Posts by Topic

Additive Combinatorics

Effective results on the size and structure of sumsets

A large gap in a dilate of a set

An Analytic Approach to the Cardinality of Sumsets

The Frobenius Postage Stamp Problem, and Beyond

Recent Progress on a Problem of Sárközy

Sidon-like Sets

Exponential Sums over Small Subgroups

Entropy and Sumsets: An example

Sum of a set and its dilate

Breaking the 6/5 threshold for sums and products modulo a prime

Monochromatic Hilbert cubes and arithmetic progressions

Covering sumsets and Plünnecke’s inequality

Convex sets have many differences

Convex sumsets and sum-product estimates

On higher energy decompositions and the sum-product phenomenon

Konyagin-Shkredov Clustering

Lattice Points in Symmetric Convex bodies

A question related to sum-product (A personal favorite)

Discrete Fourier transform (with applications to number theory)

Distinct consecutive r-differences

Number Theory

Quantitative Hilbert irreducibility and almost prime values of polynomial discriminants

On generating functions in additive number theory, II: Lower-order terms and applications to PDEs

Spacing of Quadratic Fractions

Fractal solutions of dispersive partial differential equations on the torus

Elementary techniques in a special case of Vinogradov’s mean value theorem 

An introduction to Vinogradov’s mean value theorem

Counting lattice points

A lower bound for the least prime in a arithmetic progression

Gaps between prime-like sets

Lattice Points in Symmetric Convex bodies

Breaking the Square root Barrier via the Burgess Bound

Harmonic Analysis

A short proof of the Hardy-Littlewood maximal inequality

Getting a lower bound for an L1 norm using higher moments

Gauss Sums and Hausdorff-Young

Poisson summation and the heat equation

Convergence near the boundary

Holder’s Inequality

Functional Analysis

Closed Unit Ball and Quotient Maps

A problem with sequences

Uniform boundedness and Fourier series

Probability

Some basics of entropy

Two types of convergence in probability

Complex Analysis

Cauchy’s integral formula and harmonic analysis

Riemann Surfaces

A genus calculation for quotients of upper half plane

Algebraic Number Theory

Prime ideals in number fields

Topology

Kuratowski Closure and Topological Spaces