–10 | Curve Shortening Flow & Classic Paper Reading: Section-by-section close reading of Gage–Hamilton with mentor guidance
  6. Weeks 11–12 | Research Paper & Presentation: Reconstruct omitted derivations or extend a theorem, concluding with a final presentation

Advanced Directions (tailored by mentor): Long-term mathematics research track aiming for an arXiv Preprint or manuscript (6+ months, individually scoped with mentor)

Level & Fit: High school and undergraduate students with calculus foundations exploring theoretical math research, as well as graduate applicantsInquire →
ARCHITECTUREHarvard Mentor12 Weeks

Architectural Design Research & Portfolio

Trace modern Japanese architecture and Metabolism to investigate an architect’s critical position; perform digital surveying and scaled redrawing of a canonical house; then alter a single dimensional parameter to trace the resulting spatial, structural, and tectonic transformations.

4-Board Final Review (Analysis + Redesign)Portfolio Design NarrativeFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules
  1. Modern Japanese Architecture Reading Seminar: Analyze three foundational texts on selective appropriation, distance, and modernization, writing critical responses
  2. Metabolism & Urban Systems: Situate architecture within frameworks of metabolic growth, urbanism, and technology
  3. Architect’s Critical Position: Investigate the core disciplinary questions a selected architect responds to
  4. Digital Surveying & Redrawing of a Canonical House: Produce accurately scaled drawings and renderings to test spatial and proportional understanding
  5. Single-Variable Design Transformation: Modify one critical dimension and trace all resulting formal, spatial, structural, and constructional shifts
  6. Final Review & Portfolio Integration: Complete a 4-page visual argument and translate it into a portfolio narrative with post-program mentor feedback
Level & Fit: Students applying to architecture and design programs seeking deeper critical rigor and narrative clarity in their portfoliosInquire →
BIOLOGY & MEDICINEMIT Mentor12 Weeks

Cancer Immunotherapy & Vaccines Research

Starting from how the immune system recognizes tumors, systematically study immune checkpoint blockade, CAR-T / CAR-NK cell therapies, and cancer vaccines, then engage with primary literature on combination therapies to complete an independently scoped project.

Research Paper or PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule5 Modules · Advanced Track Available
  1. Foundations of Tumor Immunology: How innate and adaptive immunity recognize and eliminate malignant cells
  2. Immune Checkpoint Blockade: Mechanisms of PD-1/PD-L1 and CTLA-4 pathways that transformed clinical oncology
  3. Cellular Immunotherapy: Engineering principles and clinical boundaries of CAR-T and CAR-NK therapies
  4. Cancer Vaccines: Neoantigen selection and vaccine delivery platforms from mechanism to therapeutic strategy
  5. Combination Therapies & Independent Inquiry: Close reading of frontier papers, independent topic formulation, mini-presentation, and review paper

Advanced Directions (tailored by mentor): mRNA Vaccine Design · Neoantigen Discovery · Protein Engineering

Level & Fit: Students interested in biomedicine, immunology, bioengineering, or translational medicine with foundational biology/chemistry knowledgeInquire →
BIOLOGY & MEDICINEMIT Mentor12 Weeks

Stem Cell Biology & Disease Modeling

Explore the differentiation mechanisms of human pluripotent stem cells (hPSCs), patient-specific disease modeling, and regenerative medicine applications through primary literature and clinical trials, culminating in a conference-style research proposal and presentation.

4–6 Page Research ProposalConference-Style PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule9 Modules
  1. Session 1 | Introduction to Human Pluripotent Stem Cells: Properties and classification of embryonic, adult, and induced pluripotent stem cells (iPSCs)
  2. Sessions 2–3 | History & Derivation of hPSCs: Reprogramming milestones, somatic cell nuclear transfer, and laboratory maintenance
  3. Sessions 4–5 | Differentiation Potential & Organoids: Directed differentiation protocols and advanced tissue models; literature synthesis on an under-studied cell lineage
  4. Sessions 6–7 | Disease Modeling & Therapeutics: Building patient-derived models and analyzing active stem cell clinical trials
  5. Session 8 | Bioethics & Regulatory Frameworks: Ethical considerations of hESCs, gene editing, and a 500-word perspective piece
  6. Session 9 | Research Journal Club: Critical discussion of an impactful recent stem cell publication
  7. Session 10 | Bench-to-Bedside Translation: Identifying unmet clinical needs addressable via stem cell platforms
  8. Session 11 | Research Topic Formulation: 1-on-1 scoping of hypothesis, specific aims, and experimental design
  9. Session 12 | Final Symposium Presentation: Deliver a 4–6 page research proposal and oral presentation in international conference format
Level & Fit: High school, undergraduate, and prospective graduate students interested in cell biology, regenerative medicine, and biomedicineInquire →
BIOLOGY & MEDICINEMonash Mentor12 Weeks

Medical Imaging Principles & AI Analysis

Compare X-ray, CT, MRI, and ultrasound imaging physics, understand signal acquisition and tomographic reconstruction, implement image filtering, segmentation, and feature extraction in Python (scikit-image & SimpleITK), and formulate an independent AI imaging study.

4–6 Page Research ReportFinal Research Presentation
View Syllabus & Schedule9 Modules · Advanced Track Available
  1. Session 1 | Modalities Overview: Physics and clinical trade-offs across X-ray, CT, MRI, and Ultrasound
  2. Sessions 2–3 | MRI & CT Reconstruction: Magnetic resonance signal processing, k-space, and CT back-projection in neuro and oncology imaging
  3. Sessions 4–5 | Ultrasound & Radiography: Acoustic physics, 2D vs. 3D ultrasound, and Doppler flow analysis
  4. Sessions 6–7 | Functional & Molecular Imaging: PET, SPECT, fMRI, multimodal fusion, and close reading of a recent paper
  5. Session 8 | Computational Image Analysis: Filtering, segmentation, and feature extraction in Python using scikit-image and SimpleITK
  6. Session 9 | Clinical AI Ethics & Regulation: Patient data privacy, FDA/clinical validation, and a 500-word ethics brief
  7. Session 10 | AI Medical Imaging Journal Club: Critical evaluation of a deep-learning radiology publication
  8. Session 11 | Research Scoping: Define a computational imaging research question and experimental pipeline
  9. Session 12 | Final Report & Defense: Present a 4–6 page written report and research presentation

Advanced Directions (tailored by mentor): Accelerated MRI Acquisition & Reconstruction: Parallel imaging, compressed sensing, low-rank models, and physics-informed deep learning

Level & Fit: Students interested in biomedical engineering, medical imaging, electrical engineering, computer vision, and AI in healthcareInquire →
ECON & BUSINESSNYU Mentor12 Weeks

Economic Growth & Macroeconomic Data Analysis

Compare cross-country income using Purchasing Power Parity (PPP), uncover empirical regularities from real macroeconomic datasets, calibrate the Solow growth model to selected countries, and incorporate human capital, innovation, and inequality metrics into a data-driven research paper.

5-Page Empirical Research Report20-Minute Research PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules
  1. Sessions 1–2 | Cross-Country Comparability: Nominal vs. real GDP, Purchasing Power Parity (PPP), and assembling national macroeconomic datasets
  2. Sessions 3–4 | Empirical Stylized Facts: Data cleaning, visualization, and structural comparisons across income tiers
  3. Sessions 5–6 | The Solow Growth Model: Capital accumulation, steady-state dynamics, and country-specific growth forecasting
  4. Sessions 7–8 | Human Capital, R&D & Endogenous Growth: Incorporating education, innovation, and total factor productivity into empirical forecasts
  5. Sessions 9–10 | Growth, Poverty & Inequality: Analyzing Gini and distributional metrics while distinguishing correlation from causality
  6. Sessions 11–12 | Empirical Synthesis: Complete a 5-page quantitative report and a 20-minute academic presentation
Level & Fit: Students interested in economics, development studies, public policy, finance, and quantitative data analysisInquire →
ECON & BUSINESSUSC Mentor12 Weeks

Global Marketing Communication Strategy

Centered on the tension between global standardization and local adaptation, examine market selection, entry modes, pricing, distribution, global brand architecture, and cross-cultural consumer behavior to produce a comprehensive case-based strategy report.

Final Case Research ReportFinal Project PresentationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules
  1. Weeks 1–2 | The Global Marketing Environment: Trade, socio-cultural dynamics, and standardization vs. local adaptation
  2. Weeks 3 & 6 | Market Selection, Entry Modes & Research: Segmentation, positioning, licensing, joint ventures, and foreign direct investment
  3. Weeks 4–5 | Global Pricing, Distribution & Brand Equity: Cross-border channel architecture and building a global brand
  4. Week 7 | Competitive Advantage & Global Strategy: Evaluating firm-level strategic positioning across regions
  5. Weeks 8–10 | Culture, Integrated Marketing Communications & Consumer Behavior: How cultural dimensions shape advertising appeals and media strategy
  6. Weeks 11–12 | Capstone Project: Final written research report and formal presentation
Level & Fit: Students interested in communications, marketing, brand strategy, consumer behavior, and international businessInquire →
COMPUTER SCIENCEStanford Mentor12 Weeks

AI for the Subsurface & Earth Sciences

Build deep learning models in Python (Google Colab) alongside foundational geoscience concepts, training neural networks on real well-log data for lithology classification or applying CNNs to seismic sections for fault interpretation, concluding with a formal scientific report.

Scientific Report with FiguresReproducible Code & Model OutputsFaculty Recommendation (Merit-Based)
View Syllabus & Schedule6 Modules · Advanced Track Available
  1. Sessions 1–2 | Deep Learning Architectures: Neural networks, RNNs, CNNs, classification, regression, and generative modeling
  2. Sessions 3–4 | Python & Deep Learning Workflows: Building, training, and evaluating neural networks in Google Colab / Jupyter
  3. Sessions 5–6 | Geoscience Foundations: Plate tectonics, rock formations, stratigraphy, and baseline lithology classification code
  4. Sessions 7–8 | Well-Log Lithology Classification: Training neural networks on real borehole sensor curves to infer subsurface rock types
  5. Sessions 9–10 | Seismic Fault Interpretation with CNNs: Applying convolutional networks to 2D/3D seismic profiles to detect geological faults
  6. Sessions 11–12 | Scientific Writing & Peer-Review Standards: Structuring abstracts, methodology, figures, and discussion in journal format

Advanced Directions (tailored by mentor): Generative Geological Modeling · Physics-Informed Neural Networks (PINNs) · Surrogate Modeling & Uncertainty Quantification for Subsurface Flow (CO₂ storage, geothermal energy, groundwater)

Level & Fit: Students interested in AI for Science, computational geoscience, energy, and environmental engineering (no prior geology background required)Inquire →
COMPUTER SCIENCECMU Mentor12 Weeks

Machine Learning & AI: Models, Games, and Privacy

Progress from supervised and unsupervised learning, gradient descent, neural networks, SVMs, and K-means clustering to combinatorial game-playing algorithms and privacy-preserving machine learning, guided by a mentor specializing in cryptography, security, and privacy.

Machine Learning Project ReportAlgorithmic ImplementationFaculty Recommendation (Merit-Based)
View Syllabus & Schedule5 Modules · Advanced Track Available
  1. Foundations of AI & ML: Supervised vs. unsupervised learning, classification, and regression formulations
  2. Linear & Polynomial Regression: Loss functions, gradient descent optimization, and multivariate matrix methods
  3. Core Machine Learning Models: Logistic regression, neural network fundamentals, Support Vector Machines (SVM), and K-means clustering
  4. Automated Game Playing: Combinatorial game theory, minimax search, and algorithmic strategies in board games
  5. Privacy-Preserving Machine Learning: Data privacy risks and cryptographic techniques for secure model training and inference

Advanced Directions (tailored by mentor): Cryptographic Protocols for Privacy-Preserving ML · Formal Definitions of Security & Differential Privacy · Primary Research Literature Reading

Level & Fit: High school, undergraduate, and prospective graduate students interested in ML theory, algorithms, and data privacy (necessary linear algebra reviewed in class)Inquire →
COMPUTER SCIENCECMU Mentor12 Weeks · 12 Hours

Modern Cryptography Theory & Security Proofs

Start by breaking classical ciphers, build the number-theoretic foundations (modular arithmetic, discrete logarithms, DDH), analyze RSA, Diffie–Hellman, and digital signatures, and explore TLS/HTTPS, blockchain consensus, and zero-knowledge proofs to complete an original research report.

Cryptography Research ReportFocused Study (Blockchain / Digital Signatures / Historical Cryptanalysis)Faculty Recommendation (Merit-Based)
View Syllabus & Schedule7 Modules · Advanced Track Available
  1. Classical Ciphers & Perfect Secrecy: Caesar, Vigenère, substitution ciphers, the one-time pad, and cryptanalytic attacks
  2. Number-Theoretic Foundations: Modular arithmetic, prime factorization, discrete logarithms, and the Decisional Diffie–Hellman (DDH) assumption
  3. Modern Cryptographic Primitives: Collision-resistant hashing, MACs, digital signatures, Diffie–Hellman key exchange, ElGamal, and RSA
  4. Internet Security Protocols: Public-key infrastructure (PKI), digital certificates, TLS/SSL, and HTTPS
  5. Blockchain & Distributed Consensus: Bitcoin architecture, Proof-of-Work vs. Proof-of-Stake, and open research challenges
  6. Advanced Topics: Zero-Knowledge Proofs (ZKPs) and cryptographic coin-flipping protocols
  7. Research Project: Complete a formal research report on blockchain mechanisms, signature efficiency/security, or WWII Enigma cryptanalysis

Advanced Directions (tailored by mentor): Formal Security Definitions & Reduction Proofs · Adversarial Threat Modeling · Introduction to Post-Quantum & Quantum Cryptography · Reading Seminar on Crypto Papers

Level & Fit: High school, undergraduate, and graduate-track students interested in theoretical computer science, discrete mathematics, and mathematical proofsInquire →
ENVIRONMENTAL SCIStanford Mentor12 Weeks

Environmental Nanoscience & Nanomaterials

Investigate how natural and engineered nanoparticles form, transform, and interact with contaminants across water, soil, and air; master advanced spectroscopy and microscopy characterization methods; and propose a nanomaterial-based solution to a real environmental or public health challenge.

Research Report & ProposalNanomaterial Application AnalysisFaculty Recommendation (Merit-Based)
View Syllabus & Schedule7 Modules
  1. Sessions 1–2 | Nanoparticle Formation & Transformation: Natural vs. anthropogenic nanomaterials and their environmental fate
  2. Sessions 2–4 | Nanoclays & Iron Oxyhydroxides: Crystal structure, surface reactivity, and roles in soil and aquatic geochemistry
  3. Sessions 5–6 | Aqueous Contaminant Interactions: Adsorption, dissolution, and precipitation mechanisms for water remediation
  4. Sessions 7–8 | Atmospheric Aerosols & Air Quality: Sources, transport, and toxicity of airborne ultrafine particles
  5. Sessions 9–10 | Advanced Characterization: Synchrotron scattering, spectroscopy, and electron microscopy (TEM/SEM)
  6. Sessions 10–12 | Nanotoxicology & Human Health: Exposure pathways, pulmonary impacts, and risk assessment
  7. Capstone Project | Formulate a research report and intervention proposal addressing an environmental or health problem using a selected nanomaterial
Level & Fit: High school, undergraduate, and prospective graduate students interested in environmental science, chemistry, and materials engineeringInquire →
MEDIA & FILMUSC Mentor12 Weeks

Screenwriting & Short Film Directing Workshop

An intensive directing and screenwriting workshop deconstructing dramatic scene construction, narrative arc, visual storytelling, blocking, and camera coverage, guiding each student from an initial pitch through three rigorous drafts of an original short-film screenplay.

Third-Draft Original Short ScreenplayDirecting & Visual Storytelling CraftFaculty Recommendation (Merit-Based)
View Syllabus & Schedule10 Modules
  1. Session 1 | Function of a Scene I: Revealing character through action and subtext
  2. Session 2 | Function of a Scene II: Propelling narrative momentum
  3. Session 3 | Story Architecture: Three-act structure, stakes, and dramatic conflict
  4. Session 4 | Visual Storytelling: Montage, dream sequences, and cinematic tone
  5. Session 5 | Blocking & Coverage: Staging actors and planning camera setups for a scene
  6. Session 6 | Frame Composition: Designing expressive shots and visual motifs
  7. Session 7 | Deconstructing Short Films: Analyzing award-winning shorts and developing story concepts
  8. Session 8 | The Pitch: Presenting loglines, character arcs, and dramatic premise
  9. Session 9 | Story Workshop & First Draft: Table read and structural critique of Draft 1
  10. Sessions 10–12 | Screenplay Workshops I–III: Page-by-page mentor notes through Draft 2 and polished Draft 3
Level & Fit: High school, undergraduate, and prospective graduate students interested in film production, screenwriting, and visual artsInquire →

How Mentoring Works

The 5-Step Research Experience

  1. 01

    Academic Evaluation & Matching

    We evaluate your coursework, interests, and academic goals to match you with a suitable faculty mentor and research topic.

  2. 02

    Foundations & Methodology

    Build essential domain foundations and learn the analytical, mathematical, or computational tools required for genuine inquiry.

  3. 03

    1-on-1 Guided Research

    Weekly 1-on-1 online sessions where you conduct authentic research tasks — derivations, coding, data analysis, or design critique.

  4. 04

    Research Report Writing

    Write a structured academic research report or paper under your mentor’s guidance, synthesizing your methods and findings.

  5. 05

    Final Presentation & Outcome

    Deliver a final presentation or defense. Strong performers may earn a faculty recommendation letter and a verifiable scholarly record.

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