# Mykhaylo Shkolnikov

## Professor

**Address:**

6128 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

412-268-2545

# Education

Ph.D., Stanford University

Postdoctoral Appointments:

- Department of Statistics, UC Berkeley
- Mathematical Sciences Research Institute, Berkeley

# Awards

- Early Career Prize by the Activity Group on Financial Mathematics & Engineering at the Society for Industrial and Applied Mathematics (SIAM)
- Erlang Prize by the Applied Probability Society of the Institute for Operations Research and the Management Sciences (INFORMS)
- E. Lawrence Keyes, Jr./Emerson Electric Co. Faculty Advancement Award by the School of Engineering and Applied Science, Princeton University
- Princeton Engineering Commendation List for Outstanding Teaching

# Research

At the moment, I am studying interacting particle systems arising in mathematical finance, mathematical physics, and neuroscience using tools from stochastic analysis and PDE/SPDE. More broadly, my interests include a variety of topics in probability theory and PDEs: random operators, integrable probability, models of random growth, concentration of measure, large deviations, and probabilistic approaches to PDEs.

# Select Publications

Almada Monter, S. A., Shkolnikov, M., Zhang, J. (2019). Dynamics of observables in rank-based models and performance of functionally generated portfolios. *Ann. Appl. Probab.* **29**, 2849-2883.

Avanesyan, L., Shkolnikov, M., Sircar, R. (2020). Construction of forward performance processes in stochastic factor models and an extension of Widder’s theorem. Finance Stoch. **24**, 981-1011.

Nadtochiy, S., Shkolnikov, M. (2020). Mean field systems on networks, with singular interaction through hitting times. *Ann. Probab.* **48**, 1520-1556.

Delarue, F., Nadtochiy, S., Shkolnikov, M. (2022). Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness. *Probab. Math. Phys.* **3**, 171-213.

Lacker, D., Shkolnikov, M., Zhang, J. (2020). Inverting the Markovian projection, with an application to local stochastic volatility models. *Ann. Probab.* **48**, 2189-2211.

Baker, G., Shkolnikov, M. (2022). Zero kinetic undercooling limit in the supercooled Stefan problem. *Ann. Inst. Henri Poincaré Probab. Stat.* **58**, 861-871.

Lacker, D., Shkolnikov, M., Zhang, J. (2023). Superposition and mimicking theorems for conditional McKean-Vlasov equations. *J. Eur. Math. Soc.* **25**, 3229-3288.

Kaushansky, V., Reisinger, C., Shkolnikov, M., Song, Z. Q. (2023). Convergence of a time-stepping scheme to the free boundary in the supercooled Stefan problem. *Ann. Appl. Probab.* **33**, 274-298.

Nadtochiy, S., Shkolnikov, M., Zhang, X. (2021). Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem. To appear in *Ann. Inst. Henri Poincaré Probab. Stat.*

Baker, G., Shkolnikov, M. (2022). A singular two-phase Stefan problem and particles interacting through their hitting times. *Submitted*.

Nadtochiy, S., Shkolnikov, M. (2023). Stefan problem with surface tension: global existence of physical solutions under radial symmetry. *Probab. Theory Related Fields* **187**, 385-422.

Mustapha, S., Shkolnikov, M. (2023). Well-posedness of the supercooled Stefan problem with oscillatory initial conditions. *Submitted*.

Guo, Y., Nadtochiy, S., Shkolnikov, M. (2023). Stefan problem with surface tension: uniqueness of physical solutions under radial symmetry. *Submitted*.

Shkolnikov, M., Soner, H. M., Tissot-Daguette, V. (2023). Deep level-set method for Stefan problems. *Submitted*.