INFORMATION ABSTRACTS - THE CONFERENCE 2021 AND - ymcstara.org
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Contents General information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Welcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Schedule of the conference . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Who are the organizers? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Note to online participants . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Zoom coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Mini courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Goulnara Arzhantseva . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Jesse Peterson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Christopher Schafhauser . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Panel Discusssions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Contributed talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Minute talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Information for in person participants . . . . . . . . . . . . . . . . . . . . 29 Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Covid restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Public transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Conference dinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Excursions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Places to eat in Münster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Practical information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2
General information Welcome We are glad to welcome you to the Young Mathematicians in C∗ -Algebras con- ference 2021, hosted in WWU Münster! Due to the pandemic, this year’s event will take on a hybrid format. This booklet contains information for both online and in person participants of the conference. Schedule of the conference YMC*A 2021 takes place over the span of two weeks: August 2-6 (afternoons) and August 9-13 (mornings). As we expect to have participants joining from many different time zones, we have tried to make the conference accessible to as many as possible. YMC*A 2021 features the following events: • Mini courses given by Goulnara Arzhantseva, Jesse Peterson and Christo- pher Schafhauser. • Panel discussions on advice for early career researchers in operator al- gebras. • Contributed talks given by participating speakers. • Sessions of 3-minute poster talks given by participants. The following tables include the detailed schedule of this year’s event. The red colored cells indicate minicourse sessions, while the green ones indicate contributed talks. 3
Week 1 Week 1: August 2 - August 6 Time in CEST Monday Tuesday Wednesday Thursday Friday Jesse Christopher Christopher Jesse 14:00-14:30 Peterson Schafhauser Schafhauser Peterson Jesse Christopher Christopher Jesse 14:30-15:00 Lucas Hall Peterson Schafhauser Schafhauser Peterson Jonathan Kevin Alistair 15:00-15:30 Apurva Seth Ali Raad Turk Aguyar Brix Miller Andrea 15:30-16:00 break break break break Vaccaro Srivatsav Kunna- Jesse Jesse 16:00-16:30 break Xin Ma walkam Elayavalli Peterson Peterson Jesse Jesse 16:30-17:00 Daniel Drimbe panel Dan Ursu Peterson Peterson 17:00-17:30 posters Sayan Das panel Konrad Wróbel 17:30-18:00 posters Krishnendu Khan panel Ishan Week 2 Week 2: August 9 - August 13 Time in CEST Monday Tuesday Wednesday Thursday Friday Goulnara Goulnara Goulnara Goulnara 09:00-09:30 Emily Korfanty Arzhantseva Arzhantseva Arzhantseva Arzhantseva Goulnara Goulnara Andrew Goulnara Goulnara 09:30-10:00 Arzhantseva Arzhantseva Mcdowell Stocker Arzhantseva Arzhantseva Samantha 10:00-10:30 Marzieh Forough Paul Herstedt Bram Verjans Alonso Delfín Pilgrim 10:30-11:00 break break break break break Christopher Christopher Roberto Hernan- 11:00-11:30 Mario Klisse panel Schafhauser Schafhauser dez Palomares Christopher Christopher Priyanga 11:30-12:00 Lise Wouters panel Schafhauser Schafhauser Ganesan Matthew J Devarshi 12:00-12:30 Anshu panel Ferrier Mukherjee Sergio Gi- 12:30-13:00 posters Jan Gundelach ron Pacheco 4
Who are the organizers? This year’s event is organized by the postdocs and PhD students of the Opera- tor Algebras team in WWU Münster, namely • Becky Armstrong • Kristin Courtney • Antje Dabeler • Samuel Evington • Eusebio Gardella • Shirly Geffen • Rafaela Gesing • Grigoris Kopsacheilis • Julian Kranz • Omar Mohsen • Petr Naryshkin • Shintaro Nishikawa • Federico Vigolo • Jeroen Winkel If you have any question or need any help, do not hesitate to contact any of the organizers. We can all be reached at ymcstara@gmail.com or individually; our contact information is included in YMC*A’s website. Either in person or virtually, many of us will be around at all times. 5
Note to online participants It is unfortunate that we cannot all be together in person in this year’s confer- ence. Besides learning and presenting one’s work, YMC*A is also about social- izing and meeting the people that are joining or already working in the field of operator algebras. If you are participating online, please try to take this opportunity and em- brace the social aspect of YMC*A. It would be particularly nice for people to keep their webcams on during the event, join the break-out rooms and engage in conversations with their fellow participants. Zoom coordinates The platform that is going to be used for virtual participation is Zoom. We ask our remote participants to connect to the conference using the names that they registered with, so that we can prevent any malicious parties from joining. The Zoom coordinates will be announced via email on July 30. If you wish to receive the coordinates after July 30, please email ymcstara@gmail.com. 6
Mini courses The conference features three mini courses, each of which consists of 4 lec- tures. These will be given by Goulnara Arzhantseva (University of Vienna), Christopher Schafhauser (University of Nebraska) and Jesse Peterson (Vander- bilt University). You can find their abstracts in the following pages. Goulnara Arzhantseva Constructions of non C∗ -exact groups A countable discrete group G is C∗ -exact or simply, exact, if its reduced C∗ - algebra C r∗ (G) is an exact C∗ -algebra (i.e. if taking the minimal tensor product with C r∗ (G) preserves short exact sequences of C∗ -algebras). Equivalently, G is exact if it admits an amenable action on some compact Hausdorff space. Ex- act groups are also said to be boundary amenable, amenable at infinity, to have Guoliang Yu’s property A or to be coarsely amenable. The exactness is viewed as a weak amenability type condition. All amenable groups, linear groups, Gromov’s hyperbolic groups, groups with finite asymptotic dimension, and many other familiar groups are known to be exact. In contrast, constructions of non-exact groups are rare and technically quite involved. We will discuss such constructions, indicate applications, and suggest some open problems. 7
Jesse Peterson Von Neumann algebras and lattices in higher-rank groups Lecture 1: Background on von Neumann algebras. We’ll briskly review basic properties of semi-finite von Neumann algebras. The standard representation, completely positive maps, group von Neumann algebras, the group-measure space construction, and some characterizations of the hyperfinite II1 factor. Lecture 2: Some approximation properties. We discuss some approximation properties that are common in "rank 1" groups: Weak amenability and biex- actness. Lecture 3: Proper proximality We discuss properly proximal groups as defined by Boutonnet, Ioana, and myself, and give some applications to group von Neumann algebras associated to higher-rank groups. m Lecture 4: Von Neumann equivalence. We’ll introduce measure equivalence (ME), W∗ -equivalence (W∗ E), and von Neumann equivalence (VNE). We’ll give examples and discuss invariants. 8
Christopher Schafhauser On the classification of simple nuclear C∗ -algebras A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C∗ -algebras are determined up to isomorphism by their K - theoretic and tracial data. Restricting to purely infinite algebras, this is the fa- mous Kirchberg-Phillips Theorem. The stably finite setting proved to be much more subtle and has been a driving force in research in C∗ -algebras over the last 30 years. A series of breakthroughs were made in 2015 through the classi- fication results of Elliott, Gong, Lin, and Niu and the quasidiagonality theorem of Tikuisis, White, and Winter. Today, the classification conjecture is now a the- orem under two additional regularity assumptions: Z -stability and the UCT. In my recent joint work with José Carrión, Jamie Gabe, Aaron Tikuisis, and Stu- art White a much shorter and more conceptual proof of the classification the- orem in the stably finite setting was provided. I hope to give an overview of the classification problem for C∗ -algebras and discuss some of the new techniques that led to the new proof. 9
Panel Discusssions On each Wednesday, we will host a panel consisting of senior mathematicians from around the world (both from academia and industry) who will address common topics such as applying for jobs, giving talks, submitting papers, nav- igating a career in and out of academia, etc. The panels are as follows: • Week 1 - Nate Brown (Penn State University) - Alcides Buss (Federal University of Santa Catarina) - Marcelo Laca (University of Victoria) - David Penneys (Ohio State University) - Thomas Timmerman (Codecentric) - Lyudmila Turowska (Chalmers University of Technology, Gothenburg) - Gouliang Yu (Texas A&M University) • Week 2 - Bernard Okello (Jaramogi Oginga Odinga University of Science and Technology) - Narutaka Ozawa (Kyoto University) - Jacqui Ramagge (Durham University) - Prahlad Vaidyanathan (Indian Institute of Science Education and Re- search Bhopal) - Sam Webster (Independent Hospital Pricing Authority) - Stuart White (Oxford University) 10
Contributed talks In this section you will find the titles and abstracts of the 20-minute contributed talks appearing in this year’s YMC*A. Anshu Connected stable rank of C∗ -algebras The goal of this talk is to discuss the connected stable rank of a C∗ -algebra. The notion of connected stable rank was introduced by Marc Rieffel in the pursuit of understanding the stability properties of C∗ -algebras. In the first part of the talk, we will define the connected stable rank and will discuss some basic examples. We will also discuss the relationship between the connected stable rank of a C∗ -algebra A and its K -theory. Then we will move on to give brief descriptions of a C (X )-algebra and a crossed product C∗ -algebra by a fi- nite group. In the later part of the talk, we will provide estimates of connected stable rank for upper semicontinuous C (X )-algebras and crossed product C∗ - algebras by finite groups. We will also prove that if A has connected stable rank one, then the crossed product C∗ -algebra by an action with the Rokhlin prop- erty also has connected stable rank one. Kevin Aguyar Brix C∗ -algebras from symbolic dynamical systems Cuntz–Krieger algebras are constructed from symbolic dynamical systems of finite type (finite graphs) and they provided the first large class of simple and purely infinite C∗ -algebras. This was the inspiration for the rich and diverse (yet tangable) class of graph C∗ -algebras. In this talk, I will advertise a different generalisation of Cuntz–Krieger algebras constructed from general symbolic dynamical systems. These C∗ -algebras are still not completely understood but 11
I will indicate how their fine structure allows us to infer properties of the un- derlying dynamics. Sayan Das On the free group factor problem, and Popa’s MV-property One of the most important outstanding problems in von Neumann algebras asks if the group von Neumann algebra of the free group on two generators, denoted by L(F2 ), is isomorphic to the group von Neumann algebra of the free group on infinitely many generators, denoted by L(F∞ ). Recently, S. Popa es- tablished a roadmap for showing the nonisomorphism of L(F2 ) and L(F∞ ). The first step of the proposed roadmap is to establish the so called mean value property (abbreviated MV-property) for L(F2 ). In this talk I shall describe the proof of the result that L(F2 ) has the MV- property, thereby establishing the first step of Popa’s roadmap. This talk is based on a recent joint work with Prof. Jesse Peterson. Alonso Delfín C∗ -like modules over L p operator algebras In this talk, we describe a new general characterization for Hilbert modules over C∗ -algebras. Motivated by this characterization, we introduce the con- cept of C∗ -like modules over L p operator algebras and present several exam- ples. For some particular C∗ -like modules (X , Y ), we associate an L p operator algebra O p (X , Y ) via a Fock space construction. The way we define O p (X , Y ) is an analogue of the Cuntz-Pimsner construction for C∗ -correspondences. Even though this is still a work in progress, we believe that it could yield an interest- ing class of L p operator algebras. In fact, we show that if d ∈ Z≥2 , p ∈ (1, ∞), p q and q is its Hölder conjugate, then the pair (`d , `d ) is a C∗ -like module over C p q p and O p (`d , `d ) is isometrically isomorphic to O d the L p -version of the Cuntz algebra introduced by N.C. Phillips back in 2012. 12
Daniel Drimbe New examples of W∗ and C∗ -superrigid groups A group G is called W∗ -superrigid (resp. C∗ -superrigid) if it is completely "re- membered" by its von Neumann algebra (resp. its reduced C∗ -algebra). An important, but challenging problem in operator algebras is to produce new examples of such groups since it clarifies the classification of these ob- jects. Although this problem goes back to the pioneers of the field, currently only a few classes of W∗ -superrigid and C∗ -superrigid groups are known in the literature. The goal of this talk is to present new constructions of W∗ and C∗ -superrigid groups arising from various natural constructions in group theory including direct products, amalgamated free products, HNN extensions, wreath prod- ucts and coinduced groups. The proofs of these results are based on Popa’s deformation/rigidity theory along with a natural interplay with C∗ -algebraic techniques such as the unique trace property and the absence of nontrivial projections. This is based on a very recent joint work with Ionut Chifan and Alec Diaz-Arias. Srivatsav Kunnawalkam Elayavalli Proper proximality for groups acting on trees We will discuss new joint work with Changying Ding, wherein we find new ex- amples of properly proximal groups. This property was introduced by Boutonnet- Ioana-Peterson in 2018, and is a very flexible dynamical property that has di- rect consequences to Cartan rigidity at the von Neumann algebra level. We show that a family of groups acting on trees naturally fits into this framework. Time permitting, I will also describe a complete classification result of proper proximality among graph products of groups. 13
Matthew J Ferrier Morita equivalence of C∗ -categories Morita equivalence for C∗ -algebras was developed by Marc Rieffel in the 1970’s. It’s possible to view this as an extension of the algebraic notion for rings, so far as two C∗ -algebras are Morita equivalent if their categories of Hilbert modules are equivalent, and the functors implementing the equivalence must satisfy some additional mild conditions. C∗ -categories are a naturally occurring generalisation of C∗ -algebras, with examples including the category of Hilbert modules over a C∗ -algebra. In this talk we will take a look at the basics of C∗ -categories, and see how we can ex- tend Rieffel’s notion of Morita equivalence to this setting. Hopefully we will also have time to see how this notion fits in with other constructions first made by Michael Joachim. Marzieh Forough Lifts of completely positive equivariant maps In this talk, I will first give a brief introduction to the lifting problem for com- pletely positive maps between C∗ -algebras. In particular, the Choi-Effros lift- ing theorem and some of its consequences in the theory of C∗ -algebras will be explained. Motivated by the wide range applications of this celebrated lifting theorem and the recent increased interests in the structure of C∗ -dynamical systems, it is natural to look for an equivariant version of the lifting result for completely positive maps. I will address this problem, more precisely, discuss the following equivariant result: Let G be a locally compact second countable group, A and B be G-algebras and let I be a G-invariant ideal of B . Then every completely positive contractive map from A into B /I admits asymptotically equivariant lifts. This talk is based on joint work with Eusebio Gardella and Klaus Thomsen. 14
Priyanga Ganesan Quantum graphs Quantum graphs are an operator space generalization of classical graphs. In this talk, I will present the different notions of quantum graphs that arise in operator systems theory, non-commutative topology and quantum informa- tion theory. I will then introduce a non-local game with quantum inputs and classical outputs, that generalizes the graph homomorphism game for clas- sical graphs. This is based on joint work with Michael Brannan and Samuel Harris. Jan Gundelach Leavitt path algebras as Cohn localisations A directed graph E = (E 0 ; E 1 ; s, r : E 1 → E 0 ) offers the framework to construct an associated graph C∗ -algebra that is designed to model vertices as orthog- onal projections and edges as associated partial isometries with well-behaved range and source projections. If one drops the analytic aspect of completion in a C∗ -norm to restrict attention to the involved ∗-algebraic Cuntz-Krieger relations, this modelling provides Leavitt path algebras instead. The key observation I want to highlight in this talk is that the Cuntz-Krieger relations for relative Leavitt path algebras L can be equivalently posed as in- vertibility postulations for path prolongation maps over some path algebra B . This justifies to treat them as Cohn localised path algebras L = Cohn(B ). Now, compatibility of quasi-freeness and Cohn localisation allows to effectively re- duce the computation of differential forms for L to the conceptually easier path algebra B . In the end we obtain a projective bimodule resolution of length one for L without much theory which can be used as a tool for further homo- logical computations. 15
Lucas Hall Coactions and skew products for topological quivers Since their introduction at the turn of the century, graph algebras have shed new light on the field of C∗ -algebras by allowing one to investigate algebraic structure in terms of a combinatorial picture. Among other things, this lens provided a new perspective for the study of nonabelian duality through the construction of skew product graphs, yielding “coactions you can see.” Here, we investigate skew products for topological quivers, a vast general- ization to directed graphs which allow for topological data and flexible range and source maps. We show that, as in the discrete case, the algebra associated to a skew product is related to a crossed product by a coaction. In this context, the coaction is nice enough that the dual action is amenable in an appropriate sense. Paul Herstedt AT-algebras associated to zero-dimensional systems We introduce a new class of zero-dimensional dynamical systems, which we call "fiberwise essentially minimal", whose crossed product is guaranteed to be an AT-algebra. Under the assumption that these systems also have no peri- odic points, the crossed product also has real rank zero, and is hence classifi- able. This work extends the results of the minimal case (Putnam ’90) and the essentially minimal case (Herman, Putnam, Skau ’95) to classify a larger class of (non-simple) crossed products obtained from zero-dimensional dynamical systems. 16
Ishan Von Neumann equivalence and group approximation properties The notion of measure equivalence of groups was introduced by Gromov as the measurable counterpart to the topological notion of quasi-isometry. Another well-studied notion is that of W∗ -equivalence which states that two groups Γ and Λ are W∗ -equivalent if they have isomorphic group von Neumann alge- bras, i.e., LΓ ' LΛ. We introduce a coarser equivalence, which we call von Neumann equivalence, and show that it encapsulates both measure equiva- lence and W∗ -equivalence. We will also discuss the stability of many group approximation properties under von Neumann equivalence, particularly, that of the new and a wide class of groups called properly proximal groups, intro- duced by Rémi Boutonnet, Adrian Ioana, and Jesse Peterson, and thereby ob- taining first examples of non-inner-amenable, non-properly proximal groups. This is based on joint work with Jesse Peterson and Lauren Ruth. Krishnendu Khan Fundamental group of certain property (T) factors Calculation of fundamental group of type II1 factor is, in general, an extremely hard and central problem in the field of von Neumann algebras. In this direc- tion, a conjecture due to A. Connes states that the fundamental group of the group von Neumann algebra associated to any icc property (T) group is triv- ial. Up to now there was no single example of property (T) factor satisfying the conjecture. In this talk, I shall provide the first examples of property (T) group factors (arising from group theoretic constructions) with trivial fundamental group. This talk is based on a joint work with Ionut Chifan, Sayan Das and Cyril Houdayer. 17
Mario Klisse A C∗ -dynamical approach to the simplicity of Hecke C∗ -algebras (Iwahori) Hecke algebras are deformations of the group algebras of Coxeter groups depending on a deformation parameter. They can be naturally rep- resented on the `2 -space of the corresponding group and thus complete to C∗ -algebras. The aim of this talk is to discuss certain topological boundaries associated with (Cayley graphs of ) Coxeter systems. These boundaries reflect combinatorial and order theoretic properties of the underlying group and are closely related to the Hecke C∗ -algebras of the system. The exploitation of their (dynamical) properties allows to answer the question for the simplicity of right-angled Hecke C∗ -algebras. I will explain the idea behind this approach. Emily Korfanty Étale equivalence relations and C∗ -algebras for iterated function systems The iteration of a collection of contractive maps on a closed subset of Eu- clidean space can produce geometrically interesting self-similar sets, or frac- tals. These collections are called iterated function systems. Many classic self- similar sets, such as the Siérpinski Gasket, can be constructed from a collection of affine maps differing only by translations. Moreover, a groupoid C∗ -algebra construction has yet to be provided for many standard iterated function sys- tems of this type. In this talk, we will introduce étale equivalence relations for this broad class of iterated function systems, and discuss the associated groupoid C∗ -algebras, with a focus on the Siérpinski Gasket as an example. 18
Xin Ma Fiberwise amenability and almost elementariness for Hausdorff étale groupoids In this talk, I will discuss two new properties for locally compact Hausdorff étale groupoids. One is from a coarse geometric view called fiberwise amenabil- ity as a new generalization of amenability for discrete groups. Another one from the dynamical view is called almost elementariness, which is a general- ization of the concept of almost finiteness introduced by Matui and refined by Kerr. I will show our almost elementariness implying tracial Z -stability of re- duced groupoid C∗ -algebras if the groupoid is minimal and 2nd countable. As an application, Matui’s almost finiteness in the groupoid setting also implies Z -stability of reduced groupoid C∗ -algebras when the groupoid is minimal, 2nd countable and topological amenable. This was open in general before. I will also present more applications if time permits. This is based on joint work with Jianchao Wu. Alistair Miller Groupoid correspondences and the ABC spectral sequence Étale groupoids provide a rich source of examples of C∗ -algebras via the groupo- id C∗ -algebra construction. To view this construction and related construc- tions as functorial, we need a notion of groupoid morphism that induces an analogue for the C∗ -algebras. Groupoid correspondences induce C∗ -correspon- dences, which are a type of morphism of C∗ -algebras useful in K-theory. One particular construction we are interested in is the ABC spectral se- quence, which V. Proietti and M. Yamashita studied in the context of a torsion- free ample groupoid. We can make the construction of the spectral sequence functorial with respect to certain groupoid correspondences, and we sketch an application of this. 19
Devarshi Mukherjee Cyclic homology and non-commutative geometry in positive characteristic The notion of a smooth subalgebra of a C∗ -algebra - analogous to the algebra of smooth functions on a manifold C ∞ (M ) embedded inside the algebra of continuous functions C (M ) - is a key insight in defining well-behaved invari- ants for C∗ -algebras. In this talk, I will explain how similar ideas can be used to study non-commutative algebras and their invariants when the underlying field has positive characteristic. The examples of non-commutative algebras that we are interested in are suitable analogues of crossed product algebras and Leavitt path algebras. Finally, I will discuss the computation of analytic cyclic homology for a Leavitt path algebra of a countable graph, showing that our result recovers expected and known results from characteristic zero. Parts of this talk is based on joint work with Guillermo Cortinas and Ralf Meyer. Sergio Giron Pacheco Symmetries of simple operator algebras In this talk I will start by giving an elementary introduction to the symme- tries of the Hyperfinite II1 factor R. I will shortly discuss classification re- sults of these by Connes, Jones, Ocneanu and Popa. I will then discuss how the existence of these symmetries carry over to a particularly nice class of C∗ - algebras, those classified by the Elliott programme. In fact, it is known that any countable discrete group G acts faithfully on any classifiable C∗ -algebra. How- ever, even for types of quantum symmetries closely related to group actions (anomalous symmetries) the existence question is subtle and it can have both positive and negative answers. This talk is based on joint work with Samuel Evington. 20
Roberto Hernandez Palomares Q-system completion for C∗ -algebras We will focus on the C∗ 2-category C∗ Alg with objects unital C∗ -algebras, 1- morphisms right C∗ Hilbert correspondences, and 2-morphisms adjointable intertwiners. Q-systems were introduced by Longo to describe the canonical endomor- phism of a finite index inclusion of infinite von Neumann factors N ⊂ M . Q- systems in C∗ Alg characterize finite Watatani index extensions of a unital C∗ - algebra B ⊂ A equipped with a faithful conditional expectation E B : A → B . Following work of Douglass-Reutter, a Q-system is also a unitary version of a higher idempotent, and Q-system completion is a unitary version of a higher idempotent completion for C∗ 2-categories. We will show C∗ Alg is Q-system complete, i.e., Q-system completion is a ∗ -2-equivalence. We prove this by constructing an inverse ∗ -2-functor called realization which turns Q-systems back into unital C∗ -algebras. These tech- niques allow for the straightforward adaptation of subfactor techniques to study- ing actions of unitary tensor categories on C∗ -algebras. This is joint work of Quan Chen, Roberto Hernandez Palomares, Corey Jones, and David Penneys. Samantha Pilgrim Isometric actions and finite approximations We demonstrate relationships between group actions which fix metrics and those which admit certain finite approximations (definitions and some ele- mentary theory of such approximations for group actions will also be explained). In particular we show that every isometric action on a Cantor set is conjugate to an inverse limit of actions on finite sets; and that every translation action by a finitely-generated, amenable subgroup of a compact group is residually finite. We also discuss the implications for C∗ -algebras arising from such ac- tions, proving in a more direct way than previously known that crossed prod- ucts of the translation actions mentioned earlier are quasi-diagonal. 21
Ali Raad Existence and uniqueness of inductive limit Cartan subalgebras in inductive limit C∗ -algebras Cartan subalgebras of C∗ -algebras have been pivotal in connecting C∗ -algebras to topological dynamics and geometric group theory. They have also featured in the UCT Problem, which has reductions in terms of whether certain C∗ - algebras contain Cartan subalgebras. Hence, the question of existence and uniqueness of Cartan subalgebras in C∗ -algebras has received a lot of atten- tion recently. One particular class of interest is in AX-algebras, which are cer- tain inductive limit C∗ -algebras. In this talk I wish to introduce this class and the notion of a Cartan subal- gebra, and specifically an inductive limit Cartan subalgebra. AF-algebras are a great example of an instance in which we find unique inductive limit Cartan subalgebras, due to a construction by Stratila and Voiculescu in 1975. I wish to present one of the results of my PhD, which answers this existence and unique- ness question for AI and AT-algebras, as well as for general AX-algebras under certain conditions on X. Apurva Seth AF-algebras and rational homotopy theory In this talk, we give a procedure to compute the rational homotopy groups of the group of quasi-unitaries of an AF-algebra. As an application, we show that an AF-algebra is K-stable if and only if it is rationally K-stable. 22
Andrew Mcdowell Stocker C∗ -algebras of expansive dynamical systems This work builds on the work done by Klaus Thomsen towards generalizing the Smale space methods developed by Putnam and Ruelle to the setting of expan- sive dynamical systems. We will present a class of dynamical systems called synchronizing systems which are expansive and generalize Smale spaces, and we will show that this class of dynamical systems generalizes Smale spaces but is still amenable to the techniques of Putnam and Ruelle. No knowledge of dy- namical systems will be assumed for this talk. Jonathan Turk Prime order subgroup correspondences If H is a closed subgroup of a locally compact group G, we may associate a C∗ -correspondence to the pair (H ,G). When G is finite and H has order 2, the Cuntz-Pimsner algebra of this correspondence only depends on how the canonical action of H on G/H partitions G/H into orbits. In many cases, K- theory, Mackey’s Subgroup Theorem, and the theory of graph algebras may be used to identify the Cuntz-Pimsner algebra up to isomorphism. The first half of the talk will be an introduction to C∗ -correspondences and will demonstrate how they’re used to induce a representation from one group to another. This introduction will also include a light description of the Cuntz-Pimsner algebra of a C∗ -correspondence without going through the heavy details. The second half of the talk will give more insight into the techniques used to identify cer- tain Cuntz-Pimsner algebras. The talk will end by discussing the speaker’s re- search aiming to apply these techniques to the more general setting where G is finite and the order of H is an arbitrary prime. 23
Dan Ursu The ideal intersection property for essential groupoid C∗ -algebras Groupoids give a very large class of examples of C∗ -algebras. For example, it is known that every classifiable C∗ -algebra arises as the reduced C∗ -algebra of some twisted groupoid. In joint work with Matthew Kennedy, Se-Jin Kim, Xin Li, and Sven Raum, we fully characterize when the essential C∗ -algebra of an étale groupoid G with locally compact unit space has the ideal intersection property. This is done in terms of the dynamics of G on the space of subgroups of the isotropy groups of G . The essential and reduced C∗ -algebras coincide in the case of Haus- dorff groupoids, and the ideal intersection property is the same as simplicity in the case of minimal groupoids. This generalizes the case of the reduced crossed product C (X ) or G done by Kawabe, which in turn generalizes the case of the reduced C∗ algebra C r∗ (G) of a discrete group done by Breuillard, Kalan- tar, Kennedy, and Ozawa. No prior knowledge of groupoids will be required for this talk. Andrea Vaccaro Games on AF-algebras In the framework of continuous model theory, two C∗ -algebras A and B are said to be elementarily equivalent if they have the same first order theory. This concretely implies, for instance, that any property which can be expressed as inf / sup max{Q 1 (x), . . . ,Q k (X )} = 0, kxk≤1 where each Q j (x) is a ∗ -polynomial, is satisfied by A if and only if it is satisfied by B . When restricting to the class of UHF algebras, elementary equivalence is the same as isomorphism. This is known to be false for AF-algebras, but finding concrete examples of AF-algebras which are elementarily equivalent but not isomorphic is not immediate (the only examples known until now were all abelian). 24
The isomorphism class of an AF-algebra is completely determined by its dimension group, K 0 (A). Similarly, we show that the theory of K 0 (A), as an abelian ordered group, determines to some extent the theory of A. This per- mits to reduce the study of elementary equivalence on C∗ -algebras to the study of elementary equivalence on abelian ordered groups, allowing to find a large class of pairwise elementarily equivalent non-isomorphic simple AF-algebras, as well as simple AF-algebras of arbitrarily high Scott’s rank. This is done by exploiting the classical characterization of elementary equivalence in terms of Ehrenfeucht-Fraïssé games. Bram Verjans Bernoulli actions of type III and their von Neumann algebras Non-singular group actions G æ (X , µ) lead to a fundamental class of exam- ples of von Neumann algebras, through the group measure space construction L ∞ (X ) o G. Classifying these von Neumann algebras in terms of isomorphism of the actions is a very challenging problem. In the past two decades, Popa’s deformation/rigidity theory has led to a lot of progress, especially in the case of probability measure preserving actions. The classification problem for actions of type III is much less understood. In this talk we consider a family of type III Bernoulli actions of free product groups. We present a non-isomorphism result of their von Neumann algebras and give examples of non-isomorphic von Neumann algebras having the same modular invariants. This is joint work with Stefaan Vaes. Lise Wouters Equivariant Jiang–Su stability for automorphisms An action of a countable group on a C∗ -algebra is called equivariantly Z -stable if it tensorially absorbs the trivial action on the Jiang-Su algebra. Analogous to ordinary Z -stability, equivariant Z -stability is an important regularity prop- erty in the context of the classification of amenable group actions on classi- fiable C∗ -algebras. In this talk I will explain the relevance and nature of this property and discuss for which actions positive results were already obtained 25
establishing the property. In particular, I will present my own recent result: I have proved that the property holds automatically for all automorphisms on algebraically simple, separable, nuclear, Z -stable C∗ -algebras for which the trace space is a Bauer simplex with finite-dimensional extremal boundary. At least for automorphisms this is a generalization of a previous result by Gardella-Hirshberg. Konrad Wróbel Orbit equivalence of wreath products Let F be a nonabelian free group. We show that, for any two nontrivial finite groups, the natural actions of the wreath product groups A o F and B o F , on A F and B F respectively, are orbit equivalent. On the other hand, we show that these actions are not even stably orbit equivalent if F is replaced with any ICC sofic group with property (T), and A and B have different cardinalities. This is joint work with Robin Tucker-Drob. 26
3 Minute talks In this section you will find the list of the 3 minute “poster talks" appearing in this year’s YMC*A. Week 1 Alon Dogon, Hilbert Schmidt stability and characters on amenable groups Cristian Ivanescu, Cu-nuclearity and applications Collin Mark Joseph, Topological Insulators Jacek Krajczok, On the radial subalgebra for the quantum O F+ group Natã Machado, Étale categories, restriction semigroups and their operator algebras Jacob Mashburn, Fock spaces with nearest neighbor coupling Robert-Mihai Neagu, On amenable and quasidiagonal traces and their behaviour under ho- motopy Eduardo Scarparo, A torsion-free C∗ -unique group 27
Sushil Singla, Orthogonality, Gateaux derivative and ideals in C∗ -algebras Joel Right Dzokou Talla, Quantum SL(2; R) and its irreducible representations Week 2 Maria Stella Adamo, Standard subspaces in AQFT and beyond Zahra Hasanpour, Morita equivalence and partial actions Shuler Hopkins, Deformations of commuting squares and complex Hadamard matrices Tomoki Uchimura, A colimit of certain diagram in the correspondence bicategory Amudhan Krishnaswamy Usha, Non-spectral operators in a tracial von Neumann algebra Gerrit Vos, BMO spaces of sigma-finite von Neumann algebras and Fourier-Schur multipliers on SU q (2) 28
Information for in person participants We are very glad to welcome you to the city of Münster! This part of the booklet includes all the information you need to get around during YMC*A. We hope you enjoy your time here! Locations YMC*A takes place at the mathematics department of WWU Münster, which is located at Einsteinstraße 64. All the lectures will be given in the M1 hall of the old flat building: just enter the main entrance and turn right at the end of the corridor. There will also be signs inside the building to guide you to M1. Here is a map of the area; the lecture hall is located in the Hörsaalgebäude. © OpenStreetMap contributors 29
Covid restrictions Due to the pandemic, there are certain rules that we need to follow in order to minimize the risk of covid-19 transmission. In particular: Ï Participants that are attending the conference in person need to take an antigen rapid test every 48 hours during the conference, even if they are fully vaccinated/recovered in the last 6 months. For rapid tests, one can either have a self-test or a test at one of the public test sites around the city. Self-tests will be provided by the conference. On Mondays (1:15 pm on the 1st week and 8:15 am on the 2nd week) the organizers will demonstrate how these work. If you wish to have a free official rapid test, you should visit • ASB Münster, Parkplatz Schlossplatz Nord (Schlossplatz 24) during 8 am - 8 pm on weekdays and 9 am - 12 pm on weekends. If you visit the test site, make sure to have your ID card or passport with you. Here is a map to help you orient: Ï Inside the university buildings, wearing a surgical or an FFP2 mask is mandatory1 . When seated in the M1 lecture hall during a talk, partici- 1 You can buy such masks at any drug store, pharmacy or grocery store in Münster. 30
pants can take off their masks, since M1 is well ventilated with a certified system and large enough for us to keep a safe distance of 1.5 meters from one another. Ï If you are experiencing any respiratory symptoms (coughing, sneezing) or fever, please refrain from participation and contact the organizers as soon as possible to discuss how to proceed. In case of a positive test, the general rules of the health department of the city of Münster apply. Besides the above rules, we encourage the participants to practice safety measures such as avoiding handshakes, maintaining a minimum distance of 1.5 meters from others and frequently using hand sanitizer. If you have any question regarding the above rules, please contact either Anja Böckenholt at anja.boeckenholt@uni-muenster.de or Carolin Gietz at carolin.gietz@uni-muenster.de Public transportation Ï Münster is also known as the "bicycle capital of Germany", the reason being that the city is very accessible by bike; everyone uses them around here, so renting a bike is a very convenient option to get around. Here is a list of some bicycle rental stations, the prices vary around 10€ per day. • Radstation Münster Hundt KG, address: Berliner Platz 27A • Canu Camp, address: Homannstraße 64 • Hof zur Linde, address: Handorfer Werseufer 1 • Landhaus Eggert, address: Zur Haskenau 81 • Fahrrad Look, address: Dingbängerweg 249 You can find more information about these rental stations, their web- sites and even more alternatives to these by following this link 31
https://www.stadt-muenster.de/en/tourismus/bike-city/ bicycle-rental Ï Münster’s main means of public transport is the city bus. There are many frequent bus routes that link the inner part of the city; the maximum waiting time is 10-20 minutes, but a lot of routes are covered by more than one line with alternating schedules. A single ticket (“Einzelticket”) (90 min ride on any bus line in any one direction– no returns) costs about 2.90€, while a short route ticket (dis- tance of 5 bus stops) costs about 1.90€. There are many alternatives to these like 24hour tickets, or tickets for one whole week. For an interac- tive overview of all the available tickets and the respective prices, follow this hyperlink. You can buy tickets for the bus from machines at central bus stops, from the Stadtwerke service centers located at BerlinerPlatz 22, Hafenweg 1 and Salzstraße 21 (you might need to check their time schedules though), or using the Deutschebahn App (available in English). Keep in mind that, due to Covid-19, surgical or FFP2 masks are manda- tory inside the city buses. For those of you speaking German, you can also install the "Münster:app" on your smartphone; this app helps you choose the most convenient line for your destination, offers information on tickets etc. A non-German alternative to this is Google maps, which offers a good deal of information on how to move around the city. Reception The reception for each week will take place on Monday evening, at 7 pm. There will be tents, benches and tables set up on the grass area behind the main building of the mathematics department. There we will have the opportunity to meet each other and talk over pizza, cold beer and soft drinks! Conference dinner There will be two conference dinners, one for each week. These will take place on Wednesday evenings at 7pm and the cost is covered by the conference. We 32
have booked the Indian restaurant Buddha Palace, which is located at Von- Esmarch-Straße 18 (this is 10 minutes away by foot from the mathematics de- partment). On Mondays we will distribute menus to the participants and take your orders for the dinner. Excursions Below you can find a list of excursions that we have planned during YMC*A along with a short description for each. Feel free to join any activity you like! Week 1 Ï Aasee Brunch Brunch with a nice view over the lake in Münster. We’ll meet on Thurs- day at 10 am on the lawn around the Giant Pool Balls at the Aasee (see map). Make sure to bring something to eat and drink. There are some nice bakeries around the city center (e.g. Essmann’s Backstube, which is very close to your hostel) and the Roestbar as well as Herr Hase make very nice coffee. If the weather does not allow us to sit outside (i.e. if it is raining), we will meet at Herr Sonnenschein (Königsstraße 43). In this case you do not need to bring your own food. Ï Macke-Exhibition at the LWL-Museum We meet on Tuesday (Aug 3) at 10 am in front of the main entrance (fac- ing the Cathedral) of the LWL-Museum (see map). The current exhi- bition features the work of expressionist painters August and Elizabeth Macke as well as a big variety of art ranging from the middle ages up to the 21st century. The admission costs 13€. Afterwards, we will get lunch downtown and then walk to the institute. Email Julian (julian.kranz@uni-muenster.de) by Monday if you are interested in participating. Ï Double-Decker City Tour See downtown Münster with a double-decker bus tour. From start to finish, it lasts 50 minutes, but the ticket is valid to hop-on/hop-off all day. The audio guide comes in German, English, Dutch, Spanish, French, and Russian. We meet on Wednesday (Aug 4) at 11 am at the pick-up point 33
on Domplatz in front of the LWL-Museum (see map). The cost is 11.50€. Afterwards, we will get lunch at the city market and then head to the math institute. (You are also welcome to check out the city market before the tour.) Email Kristin (kcourtne@uni-muenster.de) by Tuesday if you are in- terested in participating. The meeting points for the week 1 excursions can be found in the following auxiliary map. The red X denotes the meeting point for the bus tour, the green mark is for the exhibition, and the blue box points to the Giant Pool Balls where we will meet for Brunch. Week 2 Ï Kanal If the weather is nice, we will go on Wednesday to the Kanal (Münster’s closest thing to a beach). We will meet after lunch and go either by bike 34
or bus. Email Eusebio at gardella@uni-muenster.de if you’re inter- ested in joining. Ï Macke-Exhibition at the LWL-Museum We meet on Tuesday at 1:30 pm in front of the institute and walk down- town to get some lunch. After lunch, we go to the LWL-Museum. The current exhibition features the work of expressionist painters August and Elizabeth Macke as well as a big variety of art ranging from the middle ages up to the 21st century. The admission costs 13€. Email Julian (julian.kranz@uni-muenster.de) by Monday if you are interested in participating. Of course there are many other things to do besides the above activities. We mention only some of the alternatives below: • City Market: On Wednesdays and Saturdays, from 7 am to 2:30 pm, one can visit the city market of Münster, an open market set up behind St. Paulus dom in the city centre. There you can find a large variety of food products, fabrics, clothes and jewellery, as well as flowers and plants. For more information on the providers and an interactive map of the city market, you can visit the market’s web-page: https://www.wochenmarkt-muenster.de/oeffnungszeiten • Mühlenhof Open-Air Museum: This outdoor museum is a five-hectare site that preserves the culture and history of the Münsterland region from the 16th to the 19th century. On the site there are 30 buildings, many of which are original structures from that time; on the inside, the buildings are furnished with historical goods so that visitors get a real impression of the Münsterland of days gone by. The outdoor museum’s address is Theo-Breider-Weg 1 and it is open from 10am to 6pm. An adult ticket costs 6€, while a student ticket costs 4€. • Pablo Picasso Museum: The Pablo Picasso Münster Art Museum is Ger- many’s first and so far only Picasso museum. The museum shows chang- ing special exhibitions on Pablo Picasso and his fellow classical modern artists such as Georges Braque, Henri Matisse and Marc Chagall. The 35
foundation of Münster’s Picasso collection is a globally unique collec- tion of around 800 Picasso lithographs. The museum is located at Picassoplatz 1 and is open everyday except Mondays from 10am to 6pm. An adult ticket costs 10€, while a student ticket costs 8€. To visit the museum, it is necessary to book an online ticket, which you can do by following this link: https://kunstmuseum-picasso-muenster.de/home/ • City Fair: It is a pleasant coincidence that Münster’s city fair will be tak- ing place at the same time as YMC*A. The fair is located in front of the Schloss (on Schlossplatz) and can be visited every day from Monday to Thursday, from 2pm until 10pm. There will be many fun activities to do and things to see around there! The entrance costs only 1€ but the rides and food will cost more, so make sure to bring some extra cash. It is nec- essary to provide proof of covid-19 vaccination/recovery or a negative rapid test before entering the fair and surgical/FFP2 masks need to be worn. • City Zoo: Münster’s “allwetterzoo" is a large zoo that accommodates many animals from different species and different climate zones. The zoo features a 5 km network of trails connecting the large animal houses and is open every day from 9 am to 7 pm. An adult day ticket costs 18.90€, while a student day ticket costs 12.90€. The zoo is located at Sentruper Straße 315. The bus line connecting the main station Münster Hbf to the city zoo is line 14. You can find more information on the zoo’s website: https://www.allwetterzoo.de/ • City Tours: There are plenty of guided/thematic city tours offered in Münster - by foot, by bike or by bus. There are also many creative city games such as murder & mystery events, GPS rallies and much more! Some offers from different guides can be found in the following links: https://k3.de/en/muenster/tours https://www.stadtlupe-muenster.de/ https://www.stattreisen-muenster.de/ 36
Places to eat in Münster There are many places around Münster where you can get something to eat. For lunch, we can recommend the following restaurants: • Near the campus: - Gustav Grün (Wilhelmstraße 5), vegeterian & vegan menu (takeaway). - Áro (Neutor 3), fusion restaurant (takeaway) - Phoenicia (Steinfurter Str. 37), Lebanese cuisine (dine-in, takeaway) • Around the city: -Meraki (Hansaring 69), Arabic food (dine-in, takeaway) - Frauenstraße 24 (the name is also the address), multi-cultural cuisine (dine-in, takeaway) - Royals & Rice (Frauenstraße 51), Asian fusion restaurant (dine-in, take- away) - Beetschwester (Tibusstraße 6), vegeterian & vegan menu (dine-in, take- away) - Elbēn am Aasee (Scharnhorststraße 25), Syrian cuisine (dine-in, take- away) A popular option for lunch near the institute is the Mensa (for the location see the map on page 29). During the first couple of days a few of the organizers will be taking a group of people there so that anyone interested can see how this works. There are also many German restaurants in Münster that serve traditional food and beer. Here are a few suggestions: - Pinkulus (Rosenplatz 6), Westfälische cuisine - Spatzl (Am Stadtgraben 52), Bavarian cuisine - Altes Gasthaus Leve (Alter Steinweg 37) - Drübbelken (Buddenstraße 14-15) 37
All the restaurants in the above lists have updated web-pages and social media that include their menus in detail. Of course, these are only some sug- gestions and there are plenty of alternatives around Prinzipalmarkt (city-centre) and throughout the city. As for drinks, there are many bars in the Altstadt or at the Hafen, some of which also feature live music every now and then. A traditional German spot for an afternoon/ evening drink is a Biergarten. There are several around the city. Here are a few. - Biergarten.ms (Kastellstraße 1) - Klamm & Heinrich (Breul 9) - Schloss Biergarten (University of Münster, Schlossgarten 3) We can also recommend some places for breakfast, most of which are close to Nordstern hostel, or at least on the way from Nordstern to the mathematics institute: - Backhaus Jankord (Gertrudenstraße 22), bakery (takeaway) - Essmann’s Backstude (Studtstraße 64), bakery (takeaway) - Herr Hasse Kaffeeröster (Gertrudenstraße 19), coffee place (takeaway, outdoor seating) - Roestbar (Nordstraße 2), coffee place (takeaway, outdoor seating) - Bäckerei Wilhelm Middelberg (Wilhelmstraße 1), bakery (takeaway) 38
Welcome to Willkommen in Mathematics Münster! Münster! We have compiled some general information for Wir haben einige allgemeine Informationen für die planning your stay at Mathematics Münster. For Planung Ihres Aufenthaltes in Münster zusammen- more details and updates on the conference, gestellt. Für Details und Updates zur Konferenz please visit the conference webpage or besuchen Sie bitte die Konferenz-Webseite oder www.mathematics-muenster.de. www.mathematics-muenster.de. Your trip to Münster Anreise nach Münster https://www.uni-muenster.de/MathematicsMuenster/aboutmm/directions.shtml With public transport to Mit öffentlichen Verkehrsmitteln zum Münster (Westfalen) train station it takes about Bahnhof Münster (Westfalen) dauert es etwa • 2.5-3.5 hours from Frankfurt Airport (FRA). • 2,5-3,5 Stunden vom Flughafen Frankfurt (FRA). Intercity trains depart every hour, Intercity-Züge fahren stündlich, • 1.5 hours from Düsseldorf Airport (DUS). • 1,5 Stunden vom Flughafen Düsseldorf (DUS). Intercity trains depart every hour, Intercity-Züge fahren stündlich, • 1-1.5 hours from Dortmund Airport (DTM) • 1-1,5 Stunden vom Flughafen Dortmund (DTM) by hourly regional trains, mit stündlich verkehrenden Regionalzügen, • 35 minutes from Münster Airport (FMO) • 35 Minuten vom Flughafen Münster (FMO) by shuttle bus. mit dem Shuttlebus. From the train station to Mathematics Münster Vom Bahnhof zum Mathematik Campus: • 15 minutes by bus, busses for “Coesfelder • 15 Minuten mit dem Bus bis Haltestelle Kreuz” leave every 5 minutes. „Coesfelder Kreuz“, Abfahrt alle 5 Minuten. • 10-15 minutes by taxi. • 10-15 Minuten mit dem Taxi. Childcare Kinderbetreuung We gladly support parents by providing child care Gerne unterstützen wir Eltern durch Kinderbetreuung during conferences and workshops. If you are bei Tagungen und Workshops. Wenn Sie die planning to make use of the child care, please let Betreuung in Anspruch nehmen möchten, teilen Sie the organizers know as soon as possible and dies und das Alter Ihrer Kinder/Ihres Kindes bitte so inform them about the child/children’s age. bald wie möglich den OrganisatorInnen mit. Our parent-child-rooms at the cluster (Orléans- Der Eltern-Kind-Räume im Cluster (Orléans-Ring 10, Ring 10, ground floor) are equipped with toys, Erdgeschoss) ist mit Spielsachen, Büchern, einem books, a baby changing facility, child-beds and for Wickeltisch, Kinderbetten und einem separaten the parents a separate workspace. Arbeitsplatz ausgestattet. Child care is free of charge. Die Kinderbetreuung ist kostenlos. Wi-Fi access for guests WiFi Gast-Zugang Connect to the SSID “GuestOnCampus” and start Verbinden Sie sich mit der SSID „GuestOnCampus“ any web browser. You will automatically be und starten Sie einen Webbrowser. Sie werden redirected to the login page. Confirm the terms of automatisch auf die Anmeldeseite umgeleitet. use and click on "log in for free". Bestätigen Sie die Nutzungsbedingungen und klicken Sie auf "kostenlos einloggen". Pro Endgerät 1 GB data volume is available per device and day. und Tag steht Ihnen 1 GB Datenvolumen zur Please note that the connection is not encrypted. Verfügung. Die Übertragung ist unverschlüsselt. Mathematics Münster | Orléans-Ring 10 | 48149 Münster mathematics-muenster@uni-muenster.de 2020-02-26
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