# Search Research Symposium Abstracts

Page 1 of 1

## Hessian Estimates for the Lagrangian mean curvature equation

In this talk, we will derive a priori interior Hessian estimates for the Lagrangian mean curvature equation under certain natural restrictions on the Lagrangian phase. As an application, we will use these estimates to solve the Dirichlet problem for the Lagrangian mean curvature equation with continuous boundary data on a uniformly convex, bounded [Read More...]

**Presenter:**Arunima Bhattacharya, University of Washington

**Authors:**Arunima Bhattacharya

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 17, 2022; 3:30 pm

## The-time dependent thin obstacle problem for the weighted bi-Laplacian

Time dependent equations associated with fourth order operators are used to model many physical phenomena such as plane flame propagation, and phase turbulence in reaction-diffusion systems. They also appears in thin film theory to model long waves on a viscous fluid. We will present our work on a time dependent thin obstacle problem associated with the [Read More...]

**Presenter:**Alaa Haj Ali, Arizona State University

**Authors:**Alaa Haj Ali

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 17, 2022; 3:55 pm

## Regularity of edges in image processing

Edge detection is an image processing technique for finding the boundaries of objects within images. The Mumford-Shah functional was introduced by Mumford and Shah in 1989 as a variational model for image reconstruction. The most important regularity problem is the famous Mumford-Shah conjecture, which states that (in 2 dimensions) the closure of the jump [Read More...]

**Presenter:**Silvia Ghinassi, University of Washington

**Authors:**Camillo De Lellis, Matteo Focardi, Silvia Ghinassi

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 17, 2022; 4:20 pm

## Boundedness of commutators on weighted Hardy and BMO spaces

It is know that boundedness of the commutator $[b,H]$ on weighted $L^p$ spaces for $1< p< \infty$ is characterized by $b$ being in a certain BMO space adapted to the given weights. In this talk, we present the case $p=1$ and discuss the space that characterizes boundedness of $[b,H]$ on the weighted Hardy space $H^1(w)$ for certain $Ap$ [Read More...]

**Presenter:**Marie-Jose Kuffner, Johns Hopkins University

**Authors:**Marie-Jose Kuffner

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 17, 2022; 4:45 pm

## Logarithmic Sobolev inequalities on non-isotropic Heisenberg groups

We study logarithmic Sobolev inequalities with respect to a heat kernel measure on finite-dimensional and infinite-dimensional Heisenberg groups. Such a group is the simplest non-trivial example of a sub-Riemannian manifold. First we consider logarithmic Sobolev inequalities on non-isotropic Heisenberg groups. These inequalities are considered with respect [Read More...]

**Presenter:**Liangbing Luo, University of Connecticut

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 10:15 am

## Boundary Homogenization of Planes with Partially-Absorbing Patches

We investigate the capture dynamics of a Brownian particle in half-space above a reflecting plane with a periodic array of partially-absorbing patches. Prior work in this area has considered a reflecting surfaces with fully-absorbing disks. We do this via a hybrid numerical-asymptotic approach, performing matched asymptotic analysis on the survival [Read More...]

**Presenter:**Claire E. Plunkett, University of Utah

**Authors:**Claire E. Plunkett and Sean D. Lawley

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 10:40 am

## Improving and Maximal Inequalitites for Primes in Progressions

Assume that $ y < N$ are integers, and that $(b,y) =1$. Define an average along the primes in a progression of diameter $y$, given by integer $b$. $$A_{N,y,b} := \frac{\phi (y)}{N} \sum_{\substack{n < N\\n\equiv b\mod y}} \Lambda (n) f(x-n),$$ where $\Lambda$ is the von Mangoldt function and $\phi$ is the totient function. We establish improving and [Read More...]

**Presenter:**Christina Giannitsi, Georgia Institute of Technology

**Authors:**Christina Giannitsi, Michael Lacey, Hamed Mousavi and Yaghoub Rahimi

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 11:05 am

## Metalenses and Phase Discontinuity Functions

Metalenses are ultra thin surfaces that are composed of nano structures to focus light. These nano structures manipulate light waves by abrupt phase shifts over the scale of the wavelength to bend them in unusual ways. Compared to the bulky, thick shapes of the conventional lenses, metalenses offer many advantages in optical applications due to their reduced [Read More...]

**Presenter:**Irem Altiner, Temple University

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 11:30 am

## The Korányi Spherical Maximal Function on Heisenberg groups

In this talk, we will consider the problem of obtaining sharp (up to endpoints) $L^p\to L^q$ estimates for the local maximal operator associated with averaging over dilates of the Korányi sphere on Heisenberg groups. This is a codimension one surface compatible with the non-isotropic Heisenberg dilation structure. I will describe the main features of the [Read More...]

**Presenter:**Rajula Srivastava, University of Wisconsin-Madison

**Authors:**Rajula Srivastava

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 3:20 pm

## Maximal and minimal weak solutions for elliptic problems with nonlinearity on the boundary

We consider the existence of weak solutions for semilinear elliptic equation with nonlinearity on the boundary. We establish the existence of a maximal and a minimal weak solution between an ordered pair of sub- and supersolution. To prove the result, we utilize the surjectivity of a pseudomonotone and coercive operator, Zorn's lemma and a version of [Read More...]

**Presenter:**Shalmali Bandyopadhyay, University of North Carolina at Greensboro

**Authors:**Maya Chhetri, Briceyda Delgado, Nsoki Mavinga, Rosa Pardo

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 3:45 pm

## Overlaps of a spherical spin glass model with an external field

The focus of this talk will be the 2-spin spherical Sherrington Kirkpatrick (SSK) spin glass model with an external field. More specifically, I will discuss the transition between this model and the one without an external field. The talk will provide a brief introduction to the SSK model, focusing on the distribution of spins and how that distribution [Read More...]

**Presenter:**Elizabeth W. Collins-Woodfin, University of Michigan

**Authors:**Jinho Baik, Elizabeth Collins-Woodfin, Pierre le Doussal, Hao Wu

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 4:10 pm

## Reconstruction of the Shape and Boundary Condition in Inverse Scattering for an Obstacle with Partial Generalized Impedance Boundary

We consider the inverse problem of recovering the shape and boundary coefficients of an obstacle from far field measurements of the scattered field. More specifically the scatterer is impenetrable with Dirichlet boundary condition on a part of its boundary and anisotropic generalized impedance boundary condition on the complementary boundary. The latter is [Read More...]

**Presenter:**Heejin Lee, Rutgers University-New Brunswick

**Symposium Year:**2022

**Session:**Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

**Presentation Time:**June 18, 2022; 4:35 pm

Page 1 of 1