Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming Events3-Manifold Seminar, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114774&date=2018-01-23
We'll discuss a proof that knot recognition is in NP, using a certificate that encodes a sutured manifold hierarchy.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114774&date=2018-01-23Thematic Seminar: Applied Mathematics, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114402&date=2018-01-23
Fiber-reinforced structures arise in many engineering and biological applications. Examples include space inflatable habitats, vascular stents supporting compliant vascular walls, and aortic valve leaflets. In all these examples a metallic mesh, or a collection of fibers, is used to support an elastic structure, and the resulting composite structure has novel mechanical characteristics preferred over the characteristics of each individual component. These structures interact with the surrounding deformable medium, e.g., blood flow or air flow, or another elastic structure, constituting a fluid-structure interaction (FSI) problem. Modeling and computer simulation of this class of FSI problems is important for manufacturing and design of novel materials, space habitats, and novel medical constructs.<br />
<br />
Mathematically, these problems give rise to a class of highly nonlinear, moving-boundary problems for systems of partial differential equations of mixed type. To date, there is no general existence theory for solutions of this class of problems, and numerical methodology relies mostly on monolithic/implicit schemes, which suffer from bad condition numbers associated with the fluid and structure sub-problems.<br />
<br />
In this talk we present a unified mathematical framework to study existence of weak solutions to FSI problems involving incompressible, viscous fluids and elastic structures. The mathematical framework provides a constructive existence proof, and a partitioned, loosely coupled scheme for the numerical solution of this class of FSI problems. The constructive existence proof is based on time-discretization via operator splitting, and on our recent extension of the Aubin-Lions-Simon compactness lemma to problems on moving domains. The resulting numerical scheme has been applied to problems in cardiovascular medicine, showing excellent performance, and providing medically beneficial information.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114402&date=2018-01-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Jan 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114773&date=2018-01-23
The two topics for the student portion this semester are Intersection Theory and Linkage. A detailed outline of the topics for the first half of the seminar can be found at "math.berkeley.edu/~ritvik/Eisenbud-Seminar-Outline.pdf". In the meeting we will describe the main goals of this seminar and sign-up speakers for respective topics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=114773&date=2018-01-23