31 MAY 2023
16:00 - 17:00

We discuss two notions of percolation on graphs. The first one is $r$-neighbor bootstrap percolation in which an activation process of the vertices of a given graph is carried out. The process starts with some initially activated vertices and then, in each round, any inactive vertex with at least $r$ active neighbors becomes activated. The second one is the so called graph bootstrap percolation in which we activate the edges of a graph instead of vertices. Starting with some initially activated edges, we activate any inactive edge which creates a new copy of $H$, the pattern or base graph. Two problems, one of combinatorial nature and the other of probabilistic type are reviewed. The minimum size of a set of initially activated vertices leading to the activation of all vertices of a graph $G$ in the $r$-neighbor bootstrap percolation is denoted by $m(G, r)$. Computing $m(G, r)$ is a combinatorial problem. In the second problem, each vertex of $G$ is initially activated with a probability $p$ and the question is to find the probability threshold of activation of all vertices of the graph $G$. We talk about the latest developments on both problems and also the connections between $r$-neighbor bootstrap percolation and graph bootstrap percolation.

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31 MAY 2023
17:30 - 19:00

I will present joint work with Andrea Ferraguti which makes progress on a conjecture of Andrews and Petsche that classifies abelian dynamical Galois groups over number fields, in the unicritical case. I will explain how to reduce the conjecture to the post-critically finite case and the key tools to handle all unicritical PCF with periodic critical orbit over any number field and all PCF over quadratic number fields. Along the way I will present an earlier rigidity result of ours on the maximal closed subgroup of the automorphism group of a binary rooted tree, which offered us with the main input to translate the commutativity of the Galois image into diophantine equations. I will also overview progress on the tightly related problem of lower bounding arboreal degrees.

Zoom Meeting ID: 856 1386 0958
Passcode: 513992
ICS-File: https://researchseminars.org/seminar/FGC-IPM/ics

24 MAY 2023
17:30 - 19:00

I will survey some recent developments regarding the minimal model program for foliations defined over a complex algebraic variety, together with some applications towards the study of fibrations in birational geometry.

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Meeting ID: 9086116889
Passcode: 362880

24 MAY 2023
14:00 - 15:00

Argumentation has gained attention in AI disciplines such as game theory, non-monotonic reasoning, and knowledge representation, as well as in fields like philosophy, psychology, and law. Formalisms of argumentation enable the modeling and evaluation of arguments. Our presentation focuses on implementing formalisms of argumentation to assess the quality of online product reviews. Despite the importance of product reviews in decision-making, dealing with numerous inconsistent reviews is challenging. We demonstrate how argumentation formalisms can be used to evaluate the quality of online product reviews.

link: https://room.gharar.ir/ba05e1ad-99f6-4911-b60e-dbf02616a692

17 MAY 2023
17:30 - 19:00

The integration of differential forms furnishes an isomorphism between the De Rham and the Hodge realizations of a 1-motive M. The coefficients of the matrix representing this isomorphism are the so-called "periods" of M. In the semi-elliptic case (i.e. the underlying extension of the 1-motive is an extension of an elliptic curve by the multiplicative group), we compute explicitly these periods. If the 1-motive M is defined over an algebraically closed field, Grothendieck's conjecture asserts that the transcendence degree of the field generated by the periods is equal to the dimension of the motivic Galois group of M. If we denote by I the ideal generated by the polynomial relations between the periods, we have that ''the numbers of periods of M minus the rank of the ideal I is equal to the dimension of the motivic Galois group of M", that is a decrease in the dimension of the motivic Galois group is equivalent to an increase of the rank of the ideal I. We list the geometrical phenomena which imply the decrease in the dimension of the motivic Galois group and in each case we compute the polynomials which generate the corresponding ideal I.

Zoom Meeting ID: 856 1386 0958
Passcode: 513992

17 MAY 2023
14:00 - 15:00

A major breakthrough in the theory of negatively dependent - i.e., repulsive - probability measures was the introduction of "strongly Rayleigh measures" by Borcea, Branden, and Liggett in 2009. These measures are defined by means of a geometric condition on the location of the zeros of their generating polynomial which amounts to their "real stability". The class of strongly Rayleigh measures is a very well-behaved and rich class of probability measures, so much so that they are considered the "main" class of negatively dependent measures.
An important feature of negatively dependent measures is their complex dependence structure. This is essentially due to intrinsic constraints in their dependence structure. In this talk, I will present a strong manifestation of this phenomenon in the class of strongly Rayleigh measures, which we call paving property. Roughly speaking, this property means that it is possible to partition a set of strongly Rayleigh random variables to a few subsets such that the random variables in each subset are "almost independent". The proof hinges on an extension of the "paving conjecture" - which was resolved by Marcus, Spielman, Srivastava in 2013 - to real stable polynomials.




link: https://room.gharar.ir/ba05e1ad-99f6-4911-b60e-dbf02616a692