Raphael Tsiamis

Research

• Uniqueness of cylindrical tangent cones Cp,q× ℝ (with B. Firester and Y. Wang)
  [ arXiv ] 2025

• Classification of semigraphical translators (with F. Martín, M. Sáez, B. White)
  [ arXiv ] 2024, submitted. This paper supersedes arXiv:2310.06980. 

• Cohomogeneity two Ricci solitons with sub-Euclidean volume (with B. Firester)
  [ arXiv ] 2024, submitted

• Eigenvalue estimates on shrinkers (with S. Brendle)
  [ arXiv ] 2024, submitted

• Uniqueness of semigraphical translators (with F. Martín, M. Sáez)
  [ arXiv ] 2023, superseded by arXiv:2411.16889

Expository

Senior Thesis

Hyperkähler manifolds and Hyperkähler moduli spaces via reduction and GIT (advised by Richard Melrose and Yum-Tong Siu)
Harvard University, 2023. Awarded Highest Honors in Mathematics

Lecture Notes

• Fully nonlinear PDE, Monge–Ampère equation, and optimal transport (Spring 2024), notes from a seminar held at Columbia University.

• Analysis and Applications of Harmonic Maps (Fall 2023), notes from a course taught by Fanghua Lin at NYU.

Talks and Conferences

• Workshop "Topics in Differential Geometry", Brown University (2025, Providence, US)

• Calculus of Variations and PDE's in Geometric Analysis at Sapienza Università di Roma (2025, Rome, IT) 

• Rutgers University Geometric Analysis Seminar (2024, New Jersey, US)

• NYU Geometric Analysis and Topology Seminar (2024, New York, US)

• MFO Workshop "Analysis, Geometry and Topology of Positive Scalar Curvature Metrics" (2024, Oberwolfach, Germany)

• Geometry Seminar at the University of Granada (2024, Granada, Spain)

• Harvard Math Table (2023, Cambridge, US)

• Analysis and Geometry Seminar at the Aristotle University of Thessaloniki (2022, Thessaloniki, Greece)

• 15th Panhellenic Geometry Conference (2022, Ioannina, Greece)

Teaching

Course Instructor at Columbia University, 2025 - present

• Math UN2500: Analysis and Optimization (Summer 2025)

Teaching Assistant at Columbia University, 2024 - present

• Math UN1205: Partial Differential Equations, taught by Mu-Tao Wang (Fall 2025)

• Math UN3028: Partial Differential Equations, taught by Simon Brendle (Spring 2025)

• Math GU4032: Fourier Analysis, taught by Simon Brendle (Fall 2024)

Course Assistant at Harvard University, 2020 - 2023

• Math 212BR: Advanced Real Analysis, taught by Yum-Tong Siu  (Spring 2023)
  Awarded Derek Bok Center Certificate of Distinction in Teaching

• Math 137: Algebraic Geometry, taught by Fabian Gundlach (Spring 2022)

• Math 124: Number Theory, taught by Melanie Matchett Wood (Fall 2021)

• Math 232A: Graduate Algebraic Geometry, taught by Elden Elmanto (Fall 2020)

• Math 137: Algebraic Geometry, taught by Brooke Ullery (Spring 2020) 

Community

Seminar Organization at Columbia University 

• Lagrangian mean curvature flow (with Yipeng Wang, Fall 2025)

• Min-max theory for minimal submanifolds (with Yipeng Wang, Spring 2025)

• Regularity Theory of the Monge-Ampère equation (with Jingbo Wan and Yipeng Wang, Spring 2024)

Columbia Directed Reading Program, Mentor

• Minimal surfaces and the Weierstrass representation (mentee: Matthew Baisley, Spring 2025)

• Seiberg-Witten equations on symplectic 4-manifolds (mentee: Owen Lear, Fall 2024)

• Extremal metrics and K-stability (mentee: Zachary Lihn, Spring 2024)

• Spin geometry and scalar curvature (mentee: Michael Tulskikh, Fall 2023)

CV

• CV (last updated: September 2024)