Some older events may be found on the pages of the Center for Advanced Studies.

### אירועי העבר

• Online Special lecture Jul 18, 11:10—13:00, 2022, Room 104, Building 28 (BGU).

Title: Existence of outer automorphisms of the Calkin algebra is undecidable in ZFC

Speaker: N. Christopher Phillips, University of Oregon and Ben Gurion University of the Negev

##### Abstract:

The Calkin algebra $Q$ is the quotient of the algebra $L(H)$ of bounded operators on a separable infinite dimensional Hilbert space $H$ by the ideal of compact operators (the closure of the ideal of finite rank operators). It is an explicit simple $C^*$-algebra, first studied by Calkin in 1941. It takes a few lines to prove that every automorphism of $L(H)$ is inner, that is, of the form $a\mapsto ua u^{-1}$ for some unitary $u$ in $L(H)$. Are all automorphisms of $Q$ inner? Despite the concrete description of $Q$, this is undecidable in ZFC. Assuming the Continuum Hypothesis (CH), there are outer (that is, not inner) automorphisms (joint with Weaver, 2007). Assuming the Open Coloring Axiom (OCA; also called Todorcevic‘s Axiom), all automorphisms of $Q$ are inner (Farah, 2011).

In these talks, we will outline proofs of both results. The talks are intended to be accessible to people in both operator algebras and set theory. We will follow Farah‘s reproof of the existence of outer automorphisms under CH, which uses much less $C^*$-algebra machinery than the original proof, and uses some of the same ingredients as the proof of nonexistence under OCA.

We will very briefly say something about later results which have been proved, as well as problems which remain open, involving generalizations of the Calkin algebra, such as outer multiplier algebras of $C^*$-algebras and $l^p$ Calkin algebras. It remains open whether the existence of orientation reversing automorphisms of the original Calkin algebra is consistent with ZFC.

• Mathematics Excellence Day(*) Jun 19, 13:15—16:30, 2022, Deichmann building for Mathematics (58), Seminar room -101.

## Mathematics Excellence Day

#### to honor 2022 Wolf prize laureate Prof. George Lusztig (MIT) and to award the Noriko Sakurai fellowship, the Gauchman excellence scholarship and the Zabey prize

• A day of lectures on probability and dynamics; celebrating Michael Lin‘s birthday. May 31, 10:30—16:30, 2022.

Dear friends and colleagues.

We are delighted to invite you to a special day of lectures on dynamics and probability:

In honor of Michael Lin‘s 80th birthday. At Ben-Gurion university of the Negev. On Tuesday 31/5/2022 between 10:30-16:30.

There will be four lectures given by:

Jon Aaronson (Tel-Aviv University) Dmitry Dolgopyat (University of Maryland) Omri Sarig (Weizmann institute) Eli Glasner (Tel-Aviv University)

Please save the date. We will soon send an additional e-mail with more precise information.

• We are happy to invite you to an interdisciplinary meeting on Symmetry using Zoom.

There are sessions in Physics, Mathematics and CS, Biology and Chemistry.

The Math and CS sessions are scheduled for Monday Aug. 9 and Wed August 11, between 11-15.

• Online Noriko Sakurai fellowship and Hillel Gauchman Prize(*) Jul 13, 12:30—14:00, 2021.

• School on Polish Groups(*) May 22—27, 2016, Midreshet Sde-Boker.

The School will focus on Polish Groups. General theory, examples, representations of discrete groups with Polish targets, and applications to discrete groups, geometry and dynamics. The three main courses will be:

### Mini-Courses

1. General theory of Polish groups Jullien Melleray, Christian Rosendal and Todor Tsankov.
2. Algebraic groups over Polish fields. Jean Lécureux and Bertrand Rémy.
3. Infinite dimensional Lie groups and their symmetric spaces Bruno Duchesne.
• ערב חשיפה לתארים מתקדמים Apr 12, 17:00—18:30, 2016, חדר סמינרים (101-), בניין 58.

• Algebraic Combinatorics day(*) Mar 29, 2016, Room -101, Math building (58), BGU.

In honor of Prof. Mikhail Klin, on the occasion of his retirement

• Special Seminar Jun 16, 10:00—11:00, 2015, Room -101, BGU.

Speaker: Antoine Ducros (Paris 6)

Title: Stability of Gauss valuations

Abstract:

A valued field $(k,|.|)$ is said to be stable (this terminology has no link with model-theoretic stability theory) if every finite extension $L$ of $k$ is defectless, i.e., satisfies the equality $\sum e_vf_v=[L:k]$, where $v$ goes through the set of extensions of $|.|$ to $L$, and where $e_v$ and $f_v$ are the ramification and inertia indexes of $v$. The purpose of my talk is to present a new proof (which is part of current joint reflexions with E. Hrushovski and F. Loeser) of the following classical fact (Grauert, Kuhlmann, Temkin,…) : let $(k,|.|)$ be a stable valued field, and let $(r_1,\dots,r_n)$ be elements of an ordered abelian group $G$ containing $|k^*|$. Let $|.|‘$ be the $G$-valued valuation on $k(T_1,\dots,T_n)$ that sends $\sum a_I T^I$ to $\max_I |a_I|\cdot r^I$. Then $(k(T_1,\dots,T_n),|.|‘)$ is stable too.

Our general strategy is purely geometric, but the proof is based upon model-theoretic tools coming from model theory (which I will first present; no knowledge of model theory will be assumed). In particular, it uses in a crucial way a geometric object defined in model-theoretic terms that Hrushovski and Loeser attach to a given $k$-variety $X$, which is called its stable completion; the only case we will have to consider is that of a curve, in which the stable completion has a very nice model-theoretic property, namely the definability, which makes it very easy to work with.

• Operator algebras and operator theory May 13, 11:10—15:30, 2015, BGU.

Joint Operator Algebras and Operator Theory Seminar, bringing together people from Ben-Gurion University, the Technion, Tel Aviv University and the University of Haifa

• Award of the Noriko Sakurai Postdoctoral Fellowship(*) May 12, 2015, BGU.

• Distinguished Lecture Series: Prof. Ilijas Farah, York University, Canada May 7—18, 2015, BGU.

• Ergodic Theorems and Applications in Probability(*) May 3—8, 2015, Eilat.

• Action NOW(*) Mar 24, 2015, BGU.

• The Moshe Flato Lecture Series 2015 Mar 12, 2015, BGU.

• Workshop on Generalized Cohomology(*) Feb 8—12, 2015, Sde Boker.

• TRATC2014 - Tropicalization, Realization, and Algebraic-Tropical Correspondence(*) Sep 28—Oct 3, 2014, Eilat.

• Award of the Noriko Sakurai Postdoctoral Fellowship(*) May 20, 2014, BGU.

• 30th European Workshop on Computational Geometry (EuroCG 2014)(*) Mar 3—5, 2014, Ein Gedi.

• Workshop on the Central Limit Theorem(*) Jul 2, 2013, Ben-Gurion University, math. dept. building.

• Interactions between Logic, Topological structures and Banach spaces theory(*) May 19—24, 2013, Eilat.

• Action Now Seminar: Mostow and Rigidity(*) May 7, 2013, Ben-Gurion University Math dept. building.

• Workshop on Algebraic, Analytic, and Tropical Geometry (AATG2013)(*) Apr 28—May 3, 2013, Kibbutz Ein Gedi.

• Mini conference in operator algebras(*) Apr 9—10, 2013, BGU.

• Spring School on Group C*-algebras(*) Mar 17—21, 2013, Sde Boker.

• Workshop on C*-algebras and Noncommutative Dynamics(*) Mar 11—14, 2013, Sde Boker.

• Dynamics on parameter spaces 2013 Jan 27—Feb 1, 2013, Sde Boker.

• Award of the Noriko Sakurai Postdoctoral Fellowship for 2013(*) Dec 25, 2012, BGU.

• The Moshe Flato Lecture Series 2011 Mar 10, 2011, BGU.

• The Moshe Flato Lecture Series 2008 Nov 27, 2008, BGU.

• The Moshe Flato Lecture Series 2007 Mar 20, 2007, BGU.

• The Moshe Flato Lecture Series 2004 Nov 25, 2004, BGU.

• The Moshe Flato Lecture Series 2002 Nov 28, 2002, BGU.

(Star) מסמל אירועים הנתמכים בחלקם על-ידי המרכז ללימודים מתקדמים במתמטיקה באוניברסיטת בן-גוריון