Given a compact Riemannian manifold with nonnegative Ricci curvature and convex boundary it is interesting to estimate its size in terms of the volume, the area of its boundary etc. I will discuss some open problems and present some partial results.

This is a joint seminar with geometry.

The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments.
 
I ran a student internship program at Los Alamos National Laboratory for over 20 years. Recently, I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers.
 
I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can
help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life.
 
The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right. The choices you are making right now to planning your career will impact your for a lifetime.
 
Please join us for an engaging discussion on how to make the choices that
will lead to a great career.

In joint work with Daniel Hast, we recast the paper of Jon Keating and Zeev Rudnick "The variance of the number of prime polynomials in short intervals and in residue classes" by studying the geometry of these short intervals through an associated highly singular variety. We manage to recover their results for a a general class of arithmetic functions up to a constant and also obtain information about the higher moments. Recently work of Brad Rodgers in "Arithmetic functions in short intervals and the symmetric group" gives new insight into the geometry of our variety.

The Strominger system is a system of PDEs derived by Strominger in his
study of compactification of heterotic strings with torsion. It can be
thought of as a generalization of Ricci-flat metrics on non-Kähler
Calabi-Yau 3-folds. We present some new solutions to the Strominger
system on a class of noncompact 3-folds constructed by twistor
technique. These manifolds include the resolved conifold
Tot(O(-1,-1)->P1) as a special case.