This page list all events and seminars that take place in the department this week. Please use the form below to choose a different week or date range.

אשנב למתמטיקה

סדרות מתכנסות במובן של Bohr

Nov 12, 18:00—19:30, 2024, אולם 101-, בניין מתמטיקה

Speaker

יאיר גלזנר

Abstract

נסתכל על חבורה קומפקטית $G$. דוגמה טובה היא חבורת כל ההעתקות האורתוגונליות במרחב:

\[G=SO(3)=\{U\in M_{3\times 3}(\mathbb{R})|UU^t=I\}\]

בהנתן שני איברים $a,b\in G$, נדון בשאלה: האם אפשר למצוא סדרה של ביטויים ב-$a,b$ שבהכרח מתכנסת ליחידה (בלי תלות בבחירה של $a,b$).

AGNT

The power operation in the Galois cohomology of a reductive group over a number field

Nov 13, 14:10—15:10, 2024, -101

Speaker

Mikhail Borovoi (TAU)

Abstract

For a number field $K$ admitting an embedding into the field of real numbers $\mathbb{R}$, it is impossible to construct a functorial in $G$ group structure in the Galois cohomology pointed set $H^1(K,G)$ for all connected reductive $K$-groups $G$. However, over an arbitrary number field $K$, we define a diamond (or power) operation of raising to power $n$

$$ (x,n) \mapsto x^{\Diamond n}: H^1(K,G) \times Z \to H^1(K,G). $$

We show that this operation has many functorial properties. When $G$ is a torus, the set $H^1(K,G)$ has a natural group structure, and $x^{\Diamond n}$ coincides with the $n$-th power of $x$ in this group.

For a cohomology class $x \in H^1(K,G)$, we define the period $\operatorname{per}(x)$ to be the greatest common divisor of $n>0$ such that $x^{\Diamond n}=1$, and the index $\operatorname{ind}(x)$ to be the greatest common divisor of the degrees $[L:K]$ of finite separable extensions $L/K$ splitting $x$. These period and index generalize the period and index of a central simple algebra over $K$ (in the special case where $G$ is the projective linear group $\operatorname{PGL}_n$, the elements of $H^1(K, G)$ can be represented by central simple algebras). For an arbitrary reductive group $G$ defined over a local or global field $K$, we show that $\operatorname{per}(x)$ divides $\operatorname{ind}(x)$, that $\operatorname{per}(x)$ and $\operatorname{ind}(x)$ have the same prime factors, but the equality $\operatorname{per}(x) = \operatorname{ind}(x)$ may not hold.

The talk is based on joint work with Zinovy Reichstein. All necessary definitions will be given, including the definition of the Galois cohomology set $H^1(K,G)$.

BGU Probability and Ergodic Theory (PET) seminar

Enveloping Ellis semigroups as compactifications of transformations groups. Online

Nov 14, 11:10—12:00, 2024, -101

Speaker

Konstantin Kozlov (BGU)

Abstract

The notion of a proper Ellis semigroup compactification is introduced. Using Ellis’s functional approach their connection with equiuniformities on a topological group is established. Proper Ellis semigroup compactification of a topological group G from the maximal equiuniformity on a phase space in the case of isometric action (on a discrete space, on a discrete chain, as liner isometries of a Hilbert space) is described. Its connection with Roelcke uniformity on G is established.

Automorphic forms, Representation theory and Number Theory

More on rep. theory of GL(2) + Relative Langlands Duality following https://arxiv.org/abs/2309.08874

Nov 14, 13:00—15:00, 2024, 201

Speaker

Nadya G. + Eitan S. (BGU)

Abstract

The first hour will given by Nadya and it will be about 1) Two definition of \gamma, L, e-factors a) Jacquet integrals b) Godement-Jacquet integrals. 2) Weil Deligne group, different types of parameters, 3) roughly describe LLC for GL(2)

The second hour will be given by Eitan and will be about the introduction of and Section 2 in the paper https://arxiv.org/abs/2309.08874


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