<div dir="ltr"><br>Bilkent Topology Seminar on Oct 12:<div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>From: <strong class="gmail_sendername" dir="auto">Cihan Okay</strong> <span dir="auto"><<a href="mailto:cihan.okay@bilkent.edu.tr">cihan.okay@bilkent.edu.tr</a>></span><br>Date: Wed, Oct 7, 2020 at 9:00 AM<br>Subject: BilTop - Talk (Oct 12)<br>To: Math Faculty <<a href="mailto:Mathfac@fen.bilkent.edu.tr">Mathfac@fen.bilkent.edu.tr</a>>, <<a href="mailto:Mathgrad@fen.bilkent.edu.tr">Mathgrad@fen.bilkent.edu.tr</a>>, <<a href="mailto:akiferdal@gmail.com">akiferdal@gmail.com</a>>, <<a href="mailto:asli.ilhan@deu.edu.tr">asli.ilhan@deu.edu.tr</a>>, <<a href="mailto:bahra004@umn.edu">bahra004@umn.edu</a>>, <<a href="mailto:berrin@fen.bilkent.edu.tr">berrin@fen.bilkent.edu.tr</a>>, <<a href="mailto:mgelvin@gmail.com">mgelvin@gmail.com</a>>, <<a href="mailto:mpamuk@metu.edu.tr">mpamuk@metu.edu.tr</a>>, <<a href="mailto:pasemra@metu.edu.tr">pasemra@metu.edu.tr</a>>, Alex Degtyarev <<a href="mailto:degt@fen.bilkent.edu.tr">degt@fen.bilkent.edu.tr</a>>, Alihan <<a href="mailto:alihan.serim@ug.bilkent.edu.tr">alihan.serim@ug.bilkent.edu.tr</a>>, Baran Zadeoğlu <<a href="mailto:baranzadeoglu@gmail.com">baranzadeoglu@gmail.com</a>>, Betül Tolgay <<a href="mailto:tolgaybetul@gmail.com">tolgaybetul@gmail.com</a>>, Claude Schochet <<a href="mailto:clsmath@gmail.com">clsmath@gmail.com</a>>, Ergun Yalcin <<a href="mailto:yalcine@fen.bilkent.edu.tr">yalcine@fen.bilkent.edu.tr</a>>, Esat Akin <<a href="mailto:esat.akin@ug.bilkent.edu.tr">esat.akin@ug.bilkent.edu.tr</a>>, Esma Dirican <<a href="mailto:esmadirican131@gmail.com">esmadirican131@gmail.com</a>>, Laurence Barker <<a href="mailto:barker@fen.bilkent.edu.tr">barker@fen.bilkent.edu.tr</a>>, Melih Ucer <<a href="mailto:melih.ucer@bilkent.edu.tr">melih.ucer@bilkent.edu.tr</a>>, Mufit Sezer <<a href="mailto:sezer@fen.bilkent.edu.tr">sezer@fen.bilkent.edu.tr</a>>, Oguz Savk <<a href="mailto:oguz.savk@boun.edu.tr">oguz.savk@boun.edu.tr</a>>, Ozgun Unlu <<a href="mailto:unluo@fen.bilkent.edu.tr">unluo@fen.bilkent.edu.tr</a>>, Serdar Baysal <<a href="mailto:serdar.baysal@bilkent.edu.tr">serdar.baysal@bilkent.edu.tr</a>>, Servin Bagheralmoosavi <<a href="mailto:servin@bilkent.edu.tr">servin@bilkent.edu.tr</a>>, Yara Ayman <<a href="mailto:yaraayman106@gmail.com">yaraayman106@gmail.com</a>>, Zilan Akbas <<a href="mailto:zilan.akbas@bilkent.edu.tr">zilan.akbas@bilkent.edu.tr</a>><br>Cc: Gizem Ramanlı <<a href="mailto:gizem@fen.bilkent.edu.tr">gizem@fen.bilkent.edu.tr</a>><br></div><br><br><div dir="ltr">Dear all,<br><br>Here is the information for our next topology seminar:<br><br>Time: Oct 12, 2020 @ 13:40 UTC+3<br>Speaker: Aslı Güçlukan<br>Affiliation: Dokuz Eylül University<br><br>Title: Small covers over a product of simplices<br><br>Abstract: Choi shows that there is a bijection between Davis–Januszkiewicz equivalence classes of small covers over an $n$-cube and the set of acyclic digraphs with $n$-labeled vertices. Using this, one can obtain a bijection between weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over an $n$-cube and the isomorphism classes of acyclic digraphs on labeled $n$ vertices up to local complementation and reordering vertices. To generalize these results to small covers over a product of simplices we introduce the notion of $\omega$-weighted digraphs for a given dimension function $\omega$. It turns out that there is a bijection between Davis–Januszkiewicz equivalence classes of small covers over a product of simplices and the set of acyclic $\omega$-weighted digraphs. After introducing the notion of an $\omega$-equivalence, we also show that there is a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over $\Delta^{n_1}\times\cdots \times \Delta^{n_k}$ and the set of $\omega$-equivalence classes of $\omega$-weighted digraphs with $k$-labeled vertices $\{v_1, \cdots, v_k\}$ where $\omega$ is defined by $\omega(v_i)=n_i$ and $n=n_1+\cdots+n_k$. As an example, we obtain a formula for the number of weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of three simplices.<br><br>To see the upcoming talks visit: <a href="https://researchseminars.org/seminar/BilTop" target="_blank">https://researchseminars.org/seminar/BilTop<br></a><br>I will send out the Zoom link on Monday.<br><br>Best,<br>Cihan<br></div>
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