Each of the above metrics can be uniquely extended to, and completing yields the field of real numbers in the archimedean case, and the -adic fields for each prime. It implies that all triangles are isosceles, and for any two balls with nonempty intersection, one contains the other. ![]() The -adic metrics (unique up to normalization) are called ultrametrics, because they satisfy the following strengthening of the triangle inequality. The standard archimedean metric is the one we learn in grade school, and for each prime, there is also a -adic metric, where is the largest such that if it exists, and if. It’s well-known that the ring of integers admits infinitely many structures of a metrized topological ring. I’m new to this blog-posting thing, so let me know if I’ve committed a Web 2.0 faux pas. ![]() It’s just a collection of standard facts about -adic fields and counterexamples. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.Nothing in this post is particularly new, but I felt that it should be written in HTML somewhere. The scientific scope of AGNES is greatly enriched by lectures from neighboring mathematical subjects, such as arithmetic geometry, dynamics, complex geometry, and computational geometry. At the same time algebraic geometry has found important applications in many subdisciplines of applied mathematics, including cryptography, complexity theory, mathematical biology, and computer vision. It has deep connections to many other areas of pure mathematics, such as topology, arithmetic, number theory, differential geometry, dynamical systems, and homological algebra. Further information about conference events can be found at the website: Algebraic geometry is a field in the mathematical sciences concerned with solution sets of polynomial equations. This award will allow AGNES to continue to excel at its research goal while broadening the scope and diversity of outreach activities. Second, each conference includes several activities designed to support under-represented groups and junior participants, such as panel discussions or networking events. ![]() The centerpiece of each conference is a series of research lectures by top mathematicians there are also educational talks for graduate students and events which promote new collaborations or develop peer relationships. First, each conference promotes the dissemination of cutting-edge research in mathematics. This award supports six AGNES conferences which will be held at Stony Brook University on March 27-29, 2020, at the University of Pennsylvania in Fall 2020, at Brown University in Spring 2021, at Boston College in Fall 2021, at Rutgers University in Spring 2022, and at the University of Massachusetts Amherst in Fall 2022. The conference is hosted on a rotating basis by an association of universities in the Northeast region. ![]() The Algebraic Geometry Northeastern Series (AGNES) is a series of biannual conferences in the field of algebraic geometry.
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