Abstract:
Associating a “canonical form” associated to a semi-algebraic region in the complex points of an algebraic variety, whose poles lie along its boundary, has recently risen in popularity. In this talk I will introduce the notion of "canonical function" associated to two such regions. In brief, it is a rational function which has *poles* along the boundary of the first region, and *zeros* along the boundary of the second region. Associated to this data is a canonical Picard-Fuchs recurrence relation, periods and mysterious symmetry groups. Examples constructed in this way provide rare mathematical gems: for instance Apéry’s famous approximations to zeta(2), zeta(3), surprising connections with modular forms, and much more besides.
About the speaker:
Francis Brown is a renowned mathematician recognized for his influential work in algebraic geometry, number theory, and quantum field theory. His research on multiple zeta values, periods, and the theory of motives has provided groundbreaking insights into Feynman integrals and arithmetic geometry.
The UNIVERSE+ Online Seminar Series is designed to foster dialogue and collaboration among project partners and those interested in positive geometry.
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