[ALGTOP-L] Program Seminar by John Morgan: A Topologist looks at Sheaf Theory - beginning Friday October 3

Jenny Santoso jsantoso at web.de
Wed Sep 24 11:55:12 EDT 2014


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<div>Dear all,</div>

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<div>a very interesting info for all of you:</div>

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<div>Program Seminar by John Morgan: A Topologist looks at Sheaf Theory - beginning Friday October 3</div>

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<div>With warmest greetings - Jenny</div>

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<div style="margin: 0 0 10.0px 0;"><b>Gesendet:</b> Mittwoch, 24. September 2014 um 17:32 Uhr<br/>
<b>Von:</b> "Maria Froehlich" <mfroehlich at scgp.stonybrook.edu><br/>
<b>An:</b> SCGPTALKS at lists.sunysb.edu<br/>
<b>Betreff:</b> Program Seminar by John Morgan: A Topologist looks at Sheaf Theory - beginning Friday October 3</div>

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<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 3.0px;padding: 0.0px;"><span style="color: rgb(85,85,85);font-family: Arial , sans-serif;font-size: 12.0px;line-height: 1.5em;background-color: transparent;">As part of the Simons Center program, </span><font color="#555555" face="Arial, sans-serif"><span style="font-size: 12.0px;line-height: 18.0px;">Interactions of Homotopy Theory and Algebraic Topology with Physics through Algebra and Geometry, </span></font><span style="color: rgb(85,85,85);font-family: Arial , sans-serif;font-size: 12.0px;line-height: 1.5em;background-color: transparent;">John Morgan will give a series of lectures (8 to 10 lectures) on Sheaf Theory with applications to duality.  The course will be aimed at intermediate graduate students and above. The only prerequisite is a basic course in algebraic topology.</span></p>

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<div style="border: 0.0px;outline: 0.0px;font-size: 12.0px;vertical-align: baseline;margin: 0.0px;padding: 0.0px;line-height: 18.0px;font-family: Arial , sans-serif;color: rgb(85,85,85);">
<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;"><span style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px;padding: 0.0px;text-decoration: underline;background: transparent;">These lectures will be on Fridays at 2:45pm, in the Simons Center seminar room, 313 beginning Friday October 3.</span></p>

<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;"><strong style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px;padding: 0.0px;background: transparent;">Title:</strong>  A Topologist looks at Sheaf Theory</p>

<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;"><strong style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px;padding: 0.0px;background: transparent;">Abstract:</strong></p>

<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;"><span style="line-height: 1.5em;background-color: transparent;">Sheaf theory has long been an essential tool in algebraic geometry, algebraic number theory, and complex analysis, but its inspiration comes directly from topology. This lecture course will emphasize these roots, hopefully making sheaf theory seem natural to those with a topological bent. The course will begin by covering the basic topics in sheaf theory describing the objects and the four basic maps of the theory and then will culminate with a discussion of Verdier duality, which generalizes Poincare duality.</span></p>

<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;">This theory will then be applied to define a bordism theory, called duality bordism, whose coefficient group agrees with the Grothendieck group of chain complexes satisfying Poincare duality modulo those that sit as the boundary term in an exact sequence satisfying Lefschetz duality. This bordism group is the Pontryjagin dual homology theory to the cohomology theory associated with surgery theory. This means that a surgery problem is completely classified by evaluating surgery obstructions (signatures, and Arf invariants) of its restrictions to all possible duality bordism elements.</p>

<p style="border: 0.0px;outline: 0.0px;vertical-align: baseline;margin: 0.0px 0.0px 1.2em;padding: 0.0px;line-height: 1.5em;background: transparent;">Direct analysis of this bordism theory allows one to identify it at odd primes with real K-theory and at the prime 2 with ordinary homology.</p>
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Maria Froehlich<br/>
Special Events Coordinator
<div>Room 305</div>

<div>Simons Center for Geometry and Physics</div>

<div>Stony Brook University</div>

<div>Stony Brook, New York 11794-3636</div>

<div>Tel: (631) 632- 2816</div>

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