<div dir="ltr"><div dir="ltr"><div dir="ltr"><div><p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif">Dear All,</p>
<p class="MsoNormal" style="line-height:21pt;margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><span style="font-family:"inherit",serif">You
are cordially invited to the Weekly Online Seminar “Analysis and Applied
Mathematics” on </span></p>
<p class="MsoNormal" style="line-height:21pt;margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><b><span style="font-family:"inherit",serif">Date</span></b><span style="font-family:"inherit",serif">: Tuesday, March 18, 2025 </span></p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><b>Time:</b> 14.00-15.00 (Istanbul) = 13.00-14.00
(Ghent) = 16.00-17.00 (Almaty)<br>
<b>Place:</b> Zoom link: <a href="https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fus02web.zoom.us%2Fj%2F6678270445%3Fpwd%3DSFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09&data=05%7C02%7Callaberen.ashyralyev%40bau.edu.tr%7C2c69a1c488e64e2b9bc708dd55bd50d4%7C8985f9b5679c4a398db6854329895dac%7C0%7C0%7C638760994070534085%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=Gij6wlPSQkpjoR6YOo1LU1YeYpnyd5gzziaGjQgIEDA%3D&reserved=0" style="color:blue" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09</a>,
Conference ID: 667 827 0445, Access code: 1 </p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"> </p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><b>Speaker: Onur Ağırseven Marlboro College, USA<span style="font-size:12pt">(Joint work with Dr. M. A. Ollis, Emerson College, USA)</span></b></p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><b>Title: </b> On the Buratti-Horak-Rosa conjecture</p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><b>Abstract:</b> <span style="font-size:12pt">Consider the complete graph Kv. Label the vertices with the distinct elements of Zv, the</span></p><p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><br>cyclic group of order v. Label each edge with the cyclical distance between its end-vertices. Accord-<br>ingly, each path in Kv is associated with a multiset of such edge labels. The Buratti-Horak-Rosa<br><br>(BHR) conjecture, initially proposed in 2007 and reformulated several times, asks the reverse ques-<br>tion for Hamiltonian paths through Kv. This has certain implications for graph decompositions, which, in return, have applications in computer science, including partitioning networks for structural analysis.<br>In more precise terms, a Hamiltonian path through Kv is called a realization of a multiset L of<br>size v − 1 if its edge labels are L. The BHR conjecture is that there is a realization for a multiset LL if<br>and only if, for any divisor dd of v, the number of multiples of dd in L is at most v − d. It has been<br>shown early on that the conjecture holds for multisets of support at most 2. However, only partial<br>results have been achieved so far for other supports.<br>We observe that a toroidal lattice of vertices is associated with a given multiset. This allows us<br>to construct certain useful types of realizations as building blocks [1, 2, 3]. Our current focus is mainly on multisets with support of size 3, where certain relevant lattices are cylindrical. The ongoing expansion of our constructions is considerably extending the parameters for which the conjecture is known to hold.</p><p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif">References:<br><br>[1] O. Ağırseven and M. A. Ollis, Grid-based graphs, linear realizations and the Buratti-Horak-<br>Rosa conjecture, submitted, arXiv:2402.08736.<br><br>[2] O. Ağırseven and M. A. Ollis, A coprime Buratti-Horak-Rosa conjecture and grid-based lin-<br>ear realizations, submitted, arXiv:2412.05750.<br><br>[3] O. Ağırseven and M. A. Ollis, Construction techniques for linear realizations of multisets with<br>small support, submitted, arXiv:2502.00164.</p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"> <b>Abstracts and forthcoming talks can be found on our
webpage</b></p>
<p class="MsoNormal" style="margin:0cm;font-size:12pt;font-family:Aptos,sans-serif"><a href="https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fsites.google.com%2Fview%2Faam-seminars&data=05%7C02%7Callaberen.ashyralyev%40bau.edu.tr%7C2c69a1c488e64e2b9bc708dd55bd50d4%7C8985f9b5679c4a398db6854329895dac%7C0%7C0%7C638760994070553294%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=px9DHJSRATIRC035da8GQDSSi6OryIin3aBQmeLQPgo%3D&reserved=0" style="color:blue" target="_blank">https://sites.google.com/view/aam-seminars</a><br>
With my best wishes</p></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px"><b style="font-size:12.8px">Prof. Dr. Allaberen Ashyralyev </b></div><div><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University,</b></span><b>34349</b><span style="font-size:small"><b>, Istanbul, Turkiye</b></span><b style="font-size:12.8px"> </b></div><div><div style="font-size:12.8px"><span style="font-size:12.8px"><b>Peoples' Friendship University of Russia (RUDN University),</b></span><b style="color:rgb(51,51,51);font-family:arial,helvetica,sans-serif;font-size:13px"> Ul Miklukho Maklaya 6, Moscow 117198, Russian Federation </b></div><div style="font-size:12.8px"><b style="font-size:12.8px">Institute of Mathematics and Mathematical Modelling, 050010, Almaty, Kazakhstan</b></div><div style="font-size:12.8px"><b style="font-size:12.8px">e-mail: <a href="mailto:allaberen.ashyralyev@neu.edu.tr" style="color:rgb(17,85,204)" target="_blank">allaberen.ashyralyev@bau.edu.tr</a> and </b><b style="font-size:12.8px"><a href="mailto:aallaberen@gmail.com" style="color:rgb(17,85,204)" target="_blank">aallaberen@gmail.com</a> </b></div><div style="font-size:12.8px"><b style="font-size:12.8px"> </b><a href="http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev" style="color:rgb(0,86,179);margin:0px;padding:0px;border:0px;font-stretch:inherit;font-size:14px;line-height:inherit;font-family:Roboto,sans-serif;vertical-align:baseline" target="_blank">http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev</a></div><div><p class="MsoNormal"><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a></p><p class="MsoNormal"><a href="https://ejaam.org/editorial.html" target="_blank">https://ejaam.org/editorial.html</a><br></p><p class="MsoNormal"><span style="font-size:12.8px"><b><u><a href="https://icaam-online.org/" target="_blank">https://icaam-online.org/</a></u></b></span><br></p></div></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><a href="https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1" target="_blank">https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1<br></a></b></span><br></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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