First Talk: 16:00-17:00


Geva Yashfe: The principal kinematic formula: Euler characteristic and geometry

Abstract: Let C and D be nice domains in R^d. Given some geometric data on each of the domains, the principal kinematic formula computes an integral over the group of rigid motions of R^d: it sums the Euler characteristic of the intersection of C with g.D as g ranges over the group.
We will discuss this formula and outline its proof, then use it to prove a surprising theorem of Hadwiger along with the isoperimetric inequality in the plane.

Second Talk: 17:00-18:00


Moshe White: What can harmonic analysis tell us about democratic elections?


Abstract: A Boolean function f (that is, a function which takes n arguments and returns a single value, each from a single set with two elements), can be used to model a voting system between two possible alternatives: each of n members of a society casts a vote, and the outcome of the election is determined by the function f. The "majority rule" function has certain "fairness" criteria, which we might hope to implement in a voting system choosing between three (or more) possible alternatives.
However, this turns out to be impossible: the naive attempt to use the majority between every pair of alternatives may fail due to the Condorcet paradox, and more generally, Arrow's Impossibility Theorem may be informally stated as "perfect voting systems do not exist". We will prove a quantitative generalization of these two results, using Fourier expansions of Boolean functions. No prior knowledge beyond inner product spaces and basic probability theory is required.

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Amichai Lampert is inviting you to a scheduled Zoom meeting.

Topic: Graduate Student Seminar
Time: Nov 4, 2020 04:00 PM Jerusalem

Join Zoom Meeting
https://huji.zoom.us/j/83698909188?pwd=cnBqYW1rNFRxUEpseTVpVEhESUkyZz09

Meeting ID: 836 9890 9188
Passcode: 392656