**Additive Combinatorics**

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

Exponential Sums over Small Subgroups

Entropy and Sumsets: An example

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

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**

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

A lower bound for the least prime in a arithmetic progression

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

**Functional Analysis**

Closed Unit Ball and Quotient Maps

Uniform boundedness and Fourier series

**Probability**

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**

**Topology**