My advisors are Alexei Novikov and Yuri Suhov. My interests cover several topics in partial differential equations and probability, including stochastic processes, random matrices, KPZ equations, etc.

From Gowers’ Blog

One of the holy grails of mathematics is to prove universality, which basically says that if you stand back from a self-avoiding walk so that the mesh of the lattice is too small for you to see it, then you will not be able to tell what the model is.

The large-scale behaviour of a statistical system should be largely insensitive to the precise small-scale geometry of that system, after normalising some key parameters.

Check out my publication list (currently empty).

### Notes

These include conference notes, research notes, or any significant notes that I want to write down to better understand the materials. Every note will have a respective blog post; I will sometimes $\LaTeX$ the notes for convenience. Mistakes are unavoidable, but I will write anyway.

Topic (Blog Post) |
PDF (if available) |
---|---|

KPZ Equation and Related Topics | Download |

Random Media Summer School at Colorado State | Download |

IPAM 2018 (Random Matrices) - Conference Notes | Download |

Free Probability | Download |

Stochastic Analysis | Download |

Malliavin-Stein approach - Ivan Nourdin | Download |

### Random Notes

(these are shorter notes with less specific topic, sometimes a quick proof, sometimes outside of my main research line or even in other subjects)

**math.AG - Algebraic Geometry**

**math.AT - Algebraic Topology**

**math.AP - Analysis of PDEs**

**math.CT - Category Theory**

**math.CA - Classical Analysis and ODEs**

**math.CO - Combinatorics**

**math.AC - Commutative Algebra**

**math.CV - Complex Variables**

**math.DG - Differential Geometry**

**math.DS - Dynamical Systems**

**math.FA - Functional Analysis**

**math.GM - General Mathematics**

**math.GN - General Topology**

**math.GT - Geometric Topology**

**math.GR - Group Theory**

**math.HO - History and Overview**

**math.IT - Information Theory**

**math.KT - K-Theory and Homology**

**math.LO - Logic**

**math.MP - Mathematical Physics**

**math.MG - Metric Geometry**

**math.NT - Number Theory**

**math.NA - Numerical Analysis**

**math.OA - Operator Algebras**

**math.OC - Optimization and Control**

**math.PR - Probability**

**math.QA - Quantum Algebra**

**math.RT - Representation Theory**

**math.RA - Rings and Algebras**

**math.SP - Spectral Theory**

**math.ST - Statistics Theory**

**math.SG - Symplectic Geometry**

Topic (Blog Post) |
Category |
PDF (if available) |
---|---|---|

A seemingly innocent conjecture | math.CO, math.PR | Download |