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DTSTAMP:20260328T185905
DTSTART;TZID=America/Detroit:20260402T160000
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SUMMARY:Workshop / Seminar:GEOMETRY SEMINAR.  Representations of quadratic forms via homogeneous dynamics II
DESCRIPTION:Let $q\,Q$ be two integral quadratic forms in $m < n$ variables. One can ask when $q$ can be represented by $Q$ - that is\, whether there exists an $n \times m$-integer matrix $T$ such that $Q \circ T = q$. Naturally\, a necessary condition is that such a representation exists locally\, meaning over the real numbers and modulo $N$ for every positive integer $N$. In the absence of local obstructions\, does a (global) representation of $q$ by $Q$ exist? This question is particularly delicate when the codimension $n-m$ is small\, with codimension $2$ being the most challenging.\n\nIn this second talk\, we discuss joint work with Wooyeon Kim and Pengyu Yang where we establish a local-global principle for representations of binary by quaternary quadratic forms (when $m=2$ and $n=4$) . Our proof uses a recent measure rigidity result of Einsiedler and Lindenstrauss for higher-rank diagonalizable actions on homogeneous spaces combined with soft methods in number theory. Both talks are aimed at a general dynamical audience.\n\nNote that Wieser will give a more introductory talk in the RTG Geometry\, Topology\, Dynamics on Wednesday.
UID:144724-21895766@events.umich.edu
URL:https://events.umich.edu/event/144724
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3866
CONTACT:
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