In this talk I will begin by reviewing classical geometric properties of constant mean curvature surfaces, H>0, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 with constant mean curvature, such as curvature and radius estimates. Finally I will show applications of such estimates including a characterisation of the round sphere as the only simply-connected surface embedded in R^3 with constant mean curvature and area estimates for compact surfaces embedded in a flat torus with constant mean curvature and finite genus. This is joint work with Meeks.

In recognition of a lifetime's contribution across the mathematical sciences, we are initiating a series of annual Public Lectures in honour of Roger Penrose. The first lecture will be given by his long-time collaborator and friend Stephen Hawking.

Registration will open at 10am on 4 January 2017. Please email:

@email from that time only.

When registering please give your name and affiliation - your position, department & organisation/institution as appropriate. Or if you are a member of the General Public, please say so. Places will be allocated on a first come, first served basis with only one place per person. We will only be able to respond if you have a place or are on the waiting list.

We will be podcasting the lecture live. More details to follow.

What can fashionable ideas, blind faith, or pure fantasy have to do with the scientific quest to understand the universe? Surely, scientists are immune to trends, dogmatic beliefs, or flights of fancy? In fact, Roger Penrose argues that researchers working at the extreme frontiers of mathematics and physics are just as susceptible to these forces as anyone else. In this lecture, based on his new book, Roger will argue that fashion, faith, and fantasy, while sometimes productive and even essential, may be leading today's researchers astray, most notably in three of science's most important areas - string theory, quantum mechanics, and cosmology. Yet Roger will also describe how fashion, faith, and fantasy have, ironically, also been invaluable in shaping his own work.

Roger will be signing copies of his book after the lecture.

This lecture is now SOLD OUT. Any questions, please email: @email

I will discuss on the existence and regularity results for the heat flow of the so called H-systems and for more general parabolic p-laplacian problems with critical growth.