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<span style="margin:0px;font-size:12pt;color:black;background-color:rgb(255, 255, 255)"><span style="margin:0px;background-color:white"><span style="margin:0px;font-size:15px;color:rgb(32, 31, 30);background-color:white"><span style="margin:0px"><span style="margin:0px;font-size:16px;color:rgb(49, 49, 49);word-spacing:1px"><font style="font-size:1.13em"><b>Date:</b> May
11th, Wednesday</font></span></span></span></span></span></div>
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<div style="margin:0px;font-size:16px;color:rgb(49, 49, 49);word-spacing:1px"><font style="font-size:1.13em"><b>Time: </b>12:30pm CT</font></div>
<div style="margin:0px;font-size:16px;color:rgb(49, 49, 49);word-spacing:1px"><font style="font-size:1.13em"><b>Location: </b>JCL 390</font></div>
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<b><font style="font-size:1.13em">Speaker: <span style="margin:0px"> </span><span style="margin:0px"></span>Sidhanth Mohanty</font></b></div>
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<div style="margin:0px"><b style="color:rgb(49, 49, 49);font-size:16px;word-spacing:1px"><font style="font-size:1.13em">Title: Testing thresholds for sparse random geometric graphs</font></b></div>
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<div style="margin:0px"><span style="margin:0px;font-size:16px;color:rgb(49, 49, 49);word-spacing:1px"><font style="font-size:1.13em"><b>Zoom: </b>[<a href="https://uchicago.zoom.us/j/93265734038?pwd=SkRTSTF3a0lOQVg4MWdxVS9Lb2tPdz09" title="https://uchicago.zoom.us/j/93265734038?pwd=SkRTSTF3a0lOQVg4MWdxVS9Lb2tPdz09">link</a>]</font></span></div>
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<div dir="auto" style="margin:0px"><font style="color:rgb(49, 49, 49);font-size:1.13em;word-spacing:1px"><span style="margin:0px;font-size:13pt"><b>Abstract:</b></span><b> </b><span style="margin:0px;font-size:12pt;font-family:"trebuchet ms", sans-serif;color:rgb(32, 31, 30);background-color:white;word-spacing:0px"> In
the random geometric graph model, we identify each of our vertices with an independently and uniformly sampled vector from a high-dimensional unit sphere, and we connect pairs of vertices whose vectors are sufficiently close.
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<div>A fundamental question is: when is a random geometric graph a faithful model for its underlying geometry? As the dimension grows relative to the number of vertices, the edges in the graph become increasingly independent, and the underlying geometry becomes
less apparent. This talk will cover some recent progress on this question: we show that in sparse random geometric graphs, if the dimension is at least polylogarithmic in the number of vertices, then the graphs are statistically indistinguishable from Erdős-Rényi
graphs, i.e. the underlying geometry disappears.</div>
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Based on joint work with Siqi Liu, Tselil Schramm, and Elizabeth Yang (https://arxiv.org/abs/2111.11316).</span></font></div>
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<div dir="auto" style="margin:0px"><font face="trebuchet ms,sans-serif"><b>COVID Policy:<span style="margin:0px"> </span></b>As per university policy, masking is not currently required for in-person attendance. Please note that we will have fully masked and
social-distanced tables available to accommodate any attendees who would prefer such arrangements. Please contact us if you have any questions or feedback. </font></div>
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