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TZID:America/Chicago
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DTSTART:20191103T020000
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DTSTART:20200308T020000
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BEGIN:VEVENT
UID:calendar.23784.field_event_date_2.0@math.wustl.edu
CREATED:20190827T191724Z
DESCRIPTION:Abstract: Recent advances in Free Analysis have yielded remarka
ble analogs of classical theorems in analysis\, algebra and geometry. In p
articular\, the Free Inverse Function Theorem has a stronger conclusion th
an its classical counterpart while the Free Jacobian Conjecture is true an
d its proof is quite tractable.\n\nRecall that a free polynomial mapping i
n g freely noncommuting variables sends g-tuples of matrices (of the same
size) to g-tuples of matrices (of the same size). The Free Grothendieck Th
eorem asserts that an endomorphism of the free algebra is an isomorphism i
f and only if its induced polynomial mapping is injective on all g-tuples
of matrices if and only if its free Jacobian matrix is invertible over the
tensor product of the free algebra.\n\nIn this talk\, we discuss the free
rational version of the above theorem: if we have an endomorphism of the
free skew field\, then what injectivity conditions on its induced free rat
ional mapping imply the endomorphism is an isomorphism and how does this r
elate to invertibility over the tensor product of the free skew field?\n\n
Our goal is to reduce certain implications to a conjecture about the inver
tible elements of the tensor product of the free skew field: the only inve
rtible elements are the rank one tensors.\n\nHost: Brett Wick
DTSTART;TZID=America/Chicago:20191202T150000
DTEND;TZID=America/Chicago:20191202T160000
LAST-MODIFIED:20191202T152602Z
SUMMARY:Analysis Seminar: 'Free Analysis and Tensor Products of Skew Fields
: or\, the Modern Prometheus'
URL;TYPE=URI:https://math.wustl.edu/events/analysis-seminar-free-analysis-a
nd-tensor-products-skew-fields-or-modern-prometheus
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