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.

Noncommutative Analysis

Gap labelling for electron motion in quasicrystals and C*-algebra of minimal actions of Z^d on the Cantor set

Jun 13, 11:00—12:00, 2022, seminar room, minus 101

Speaker

N. Christopher Phillips (University of Oregon)

Abstract

This talk will be a survey of the mathematics of the gap labelling problem for quasicrystals, but will assume no knowledge of physics.

In one standard approximation, the possible energy levels of an electron moving in a crystal form a collection of bands. These energy levels constitute the spectrum of a suitable Schr$\"{o}$dinger operator, and the gaps between the bands are gaps in the spectrum.

Quasicrystals are not periodic, but exhibit long range order. The structure of the spectrum of the Schr$\"{o}$dinger operator for quasicrystals is addressed by the ``Gap Labelling Conjecture’’. This conjecture was made in 1989, and some results are known.

An infinite quasicrystal has an associated action of ${\mathbb{Z}}^d$ on the Cantor set $X$, and thus a transformation group C*-algebra $A$. The physics is supposed to give an invariant measure on $X$, and hence a tracial state on $A$. The gaps in the spectrum of Schr"{o}dinger operator correspond to the values of this tracial state on projections in $A$, and the Gap Labelling Theorem states that these values all already occur as values of the measure on compact open subsets of $X$.

In this talk, I will give a more careful description of the situation, including sketches of how the objects above are constructed and how they are related to each other. Then I will say something about the results that have been proved, and outline what goes into their proofs.

Colloquium

Asymptotic representation theory, old and new

Jun 14, 14:30—15:30, 2022, Math -101

Speaker

Natalia Tsilevich (PDMI, Saint Petersburg, Russia)

Abstract

Asymptotic representation theory is an important and quickly developing area of mathematics rich in connections to other fields, such as, e.g., probability, algebraic combinatorics, and mathematical physics. I will survey the basic ideas and results of asymptotic representation theory, mostly of symmetric groups, and then focus on some recent contributions.

אשנב למתמטיקה

פיתרון אנליטי לבעיית אופטימיזציה Online

Jun 14, 16:10—17:30, 2022, אולם -101, בניין מתמטיקה

Speaker

אור אלמכיאס

Abstract

נניח שלמערכת המשוואות הלינאריות $Ax=b$ יש יותר מפיתרון אחד. האם קיים למערכת פיתרון אופטימלי, כלומר פיתרון בעל נורמה מינימלית? איך מוצאים את הנורמה האופטימלית ואת הפיתרון עם נורמה זו?

על השאלות האלו אנחנו נענה באמצעות כלים של דואליות, ונשתמש באחד המשפטים החשובים ביותר באנליזה פונקציונלית. בהמשך נציג רעיון פיסיקלי שיכול להסביר את המוטיבציה מאחורי השימוש בדואליות.

AGNT

Arakelov motivic cohomology

Jun 15, 16:00—17:00, 2022, -101

Speaker

Jakob Scholbach (online meeting) (Munster)

Abstract

Jakob has kindly agreed to speak about his old work on Arakelov motivic cohomology and comparison with the arithmetic intersection pairing of Gillet-Soul'e.

BGU Probability and Ergodic Theory (PET) seminar

(Non-)Integrability of quaternion-Kähler symmetric spaces Online

Jun 16, 11:10—12:00, 2022, room 106, building 28

Speaker

Anton Hase (Ben-Gurion University)

Abstract

It is a famous result of Harish-Chandra that every non-compact Hermitian symmetric space can be realized as a bounded domain in a complex vector spaces. If we replace the complex numbers by the division algebra of quaternions in the definition of Hermitian symmetric spaces, we obtain the class of quaternion-Kähler symmetric spaces. While these spaces emerge in an analogous way, we show that there is no quaternionic analogue of Harish-Chandra’s embedding theorem: A quaternion-Kähler symmetric space is integrable if and only if it is a quaternionic vector space, quaternionic hyperbolic space or quaternionic projective space. In the talk I will explain some of the background and some of the tools used in the proof.


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