Topics

-Regularity Theory for Maximal Functions: Boundedness and continuity of maximal operators on Sobolev spaces and BV spaces, including the classical maximal operators of Hardy-Littlewood, fractional maximal operators, maximal operators of convolution type and non-tangential maximal operators.

-Discrete Analogues in Harmonic Analysis: discrete Hardy Littlewood maximal operators, discrete averaging operators along polynomial, averaging operators along primes, maximal functions on graphs, etc.

-Classical Fourier Analysis: Optimal autocorrelation inequalities, decoupling inequalities, Beurling-Selberg extremal problems, etc.

-Other topics on the interface between analysis and number theory/ergodic theory/combinatorics: Generalized Collatz conjecture, Roth type theorems, generalized additive energy, etc