Having grown up in East Los Angeles, California, Dr. Erika Camacho understands many of the struggles that students and women of color must endure in striving to attain their academic and professional goals. Dr. Camacho will be sharing her life experiences and the challenges she had to overcome to help her achieve her personal and professional goals. She will share stories about the key individuals and decisions that contributed to her success and transformation, including highlights of her research and the adversities she faced. Dr. Camacho will also share her passion for social activism and continual drive to transform the world of academia and strengthen our communities. Her life story is full of insights and lessons of empowerment for all. 

There will be a small reception for the speaker at 4pm. Please RSVP by either signing up or emailing apantano@uci.edu by March 31st.

Dr. Erika T. Camacho received her B.A. in Mathematics and Economics from Wellesley College in 1997 and her Ph.D. in applied mathematics at Cornell University in 2003. She is currently an Associate Professor in the School of Mathematics and Natural Sciences at Arizona State University. Her leadership, scholarship, and mentoring have won her national recognition including the SACNAS Distinguished Undergraduate Mentoring Award in 2012, the Hispanic Women Corporation (HWC) National Latina Leadership Award in 2011, recognition as one of 12 Emerging Scholars of 2010 by Diverse: Issues in Higher Education, and a citation for mentoring and guiding undergraduates in research by the U.S. National Security Agency, among others. In addition to maintaining a high-profile research activity, Dr. Camacho has embraced a lifelong journey to change the landscape of the field of Mathematics by greatly diversifying it. 

Partial differential equations posed on surfaces arise in mathematical models for many natural phenomena:  diffusion along grain boundaries, lipid interactions in biomembranes, pattern formation, and transport of surfactants on multiphase flow interfaces to mention a few. Numerical methods for solving PDEs posed on manifolds recently received considerable attention. In this talk we review some existing approaches and focus on an Eulerian finite element method for the discretization of elliptic and parabolic partial differential equations on surfaces which may evolve in time. The method uses traces of volume finite element space functions on a surface to discretize equations posed on the surface. The approach is particularly suitable for problems in which the surface is given implicitly by a level set function and in which there is a coupling with a problem in a fixed outer domain. If the surface evolves, then we employ space-time finite elements for a space-time weak formulation of a surface PDE problem. The talk presents analysis and demonstrates results of numerical experiments.
 

I will discuss the homogenization of periodic oscillating Dirichlet
boundary problems in general domains for second order uniformly elliptic
equations. These problems are connected with the study of boundary layers
in fluid mechanics and with the study of higher order asymptotic expansions
in interior homogenization theory. The talk will be aimed at a general
audience. I will explain some recent progress about the continuity
properties of the homogenized problem which displays a sharp contrast
between the case of linear and nonlinear interior equations. This is based
on joint work with Inwon Kim.

We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal conjectured bound in terms of the length of  the cut locus of a point on the surface. We also prove that the natural extension of the conjecture to general dimension holds among closed convex spherically symmetric Riemannian manifolds. Our results are based on a new symmetrisation procedure which we believe to be interesting in its own right.

This is joint work with Pedro Freitas accepted for publication in the Tohoku Mathematical Journal, preprint on http://arxiv.org/abs/1406.0811.