I'm an assistant professor in the mathematics department at Princeton University.

I can be emailed at yshlapen AT math DOT princeton DOT edu.

My office is Fine Hall 404.

I'm an organizer of the analysis seminar here at Princeton.

PhD: MIT (2015). BS with Honors: Stanford (2010).

Partial Differential Equations, General Relativity, Geometric Analysis

Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime, Journal: [Ann. Henri Poincaré 16 (2015), is. 1, 289-345]. Exponentially growing finite energy solutions for the Klein-Gordon equation on sub-extremal Kerr spacetimes, Journal: [Comm. Math. Phys. 329 (2014), no. 3, 859-891]. (joint with Mihalis Dafermos and Igor Rodnianski) Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a| < M, Journal: [Annals of Math. 183 (2016), no. 3, 787-913]. (joint with Mihalis Dafermos and Igor Rodnianski) A scattering theory for the wave equation on Kerr black hole exteriors, Journal: [Annales scientifiques de l'ENS, 51 (2018), no. 2, 371-486]. (joint with Otis Chodosh) Stationary axisymmetric black holes with matter (2015), to appear in Communications in Analysis and Geometry. (joint with Otis Chodosh) Time-Periodic Einstein–Klein–Gordon Bifurcations of Kerr, Journal: [Comm. Math. Phys. 356 (2017), no. 3, 1155-1250]. (joint with Mihalis Dafermos) Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes, Journal: [Comm. Math. Phys. 350 (2017), no. 3, 985-1016]. (joint with Igor Rodnianski) The Asymptotically Self-Similar Regime for the Einstein Vacuum Equations, Journal: [Geom. Funct. Anal. 28 (2018), no. 3, 755-878.]. (joint with Christoph Kehle) A scattering theory for linear waves on the interior of Reissner-Nordström black holes, Journal: [Ann. Henri Poincaré 20 (2019), no. 5, 1583–1650]. (joint with Mihalis Dafermos) Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ > 0, Journal: [Classical and Quantum Gravity, 35 (2018), no. 19]. (joint with Igor Rodnianski) Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, (2019) submitted.

MAT 325, Analysis I: Fourier Series and Partial Differential Equations, Princeton-Spring 2020

DAMTP: Oct 25, 2012 FRG Mathematical GR Workshop at University of Miami: Dec 18-21, 2012 Analysis seminar at MIT: Mar 5, 2013 Analysis seminar at UPenn: Mar 12, 2013 Analysis seminar at Chapel Hill: Apr 2, 2014 Astrophysics seminar at University of Florida: Apr 18, 2014 Analysis and Applied Math seminar at University of Toronto: Mar 6, 2015 Geometry and Analysis seminar at Imperial College London: Apr 23, 2015 New York General Relativity Seminar at Columbia University: May 8, 2015 Singularities in General Relativity at the Fields Institute: Jun 17, 2015 Mathematical Problems of General Relativity (mini-symposium at EquaDiff 2015): Jul 7, 2015 Hyperbolic Equations on Spacetimes: Stability, Microlocal Analysis and Quantum Field Theory at the Erwin Schrödinger Institute: Sep 8, 2015 Analysis Seminar at Princeton University: Sep 21, 2015 Workshop on Geometric Hyperbolic PDE at Imperial College London: Oct 30, 2015 Informal Geometric Analysis Seminar at the University of Maryland: Dec 3, 2015 Geometric Analysis Seminar at the University of Oregon: Feb 2, 2016 Geometry and Analysis Seminar at Oxford University: Feb 18, 2016 Geometric Analysis and Partial Differential Equations Seminar at Cambridge University: Feb 22, 2016 Seminar at Mathematical GR Group Meeting at Queen Mary University of London: Feb 29, 2016 Section in Mathematical General Relativity at AMS meeting at Stony Brook: March 19, 2016 Geometric Analysis Seminar at Rutgers University: March 29, 2016 Analysis and PDE Seminar at Stanford: May 24, 2016 Analysis and PDE Seminar at University of Kentucky: Oct. 18, 2016 Analysis and PDE Seminar at Johns Hopkins: Oct. 31, 2016 AMS Special Session on Geometric Analysis and General Relativity: March 11, 2017 Analysis Seminar at MIT: May 2, 2017 Advances in General Relativity at the Erwin Schrödinger Institute: Aug 30, 2017 2017 FRG-PDE Meeting at Princeton University: Oct 22, 2017 Special Section on the Mathematics of Gravitational Waves at the Joint Math Meetings at San Diego: Jan 12, 2018 Special Session on Mathematical Problems of Relativistic Physics: Classical and Quantum at Northeastern: April 21, 2018 Conference on Mathematical General Relativity at IHP: May 30, 2018 ICMP section on General Relativity in Montreal: July 24, 2018 Oberwolfach: Aug 7, 2018 Analysis Seminar at Courant: Sept 27, 2018 PDE Seminar at Brown: Nov 9, 2018 Analysis and PDE Seminar at Johns Hopkins: Feb. 18, 2019 Calderón-Zygmund Analysis Seminar at Chicago: May 13, 2019

18.01A/18.02A Recitation, MIT-Fall 2014 18.02A Recitation, MIT-IAP 2015 Boston City Limits Summer School on the Geometric Analysis of Waves and Fluids, MIT Summer 2016 MAT 103, Calculus I, Princeton-Fall 2016 MAT 202, Linear Algebra with applications, Princeton-Spring 2017 Junior Seminar: Introduction to Nonlinear Wave Equations, Princeton-Fall 2017 MAT 104, Calculus II, Princeton-Spring 2018 MAT 103, Calculus I, Princeton-Fall 2018 MAT 325, Analysis I: Fourier Series and Partial Differential Equations, Princeton-Spring 2019 MAT 103, Calculus I, Princeton-Fall 2019