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PRODID:Faculty of Science and Engineering - Research
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SUMMARY:Ian Morris (QMUL): Projections of self-affine fractals
DESCRIPTION;ENCODING=QUOTED-PRINTABLE: A landmark 1988 theorem of Falconer gave a formula for the Hausdorff dimensions of self-affine fractals which are "typical" in a certain measure-theoretic sense. I will describe some joint work with Çağrı Sert in which we extend Falconer's result to the linear images of self-affine fractals. Our result is more algebraically delicate than Falconer's: we show that the dimension of the image depends nontrivially on the algebraic group generated by the underlying affine transformations, and in particular depends on the position of the projection's kernel within an associated invariant filtration of the Grassmannian. Some other consequences of the result include new examples of fractal sum sets with a dimension drop, and new examples of dynamically natural measures which are not exact-dimensional.=0D=0A=
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LOCATION:MB-503
DTSTART:20261015T130000
DTEND:20261015T140000
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