Title: Best constants for maximal operators Abstract: In this talk I will survey some known results concerning best constants for the Hardy-Littlewood maximal operator and it’s variants.  We will go over the sharp one dimensional theory for the uncentered maximal function. We will also talk about best constants for the dyadic maximal function and some

Title:  Everything I knew (and maybe that you know) about the Stieltjes integral is wrong. Abstract:  I will discuss three definitions of the Riemann integral (the Riemann integral, the Darboux integral, and a variant of the Darboux integral) and why they are equivalent.  I will then introduce the generalizations of these results to define the

Title:  Standing Waves of the Schrodinger Equation with Concentrated Nonlinearity   With Atanas Stefanov, we study the concentrated Nonlinear Schrodinger Equations in n-dimensions, with power non-linearities, driven by the fractional Laplacian.  We construct the solitary waves explicitly, in an optimal range of the parameters, so that they belong to the natural energy space $H^s$. We

Title: Mixed Weak-Type Estimates for Classical Operators   Abstract: We prove new mixed weak type estimates for various classical operators of Harmonic analysis. Mixed weak type inequalities were first studied by Muckenhoupt and Wheeden and later by Sawyer to prove the $L^p$ boundedness of the Hardy-Littlewood maximal operator as a consequence of the Jones factorization

Title: On the long term dynamics of the Landau-DeGennes gradient flow Abstract: We study the gradient flow of the Landau-deGennes energy functionals, in the physically relevant spatial dimensions $d=2,3$.  We establish global well-posedness and global exponential time decay bounds for large $H^1$ data in the 2D case, and uniform bounds for large data in 3D.