If you are interested, you can find more details in my PhD thesis: Īlso, at the moment, I am working on a control problem in robotics. Although we built a 3d printed prototype, I believe that this gripper can be manufactured for different applications. We used these singularities to build a compliant gripper that can have angular and parallel grasping capabilities. We can thus deduce that the mecanism has singularities between these modes (which are nothing but the singularities of the algebraic variety corresponding to its motion). Concepts from algebraic geometry (such as prime decomposition of ideals) tell us that this mechanism can have three different kinds of degrees of freedom (called operation modes in the kinematics lingo): two rotations and a translation. One of the examples that I can give you is the kinematic analysis of a simple four-bar linkage with equal link lengths. I used computational algebraic geomtery (CAG) to analyse them. I finished my PhD last year and it was on the kinematic analysis of some special robots. I'm really trying to do some soul searching here and you could really help me with it. Thank you so much! I really appreciate your help. I don't think I have the knowledge of AG to understand the details, so I am more interested in the statement of the "real"-life problem and the non-trivial result of its mathematical modelling using concepts in algebraic geometry. I think you would really answer my question if you could give me an example of a real life problem (not in excessive detail) that was solved thanks to techniques of algebraic geometry. I'm very much interested in algebraic geometry (and I am being honest when I say that it is one of the rare things that makes me truly giddy thinking about it). My question is: If I changed my mind, applied to do a graduate degree in mathematics and decided to work in a field outside of academia, would I have useful applications of what I studied (and not just a tiny fraction of what I studied, e.g. something is a "group", but the recognition that it is was completely useless since the application did not produce a result that would have been otherwise unknown. Galois theory, I got two sorts of answers:Īn application of the concept in another area of mathematics.which is not what I was looking for.Ī trivial application where a physical/computational/etc system is "modelled" with the concept, e.g. One of the reasons was that, seeing my professors, it seemed that mathematicians were very much living in a world of their own and every time I asked for an application of what I was studying, e.g. However, every once in a while I have doubts about my decision because it was made on more than one basis, i.e. I decided not to proceed with math and am continuing on to a professional degree. I did my undergraduate degree in mathematics, taking a pretty heavy course load in theoretical math and doing really well in it. The Journal of Algebraic Geometry is sponsored by Tsinghua University and is distributed by the American Mathematical Society for University Press, Inc.Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. Submission information can be found on the journal's Initial Submissions page. Subscription information is available here. Indexing: This journal is indexed in Science Citation Index™-Expanded, ISI Alerting Services, CompuMath Citation Index®, and Current Contents®, Physical, Chemical & Earth Sciences. In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. JAG Home Author Packages Initial Submissions Where to send files for accepted papers Consent to Publish and Copyright Agreement Manuscript tracking Editorial Board Subscribe from the AMS Bookstore License agreement
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