BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:Mathematics Colloquium | From Linear Codes to Noncommutative Al gebra\, March 28\n\nThe Mathematics Colloquium series features Miodrag Iova nov from the University of Iowa discussing "From Linear Codes to Noncommuta tive Algebra" on Tuesday\, March 28\, from 4-5 p.m. via Zoom.\n\n \n\nAbstr act: One of the landmark results that sits at the foundations of a part of coding theory is MacWilliams' Extension Theorem on linear codes. A linear c ode can classically be defined simply as a linear subspace of the n-dimensi onal vector space over the field with two elements. Codes have quickly prov ed to be useful over other finite fields and even finite rings\, at which p oint it became clear\, through work of J.A.Wood\, that the above mentioned fundamental property is very tightly related to the notion of Frobenius alg ebras. Frobenius rings go back to work of - well\, Frobenius - as well as N akayama\, and play a central role in groups and quantum groups. It turns ou t that the categorical properties of these rings are still tightly related to a general version of the Extension property\, which can be rephrased in homological terms. These general considerations (of "Infinite Linear Codes" ) lead to some surprising new results in non-commutative rings\, tied to wo rk of S. Lopez-Permouth and others. \n\nhomological terms. These general c onsiderations (of "Infinite Linear Codes") lead to some surprising new resu lts in non-commutative rings\, tied to work of S. Lopez-Permouth and others . DTEND:20230328T210000Z DTSTAMP:20241005T072910Z DTSTART:20230328T200000Z LOCATION: SEQUENCE:0 SUMMARY:Mathematics Colloquium | From Linear Codes to Noncommutative Algebr a\, March 28 UID:tag:localist.com\,2008:EventInstance_42729264120270 URL:https://calendar.ohio.edu/event/mathematics_colloquium_from_linear_code s_to_noncommutative_algebra_march_28 END:VEVENT END:VCALENDAR