MAT 216
Accelerated Honors Analysis
Gunning, An Introduction to Analysis
Academic / research experience
My educational
universe.
Every course I took, every textbook that shaped me, and every research project along the way. I built this page for students who care about learning and want a map, not a highlight reel.
Education
- 2025Harvard University M.S. in Applied Mathematics
- 2023Princeton University B.A. in Mathematics, with honors
- 2019Specialized Education and Research Center (SERC), Ural Federal University, Ekaterinburg High school diploma
- 2016ЕДМШ #14, Ekaterinburg Music school
Graduated from six years of music school, play domra, and won twenty-plus regional and national music competitions.
Publications
Full list on Google Scholar →
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Trentini B, Hume J, Isoldi VA, Misof P, Ivshina ES, Maggs K. Neural Point-Forms.
Submitted to NeurIPS.
-
Wang E, Ivshina ES, et al. Sentence Processing is Surprisingly Robust to Verbatim Repetition.
39th Annual Conference on Human Sentence Processing (2026).
- Roggeveen JV et al. HARDMath2: A Benchmark for Applied Mathematics Built by Students as Part of a Graduate Class.
NeurIPS 2025.
- Ivshina ES, Anikeeva G, Zhou L. Doughnut or Mickey Mouse? Detecting Toroidal Structure in Data through Persistent Cup-Length.
ArXiv preprint (2025).
- Ivshina ES. Patterns in Knot Floer Homology.
ArXiv preprint (2023).
- Ivshina ES. On Slice Knots and Patterns in Knot Floer Homology.
Senior thesis (2023).
- Ivshina ES, Winn JN. TESS Transit Timing of Hundreds of Hot Jupiters.
Astrophysical Journal Supplement Series (2022).
Programs I attended
Intensive summer schools and fellowships that shaped my path. Links go to each program's official site.
- Analytic Connectionism Summer School
Flatiron Institute, New York City.
- Machine Learning and Math program
Institute for Advanced Study, Princeton.
- AI Safety Fundamentals Fellowship
MIT AI Alignment (MAIA). Introductory fellowship on technical AI safety.
- Princeton Astrophysics Undergraduate Summer Research Program (USRP)
Summer research school in astrophysics at Princeton.
- Princeton Summer School in Geometry & Topology
NSF RTG summer school and mini-conferences at Princeton Mathematics.
- Engineering Summer Academy at Penn (ESAP) High school
University of Pennsylvania School of Engineering and Applied Science.
- European Summer Program on Rationality (ESPR) High school
Immersive workshop on applied rationality for mathematically talented students.
- Yale Young Global Scholars (YYGS) High school
Summer academic enrichment program. I later returned as a seminar instructor.
Courses I took
Princeton (28 courses)
Mathematics, physics, astrophysics, economics, and more. Textbooks and resources included wherever I have them.
MAT 217
Honors Linear Algebra
Axler, Linear Algebra Done Right
MAT 335
Analysis II: Complex Analysis
Stein, Complex Analysis
MAT 340
Applied Algebra
Armstrong, Groups and Symmetry
MAT 365
Topology
Munkres, Topology
MAT 377
Combinatorial Mathematics
MAT 385
Probability Theory
Koralov & Sinai, Theory of Probability and Random Processes
MAT 457
Algebraic Geometry
Shafarevich, Basic Algebraic Geometry I
MAT 550
Differential Geometry
MAT 560
Algebraic Topology
Hatcher, Algebraic Topology
PHY 106
Electromagnetism
Purcell, Electricity and Magnetism, 3rd ed.
PHY 205
Classical Mechanics
Lagrangian formulation of mechanics.
Landau & Lifshitz, Mechanics
PHY 208
Principles of Quantum Mechanics
Griffiths & Schroeter, Introduction to Quantum Mechanics, 3rd ed.
PHY 301
Thermal Physics
Thermodynamics and statistical mechanics.
Schroeder, An Introduction to Thermal Physics
PHY 509
Quantum Field Theory
Peskin & Schroeder, Quantum Field Theory
PHY 539
Gravity and Quantum Mechanics
Taught by Edward Witten.
PHY 563
Cosmology
Peebles, Principles of Physical CosmologyMukhanov, Physical Foundations of Cosmology
AST 204
Topics in Modern Astronomy
Introductory astronomy; skipped the assigned textbook.
AST 303
Research Methods in Astrophysics
PHI 201
Introductory Logic
ECO 310
Microeconomic Theory: A Math Approach
ECO 462
Portfolio Theory and Asset Management
EGR 219
Professional Responsibility & Ethics
EGR 395
Venture Capital & Finance of Innovation
NES 365
Modern Iran
GLS 336
Indian Democracy
GLS 318
Vienna: Birthplace of Psychoanalysis
MUS 316
Computer & Electronic Music Composition
Graduate coursework
Harvard & MIT (8 courses)
APMTH 220 Harvard
Geometric Methods in Machine Learning
APMTH 226 Harvard
Theory of Neural Computation
MIT 6.7930 MIT
Machine Learning for Healthcare
APMTH 201 Harvard
Physical Mathematics
APMTH 210 Harvard
Algebraic Fundamentals of Representing Data
MATH 230A Harvard
Differential Geometry
Taubes, Differential Geometry: Bundles, Connections, Metrics and Curvature
STAT 210 Harvard
Probability I
MIT 9.390 MIT
Language in the Mind and Brain
Research
Where I have worked
- Researcher Harvard UniversityJul 2025 – present
Developing a framework using learnable finite differential forms for point-cloud representation learning, motivated by oversmoothing in graph neural networks.
- Researcher Harvard UniversityJun 2024 – present
Implemented and proved a persistent cup-length algorithm extending persistent homology; demonstrated toroidal structure in grid cell population activity, supporting continuous attractor network models of spatial navigation.
- Researcher MIT, Brain and Cognitive SciencesJul 2024 – Feb 2025
Analyzed representational alignment in language and vision models using curvature as a geometric metric.
- ML Intern Apple Inc., Camera & PhotosJun 2022 – Aug 2022
Proposed and implemented a music source separation model; presented work to Apple's VP of Camera & Photos.
- Senior Thesis Researcher Princeton University, MathematicsSept 2022 – May 2023
Computational experiments establishing conjectures relating hyperbolic volume, knot determinant, and total rank of knot Floer homology.
- Researcher Princeton University, PhysicsJan 2022 – May 2022
Built ML models predicting solar wind minimal value of the z-component of the magnetic field from coronal mass ejection observations.
- Researcher MIT, Brain and Cognitive SciencesJul 2021 – Feb 2022
Designed a self-paced reading study on repeated sentence presentation and language processing.
- Researcher Princeton University, AstrophysicsFeb 2020 – Jan 2022
Developed parallelized transit-timing code for 382 planets; contributed to discovering NGTS-11c.
Honors & conferences
Accomplishments
- NSF Graduate Research Fellowship (2023)
A highly competitive U.S. federal fellowship that funds graduate study in science and engineering for three years.
- Harvard Graduate School of Arts and Sciences Prize Fellowship (2023)
A merit-based fellowship awarded to outstanding incoming doctoral students at Harvard GSAS.
- Inducted into Sigma Xi honor society, Princeton Mathematics Department (2023)
Membership in Sigma Xi, the scientific research honor society, recognizes distinguished research achievement.
- Alberto Santos-Dumont Prize for Innovation, Princeton Office of the Dean of Undergraduate Students (2022)
A Princeton prize for undergraduate projects that demonstrate exceptional creativity and innovation.
- Manfred Pyka Memorial Prize in Physics, Princeton Department of Physics (2021)
The Princeton physics department's prize for outstanding achievement by an undergraduate physics student.
- All-Russian National Astronomy Olympiad: top 3 in state, top 50 nationally (2018, 2019)
- All-Russian National Physics Olympiad: bronze medalist (2019)
- Poster presentation, LOGML (London Geometry and Machine Learning), Imperial College London (2026).
- Research talk, Young Topologists Meeting , Stockholm (2026).
- Invited research talk, Computational Geometry Week , Japan (2026).
- Poster presentation, Exoplanets IV meeting , Las Vegas (2022).
The rest of the universe
Creative & public work
Research is one lane. Explore the others.