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<div class="pre" style="margin: 0; padding: 0; font-family: monospace"><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Değerli Matematikçiler,</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Aşağıda bu Salı saat 16:00'da Zoom üzerinden gerçekleşecek Feza Gürsey Fizik ve Matematik UygAr Merkezi Yüksek Yapılar Seminer Dizimizin detaylarını bulacaksınız.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">İyi çalışmalar dilerim,</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">ilhan ikeda</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">-------- Özgün ileti --------</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Dear friends, </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">I hope you are all doing fine... After a long break, on the 12th of </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">November 2024 Tuesday at 16:00 Istanbul local time, David Ayala from </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Montana State University will be the speaker of Feza Gursey Center for </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Physics and Mathematics Higher Structure Research Group Seminars.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">The details of David's seminar talk are as follows: </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Speaker:</strong> David Ayala (Montana State University).</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Date:</strong> November 12, 2024, Tuesday.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Time:</strong> 16:00 Istanbul local time / 06:00 Bozeman local time.</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Title:</strong><em> Factorization homology of higher categories</em></span><br /><br /><strong><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Abstract: </span></strong><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">The "alpha" version of factorization homology pairs (framed) n-manifolds </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">with En-algebras. This construction generalizes classical homology of a </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">manifold, yields novel results concerning configuration spaces of points </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">in a manifold, and supplies a sort of state-sum model for sigma-models </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">(ie, mapping spaces) to </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">(n-1)-connected targets. This "alpha" version of factorization homology </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">novelly extends Poincaré duality, shedding light on deformation theory </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">and dualities among field theories. Being defined using homotopical</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">mathematical foundations, "alpha" factorization homology is manifestly </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">functorial and continuous in all arguments, notably in moduli of </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">manifolds and embeddings between them, and it satisfies a </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">local-to-global expression that is inherently homotopical in nature. </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Now, En-algebras can be characterized as (∞,n)-categories equipped </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">with an (n-1)-connected functor from a point. The (full) "beta" version</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">of factorization homology pairs (framed) n-manifolds with pointed </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">(∞,n)-categories (with adjoints). Applying 0th homology, or π0,</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">recovers a version of the String Net construction of surfaces, as well </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">as of Skein modules of 3-manifolds. In some sense, the inherently</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">homotopical nature of (full) "beta" factorization homology affords </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">otherwise unforeseen continuity in all arguments, and local-to-global</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">expressions. </span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">In this talk, I will outline a definition of "beta" factorization </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">homology, focusing on low-dimensions and on suitably </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">reduced (∞,n)-categories (specifically, braided monoidal categories). </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">I will outline some examples, and demonstrate some operational practice </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">of factorization homology. Some of this material is established in </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">literature, some a work in progress, and some conjectural -- the status</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">of each assertion will be made clear. I will be especially interested </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">in targeting this talk wot those present, and so will welcome comments </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">and questions.</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">All of this work is joint with John Francis. </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">link is provided by The Science Academy. </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Zoom link details:</strong> </span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">(As usual the Zoom link will be active 30 minutes before the seminar </span><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">time; that is at 15:30 Istanbul time.) </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Topic:</strong> FGC-Higher Structures Seminars</span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"><strong>Date and Time:</strong> Nov 12, 2024 active at 15:30 Istanbul</span><br /><br /><strong><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;">Join Zoom Meeting</span></strong><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><a style="background-color: #f1c40f;" href="https://us02web.zoom.us/j/81515082956?pwd=3GFxY9q3pp9jNXAA3E7qI2Ya8DItA8.1" target="_blank" rel="noopener noreferrer">https://us02web.zoom.us/j/81515082956?pwd=3GFxY9q3pp9jNXAA3E7qI2Ya8DItA8.1</a></span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><strong>Meeting ID</strong>: 815 1508 2956</span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt; background-color: #f1c40f;"><strong>Passcode:</strong> 613918 </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Best regards, </span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Ilhan </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Organized by Feza Gürsey Center for Physics and Mathematics </span><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;">Supported by Bilim Akademisi - The Science Academy </span><br /><br /><span style="font-family: 'times new roman', times, serif; font-size: 11pt;"> <img src="cid:1731148298672f3a0a38b75837917711@bogazici.edu.tr" alt="" width="237" height="104" /> <img src="cid:1731148298672f3a0a38c3e659048136@bogazici.edu.tr" alt="" width="266" height="81" /></span></div>
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