My advisors are Alexei Novikov. 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 |

Gaussian Correlation Inequality | math.PR | Download |