good evening i mean van stap and i welcome your science for the public's contemporary science issues and innovations program tonight we learn how geometry determines what is possible in structure and in motion our guests our professors strain you and keep for chat both on fellowships this year at radcliffe institute for advanced research their project at radcliffe institute is a book that explains the geometry behind everything from can few men and robotic motion to protein folding expansion of crystals and numerous other things dr steyn who is the charles clarke professor of computer science and mathematics at smith college and that's juice it's she is also a fellow of the american mathematical society has received many awards dr keep on board is professor of mathematics and applied sciences at rider university in new jersey and his award winning work in algebraic geometry has contributed significantly to the understanding of structure and motion in animate and in an unmet forms number of fields including robotics it's an honor to welcome dr strange and dr both welcome could you give us a little background about since you deal with both structure and motion leave it provides the mathematical tools to think about it ok they had so would it be fair to say then that there is a geometry underlying all of this stuff so that it's a question of say motion in terms of motion how does that geometry influence what is possible in motion the constraints are asked you have a distinct comprehensive approach there see seems to be a trend now toward multi disciplinary research and development of things robotics would be a very good example perhaps but you have pursued this approach of being much more comprehensive could you give us a just a rough idea of what that includes st of all none of us started this applied none of us started in robotics or in engineering or so we were both interested in mathematical questions and by the way we're also working in quite these joint areas of mathematics it is the challenge that the problem we were facing we we that we could address these problems then we found that these problems actually came i would engineering competition biology in my tito science so it is not that we started there it's we learned that these problems have relevant in those fields in the new start treaty and then you discover new questions and then you talk to people yeah right and as always there's a mixture of  success with it with one problem encourages you to look at that other problems and of course mathematics is with structures or with add abated forms but with where these kinds of principles are sort of really important really helpful yes probably   and you start breeding and then yes this is a little bit of a piece of a big bone of a protein consists in the number of atoms in the atoms cannot move arbitrarily they are constrained by some bonds yes so it started in this way and then we started talking with people and the explanation this is the kind of mathematics we want to apply to a problem this is the kind of analysis we want to need physics and yes chemistry so you started out by just talking with other people and discovered that you had many contributions in a way think yes contributions in a way thing t refined language and simplifying language for for putting together a multitude of in direct of what you were looking for right i think that double helix is a wonderful example it's a familiar one for one thing for people but they had to work to find out what that structure was that was a most important thing we were talking a little bit before about things like just motion we take this for granted but in fact there are underlying restrictions on how animate things might move and you get to the mathematics can you tell us anything about that that so let's use the molecules again ok so the  functions in our bodies and those functions depend both on the structure on the shape they also depend on the motion so there are some molecules for instance in the cell that that move to allow certain processes to happen and if you inhibit that motion you may stop that process so it may be the case that you want to stop the action for instance if there is a disease where the action exactly is facilit is that there might be a set of restrictions geometric restrictions that feed a great number of actual applications is that your idea ye other so what is it the constraints in this motion are so that this is the whole motion is the term it is called one degree of freedom it's a single trajectory that it can have that is what was the term again structural element that we are trying to discover that is one thing ok the other structural thing is that when parts move some of these parts are strictly are moving together yes for situation at least in imagination you can see more easily perhaps what are the key factors and and then you can but less is more can be can be fruitful yet finding at the same time how fruitful busy this combination of your talents is have you worked together for a long the revelations coming out that could make what have been your favorites like your your your things that have been most exciting there are a few examples the best examples are problems that can be stated very easily yeah but that's worth getting yet so you learn about the problem is so simple to state it starts becoming an observation they should t he starts folding this or but you are interested in if things get too close to each other they may collide right so we want to know how what is the maximum distance to which two atoms for instance yes can get given the constraints of the backbone of the protein right it's a problem that has been robotics his beliefs forty years ago there where experiments that were experimental information  or rather yeah validation of certain assumptions but together working together we were able to get a very very simple mathematical discr and that's also it has lead to breakthroughs can you tell us about anything that you've had thought was particularly rewarding in that an example that where you made one of these discoveries  materials science for example was a huge field and they need that very much so it really informs that we don't have a lot of time left and i need to ask you about your book project could you give us an idea of what it is it is about explaining all their abstract mathematics and all the concepts distilling them to the simplest way want to insert there i don't know if it's common knowledge but when einstein worked on i think was on when general relativity he needed a particular kind of math that he didn't know and so coming up i think i'm thinking of matrix math but i may be in the wrong but he needed something different to explain it so you could be brilliant in one field and so this is the problem today that there or sometimes that that is what what we found is a challenge in addressing all this question right so in writing your book you're writing this these principles or whatever yes maybe not necessarily the equations or something but the principles for people that are in sciences that will find these things useful that's just what they're looking for yes and fortunately way you think about these different problems which we believe so up we value and you have to look back and see that most major discoveries are done by people who are not mrs certainly you know one right right so if it is a general principle yeah it had to be more wide or recognizable right i think it sounds wonderful i hope that your book is a big success i'm sure that it will be it sounds like it's very timely kind of project and i envy you your bill billeted to get at the very base of a great number of problems thank you very much for joining us and for giving us this wonderful information think you even thank