In this talk, using the local Ricci flow, we prove the short-time
existence of the Ricci flow on noncompact manifolds, whose Ricci curvature
has global lower bound and sectional curvature has only local average integral
bound. The short-time existence of the Ricci flow on noncompact manifolds
was studied by Wan-Xiong Shi in 1990s, who required a point-wise bound of
curvature tensors. As a corollary of our main theorem, we get the short-time existence part of Shis theorem in this more general context.

In this talk by using the idea in the proof of Perelman's pseudo locality theorem we will derive a local curvature bound in Ricci flow assuming only local sectional curvature bound and local volume lower bound for the initial metric.

This result is closely related to Theorem 10.3 in Perelman's entropy paper.

* Workshop for Undergraduate Students on preparing for and applying to graduate school. All levels of students are encouraged to attend. The workshop will feature a presentation on what students should do in their Sophomore-Senior years to prepare for graduate studies and how to apply for graduate school. Also, there will be a panel of current UCI students to offer advice on the application process and selecting a school.

In 1970s S.Newhouse discovered that a generic homoclinic bifurcation of a smooth surface diffeomorphism leads to persistent homoclinic tangencies, infinite number of attractors (or repellers), and other unexpected dynamical properties (nowadays called "Newhouse phenomena"). More than 20 years later P.Duarte provided an analog of these results in conservative setting (with attractors replaced by elliptic periodic points). We will discuss these and other recent results on conservative homoclinic bifurcations, and list some related open problems in the field.