[PHK_seminar] [Cohomology]Wednesday 11 Feb, Tobias Fritz

[Petr Somberg]

 We are starting soon!

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Wednesday, 11 February 2026 - 13:30 to 14:30
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting

Speaker: Tobias Fritz, University of Innsbruck, Austria
Title: Optimizing over iid distributions and the Beat the Average game

Abstract

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?



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.



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).

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We shall open the ZOOM meeting at 13.15 for (virtual) coffee and close
ZOOM at 15.00



Join Zoom Meeting



https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09



Meeting ID:99598413922

Passcode:Galois

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On Wednesday, February 8, Rita Fioresi shall give a talk ``Geometric Deep
Learning meets Quantum Groups"

For more information see the seminar web page at
https://www.math.cas.cz/…/16

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phk_seminar at math.cas.cz
https://list.math.cas.cz/….cz

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