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.

Check out my publication list (currently empty).

### Research diary

### 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) |
---|---|

Schrammâ€“Loewner Evolution | Download |

KPZ Equation and Related Topics | 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 on less specific topics, sometimes a quick proof, sometimes outside of my main research line or even in other subjects)

≡ Mathematics Categories (borrowed from arXiv)

**math.AG - Algebraic Geometry**

Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology

**math.AT - Algebraic Topology**

Homotopy theory, homological algebra, algebraic treatments of manifolds

**math.AP - Analysis of PDEs**

Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics

**math.CT - Category Theory**

Enriched categories, topoi, abelian categories, monoidal categories, homological algebra

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

Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics

**math.CO - Combinatorics**

Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory

**math.AC - Commutative Algebra**

Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics

**math.CV - Complex Variables**

Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves

**math.DG - Differential Geometry**

Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis

**math.DS - Dynamical Systems**

Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations

**math.FA - Functional Analysis**

Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory

**math.GM - General Mathematics**

Mathematical material of general interest, topics not covered elsewhere

**math.GN - General Topology**

Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties

**math.GT - Geometric Topology**

Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures

**math.GR - Group Theory**

Finite groups, topological groups, representation theory, cohomology, classification and structure

**math.HO - History and Overview**

Biographies, philosophy of mathematics, mathematics education, recreational mathematics, communication of mathematics

**math.IT - Information Theory**

Covers theoretical and experimental aspects of information theory and coding.

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

Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras

**math.LO - Logic**

Logic, set theory, point-set topology, formal mathematics

**math.MP - Mathematical Physics**

Mathematical methods in quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics

**math.MG - Metric Geometry**

Euclidean, hyperbolic, discrete, convex, coarse geometry, comparisons in Riemannian geometry, symmetric spaces

**math.NT - Number Theory**

Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory

**math.NA - Numerical Analysis**

Numerical algorithms for problems in analysis and algebra, scientific computation

**math.OA - Operator Algebras**

Algebras of operators on Hilbert space, C^*-algebras, von Neumann algebras, non-commutative geometry

**math.OC - Optimization and Control**

Operations research, linear programming, control theory, systems theory, optimal control, game theory

**math.PR - Probability**

Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory

**math.QA - Quantum Algebra**

Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory

**math.RT - Representation Theory**

Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra

**math.RA - Rings and Algebras**

Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups

**math.SP - Spectral Theory**

Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices

**math.ST - Statistics Theory**

Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies

**math.SG - Symplectic Geometry**

Hamiltonian systems, symplectic flows, classical integrable systems

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

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

Random Media Summer School at Colorado State | math.AP, math.PR | Download |