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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 13 March 2024 - 15:00 to 16:00 <br />
Place: ZOOM meeting
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Speaker: Vladimir Chernov, Dartmouth College<br />
Title: Virtual Legendrian knots and possible relations to causality in Borde–Sorkin spacetimes
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Abstract <br />
<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">We review our results with Stefan Nemirovski on the relation</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">of Legendrian linking and causal structure in globally hyperbolic</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">spacetimes. After that we discuss virtual Legendrian knots defined as</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">Legendrian knots in ST^∗M studied up to isotopy and modification of</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">ST^∗M induced by surgery on M that were introduced by Patricia Cahn</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">and Asa Levi. We formulate a few conjectures about them and</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">conjecturally relate them to causality in Borde–Sorkin spacetimes that</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">are manifolds with a Lorentz metric that is degenerate at critical</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">points of a Morse "timelike" function and that consist of globally</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">hyperbolic pieces between critical levels. We prove these conjectures</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">for 2+1 dimensional Borde–Sorkin spacetimes.</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">The talk is based on the joint work with Rustam Sadykov.</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">-----------------------------------------------------------------------------------------------------------------------</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">We shall open ZOOM at 14.45 for virtual coffee</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">Join Zoom Meeting</span></p><p><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 204);" class="ql-font-monospace">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">MeetingID:99598413922</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">Passcode:Galois</span></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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