Speaker: Benny Sudakov, ETH, Zurich
Title: Subgraph statistics
Abstract:
Consider integers $k,\ell$ such that $0\le \ell \le \binom{k}2$. Given
a large graph $G$, what is the fraction of $k$-vertex
subsets of $G$ which span exactly $\ell$ edges? When $G$ is empty or
complete, and $\ell$ is zero or $\binom k 2$,
this fraction can be exactly 1. On the other hand if $\ell$ is not one
these extreme values, then by Ramsey's theorem, this
fraction is strictly smaller than 1.

Speaker: Wojciech Samotij, TAU
Title: Subsets of posets minimising the number of chains
Abstract:

The proof of decoupling grew out of an area of Fourier analysis called restriction theory. In this talk, we will describe some of the basic problems and tools of restriction theory, especially wave packets, which are a crucial idea in the proof of decoupling.

The general theme is game dynamics leading to equilibrium concepts.
The plan is to deal with the following topics (all concepts will be defined, and proofs / proof outlines will be provided):
(1) An integral approach to the construction of calibrated forecasts and their use for Nash equilibrium dynamics.
(2) Blackwell's Approachability Theorem and its use for correlated equilibrium dynamics (regret-matching).
(3) Communication complexity and its use for the speed of convergence of uncoupled dynamics.

The general theme is game dynamics leading to equilibrium concepts.
The plan is to deal with the following topics (all concepts will be defined, and proofs / proof outlines will be provided):
(1) An integral approach to the construction of calibrated forecasts and their use for Nash equilibrium dynamics.
(2) Blackwell's Approachability Theorem and its use for correlated equilibrium dynamics (regret-matching).
(3) Communication complexity and its use for the speed of convergence of uncoupled dynamics.

פרופ' תמר ציגלר : אילו הפתעות יש בתתי קבוצות גדולות?

מה ניתן למצוא בתתי קבוצות גדולות של מרחב וקטורי V מעל שדה סופי? 
ישנו עיקרון יפה הנקרא עקרון רמזי, לפיו בתתי קבוצות גדולות של קבוצה עם מבנה ניתן למצוא ״תת מבנה״.
נדון בשאלות - כמה גדולה יכולה להיות תת קבוצה מקסימלית של V שלא מכילה ישר? מישור?

הדלקת נרות בשעה 17:45
הרצאת אשנב בשעה 18:30

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I will talk about old and new results relating curve counting on complex surfaces and quiver representations.

Title: The Modal Logic of Forcing


Abstract: Modal logic is used to study various modalities, i.e. various ways in which statements can be true, the most notable of which are the modalities of necessity and possibility. In set-theory, a natural interpretation is to consider a statement as necessary if it holds in any forcing extension of the world, and possible if it holds in some forcing extension. One can now ask what are the modal principles which captures this interpretation, or in other words - what is the "Modal Logic of Forcing"?

Abstract: we give an overview of Gowers' proof for the existence of 4-term progression in subsets of positive density in the integers. We will discuss the tools from additive combinatorics that are used in the proof as well as some related conjectures.

Abstract: we give an overview of Gowers' proof for the existence of 4-term progression in subsets of positive density in the integers. We will discuss the tools from additive combinatorics that are used in the proof as well as some related conjectures.