学术报告
Counting the infinity: at the crossroad of algebra and analysis，Sylvie Paycha (University of Potsdam)
题目：Counting the infinity: at the crossroad of algebra and analysis
报告人： Sylvie Paycha (University of Potsdam)
摘要：Counting non-negative integers, namely evaluating the divergent expression 1 + 1 +......, can be carried out by means of various analytical regularisation methods, which lead to rather surprising and sometimes non coinciding results. Since non-negative integers correspond to the integer points on the cone [0;+1[, a natural question is how to count integer points on a higher dimensional cone. While the dimension increases, divergences accumulate leading to subdivergences in a multiple sum.
Physicists have developped sophisticated methods to deal with subdivergences, which have since then been been interpreted in mathematical terms thanks to algebraic tools such as the coproduct. The latter provides means to "undo" awkward divergences in order to reorganize subdivergences.
We shall present renormalisation methods borrowed from quantum eld theory to count integer points on polyhedral cones. This leads to conical zeta values associated with cones which generalise the usual multizeta values arising from Chen cones. Alternatively, one can generalise multizeta values to branched zeta values associated with trees. Both generalisations of multizeta functions, whether via cones or via trees, require a careful study multivariate meromorphic functions with linear poles, which also arise in quantum field theory. We generalise the notion of residue and Laurent expansion to this class of multivariate functions. This is based on joint work with Li Guo and Bin Zhang.
时间：8月22日（周一）上午10:30-11:30
地点：首都师范大学北一区707教室
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