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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 11 February 2026 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
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Speaker: Tobias Fritz, University of Innsbruck, Austria<br />
Title: Optimizing over iid distributions and the Beat the Average game
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Abstract <br />
<p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">A casino offers the following game. There are three cups each containing a die. You are being told that the dice in the cups are all the same, but possibly nonstandard. For a bet of $1, the game master shakes all three cups and lets you choose one of them. You win $2 if the die in your cup displays at least the average of the other two, and you lose otherwise. Is this game fair? If not, how should the casino design the dice to maximize their profit?</span></p><p><br></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">In this talk, I will answer this question, explain what it is an example of, and outline our partial results on a more difficult question of the same type: how likely can we make the event X1 + X2 + X3 < 2 X4, given the constraint that the random variables X1, ..., X4 must be iid? Surprisingly, obtaining good bounds involves solving challenging combinatorial optimization problems.</span></p><p><br></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">Based on joint work with Pierre C Bellec (arXiv:2412.15179), which has recently been featured as a test case for the AI tool AlphaEvolve (arXiv:2511.02864).</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);" class="ql-font-monospace">-----------------------------------------------------</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">We shall open the ZOOM meeting at 13.15 for (virtual) coffee and close ZOOM at 15.00</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Join Zoom Meeting</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="color: rgb(17, 85, 204); background-color: rgb(255, 255, 255);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Meeting ID:99598413922</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Passcode:Galois</span></p><p>--------------------------------------------------------------------------------------------------------</p><p><br></p><p>On Wednesday, February 8, Rita Fioresi shall give a talk ``<span style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);">Geometric Deep Learning meets Quantum Groups"</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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