XIIIth RENCONTRES DU VIETNAM

CIMPA Research School — Rencontres du Vietnam

Noncommutative Geometry andApplications toQuantum PhysicsJuly 12th – 22nd, 2017,Quy Nhon, Vietnam

(Updated on July 10, 2017)

ICISE

ncg2017.cpt.univ-mrs.fr

The International Centre for Pure and Applied Mathematics (CIMPA) is a non-profit international organization establishedin Nice (France) in 1978. Its aim is to promote international cooperation in higher education and research in mathematics andrelated subjects, particularly computer science, for the benefit of developing countries.

The International Centre for Interdisciplinary Science Education (ICISE) is located in a pleasant place at the seaside of thecity of Quy Nhon (Central Vietnam) where conferences to the international standard can be organized. It contributes to thedevelopment of research and education in Vietnam and in this region of Asia. With this motivation in mind, Asian scientistsare encouraged to meet for events (conferences, schools and workshops) and to share knowledge / expertise with their foreigncounterparts.

Since 1993, the institution “Rencontres du Vietnam”, which is an official partner of UNESCO, has organized internationalmeetings (conferences and schools) to high scientific level with the motivation of foster exchanges between Vietnamese re-searchers or from Asia-Pacific and their colleagues coming from other parts of the world.

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The aims of the school

This international CIMPA Research School is held at ICISE hosted by the “Rencontres du Vietnam”.

In these last years, the interest on Noncommutative Geometry (NCG) and its application to Physics has increasedin South East Asia countries (Japan, Autralia, China, Thailand, Korea…). In accordance with the ICISE’s aim todevelop research and education in Vietnam and in this region, this CIMPA Research School provides an opportunityto enlarge its contribution to the Mathematics and its application to Physics. With this in mind, the aim of thisschool is to create strong relationships between European and South East Asian researchers in NCG, as well as tohelp for the development of this research activity in this region.

In the city ofQuy Nhon, there are two universities with 30,000 students, including a Science faculty, with about300 lecturers and 15,000 science students. Nowadays, the Mathematics department, which was borned 40 years ago,has active researchers with international collaborations. Two of them are involved in the organisation of the school.NCG is welcome by colleagues of this department involved in Analysis, Algebra and Geometry.

The school will focus on some recent developments in the Mathematics of Noncommutative Geometry andits applications to Quantum Physics. Lectures will provide the basic knowledge and general concepts required inMathematics and Physics.

Noncommutative Geometry (NCG) is a vivid research subject in Mathematics and Physics. The main goal of thisschool is to train local researchers and students in these topics and to establish strong research collaborations withcolleagues, students and researchers. Leading experts in NCG will give an overview of the main well-establishedresults, the essential tools, and some of the present active research activities:

— Connes-Chern Character Theorem— Noncommutative Integration Theory (Dixmier Traces, Singular Traces…)— Unbounded KK-theory and Kasparov Product— Dynamical Systems and KMS States— Quantum Groups— Fuzzy Spaces— Noncommutative Standard Model of Particle Physics— Application to the QHE…

We expect that participants will greatly benefit from this school as part of their training as in their future po-sitioning in research. We wish you success in your academic careers and hope to see many of you at our futuremeetings.

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Content

The aims of the school . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Committees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Local Organizing Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5International Advisory Committee . . . . . . . . . . . . . . . . . . . . . . . . . . 5

General information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Useful information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Wednesday, July 12, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Thursday, July 13, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Friday, July 14, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Saturday, July 15, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Sunday, July 16, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Monday, July 17, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Tuesday, July 18, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Wednesday, July 19, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Thursday, July 20, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Friday, July 21, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Saturday, July 22, 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Unbounded KK-theory in Noncommutative Geometry and Physics . . . . . . . . . . . . 14Equilibrium states on operator-algebraic dynamical systems . . . . . . . . . . . . . . . 14Noncommutative Geometry and Field Theory . . . . . . . . . . . . . . . . . . . . . 14Introduction to Noncommutative Analysis and Integration . . . . . . . . . . . . . . . 14Formal and non-formal Quantization and Index Theorems . . . . . . . . . . . . . . . . 15Noncommutative Topology and Topological Quantization . . . . . . . . . . . . . . . . 15

Seminars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Posters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Conference Secretariat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Committees

Local Organizing Committee

Thanh Duc Dinh (University of Quy Nhon) – co-ChairThierry Masson (Centre de Physique Théorique, Marseille) – co-ChairRoland Triay (Centre de Physique Théorique, Aix Marseille University)Jean Tran Thanh Van (Les Rencontres du Vietnam)Thi Thanh Tam Lam (Relationships with the Vietnamese Universities)

International Advisory Committee

Alan Carey (Australian National University, Canberra, Australia)Wicharn Lewkeeratiyutkul (Chulalongkorn University, Thailand)Fedele Lizzi (Università di Napoli Federico II, Napoli, Italy)Yoshiaki Maeda (Tohoku University, Sendai, Japan)Patrizia Vitale (Università di Napoli Federico II, Napoli, Italy)

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General information

RegistrationThe registration of the Conference will take place on Wednesday July 12th at 5pm at Seagull Hotel.Khách Sạn Hải Âu - Seagull HotelAddress: 489 An Dương Vương, Quy Nhơn, Bình ÐịnhPhone: +84 56 3846 377Please register as soon as you arrive at the hotel, fill in an ARRIVAL FORM and hand it to the conference secre-taries. All payments must be completed by Friday July 14th evening. The accommodation fee should be paid to theconference secretariat by cash or credit card (not be paid directly to the hotel). Our conference secretariat is locatedat ICISE, open from 8:30 to 12:00 and from 13:00 to 17:30.

Welcome CocktailAll participants, their families and guests are invited to have a welcome drink at 19:00 on Wednesday, July 12th atSeagull Hotel. A buffet dinner will be served at 19:30.

MealsPlease do not forget to wear your badge and bring along with you the meal coupons, provided to you at registrationtime.Alcoholic or soft drinks will be charged to you. If you are sharing a room, please find an arrangement with yourroom mate for your telephone.Breakfast will be served at your hotel: you will need the daily coupon provided by the hotel (together with yourroom key).

— Lunch for participants will be served at 12:00 at ICISE.— Dinner: for those who take the hotel package, dinner will be at the Seagull Hotel at 19:00.— Conference Dinner: It will be held at 18:30 on Thursday July 20th, 2017 at ICISE if the weather permits.

Transport from Seagull hotel to ICISE for accompanying persons will be arranged at around 18:00.Please let us know your preference (vegetarian, vegan…) so that we can inform the hotel, and mention it to thewaiter too.

The school at ICISEThe school is located at ICISE (International Centre for Interdisciplinary Science and Education):Trung Tâm Quốc tế Khoa học và Giáo dục Liên ngành (ICISE)Address: Quốc lộ 1D, khu vực 2, phường Ghềnh Ráng, Thành phốQuy Nhơn, tỉnh Bình ÐịnhPhone number: (+84)056.3540099 - 056 3646609

Bus departures from the Seagull hotel to ICISEThe first bus will leave at 7:45 and the last one will leave at 8:00.Bus back to the hotel: the first bus will leave after the last session and the second bus at 18:15 (with few exceptionsthat will be announced).You can also go by yourself via the main road by taxi (10-15 min, it costs about 100 000 – 150 000 VND dependingon the taxi’s waiting time and rate).It is also possible to walk to and from the ICISE center following the coastline road about 6 km.Tea and coffee will be served during the breaks at the cafeteria of ICISE.

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Useful information

InternetWIFI is available at the ICISE. Password is ICISE20130812 for guests.Wifi is available almost anywhere in Vietnam: for example, you can get wifi access in any local cafes if you askwaiters for the password.

Beach timeThere are shower rooms and changing rooms at the beach of the ICISE center. Your laptops – NOT YOUR OWNBELONGINGS – can be stored in the conference room. Bring along your towel, bathing suit and sun screen if youwant to swim.At the hotel beach, local people use to swim during sunrise (05:30 - 06:30 am): you should try that too!

Prepaid Mobile phone and 3G internet SIM cardPrepaid phone and internet providers who provide a Tourist SIM card which costs around 200000 VND or 10 USD.These tourist SIM cards offer you around 50 minutes for international call, 100 minutes for domestic call, free textmessages, 3G internet connection (depending on the provider). These SIM cards can be bought at the airport, elec-tronic or phone shops.

TelephoneIf you share a room, please keep track of your calls because there is only one telephone per room and the billing isdone for each room. Telephone bills should be settled before you leave.

Banking facilitiesExchange currency service is available at the hotel reception, local bank branches or any jewellery shops. ATMmachines can be found on the opposite side of the hotel.

Departure to the airportIf your departure is on Friday July 21st you MUST inform the conference secretariat of your flight number and thescheduled departure time before Wednesday July 19th in order to arrange the transportation for you.For the departure from hotels to the airport on Saturday July 22nd, there will be a transfer by bus:For the flights VN 1393 (HCM City) and VN 1620 (Hanoi) or others…At 7:10 from the Seagull hotel (Breakfast served at 6:15).For the flight VN 1397 (HCM City)At 15:00 from the Seagull hotel. Lunch served at Seagull hotel at 12:00.For the other days: Please contact the conference secretaries to arrange a taxi transfer.DON’T FORGET TO GET BACK YOUR PASSPORT AT THE HOTEL RECEPTION DESK BEFORE YOU LEAVE!

Special announcementsA paperboard in ICISE entrance hall, near the Secretaries’ office, will be used for special announcements.For accompanying persons, a paper board will be placed in the hotel reception hall. Please check it regularly.The accompanying person can take a taxi to go to the Center ICISE to enjoy the beach or to rest in the park.Directions to ICISE in Vietnamese to show to the taxi driver: (Fare: about 5 USD)Trung tâmQuốc tế Khoa học và Giáo dục Liên ngành (ICISE) Phường Ghềnh Ráng1. Từ đường Tây Sơn, đi theo QL 1D, đến trạm Kiểm Dịch, rẽ trái.2. Cuối đường nhựa, Trung tâmQuốc tế Khoa học ICISE nằm bên tay phải

Emergency contactsYou can call us any time if you have any emergency request including pick up, medical help…Hotel: +84 56 3846 37

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Schedule

Wednesday, July 12, 2017 — Arrival of participants at the hotel

17:00 – 19:00 Registration at Seagull hotel19:00 – 19:30 Welcome cocktail at the hotel19:30 – 21:00 Dinner at the hotel

Thursday, July 13, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 08:50 Welcome address by Jean Trân Thanh Vân (ICISE)08:50 – 09:30

Thierry Masson (CPT)Introduction to the School and its content

09:30 – 10:30 LectureRyszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 1/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Nathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 1/6

12:00 – 13:30 Lunch13:30 – 14:30 Lecture

Johannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 1/6

14:30 – 15:30 LectureRyszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 2/6

15:30 – 16:00 Coffee Break16:00 – 17:00 Lecture

Fedele Lizzi (Unina)Noncommutative Geometry and Field Theory – 1/6

17:00 – 18:00 Training and group activities, leisure time18:00 – 18:30 Shuttles departure from ICISE to Seagull Hotel19:00 – 20:30 Dinner

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Friday, July 14, 2017Morning session exceptionally atQuy Nhon University08:10 – 08:30 Welcome address by the President of theQuy Nhon University08:30 – 09:30 Lecture

Fedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 1/6

09:30 – 10:30 LectureRyszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 3/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Nathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 2/6

12:00 – 13:30 Lunch at theQuy Nhon University13:30 – 14:00 Shuttle to ICISEAfternoon session at ICISE14:00 – 15:00 Lecture

Patrizia Vitale (UNINA)Noncommutative Geometry and Field Theory – 2/6

15:00 – 16:00 LectureJohannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 2/6

16:00 – 16:30 Coffee Break16:30 – 17:30 Lecture

Ryszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 4/6

17:30 – 18:00 Training and group activities, leisure time18:00 – 18:30 Shuttles departure from ICISE to Seagull Hotel19:00 – 20:30 Dinner

Saturday, July 15, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

BramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 1/6

09:30 – 10:30 LectureRyszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 5/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Fedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 2/6

12:00 – 13:30 Lunch13:30 – 19:00 Free Afternoon19:00 – 20:30 Dinner

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Sunday, July 16, 2017 — Free Activities, Excursion

Day reserved for tourism

Monday, July 17, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

Fedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 3/6

09:30 – 10:30 LectureRyszard Nest (KU)Formal and non-formal Quantization and Index Theorems – 6/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Nathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 3/6

12:00 – 13:30 Lunch13:30 – 14:30 Lecture

Johannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 3/6

14:30 – 15:30 LecturePatrizia Vitale (UNINA)Noncommutative Geometry and Field Theory – 3/6

15:30 – 16:00 Coffee Break16:00 – 17:00 Lecture

BramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 2/6

17:00 – 18:00 Posters Session18:00 – 18:30 Shuttles departure from ICISE to Seagull Hotel19:00 – 20:30 Dinner

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Tuesday, July 18, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

Patrizia Vitale (UNINA)Noncommutative Geometry and Field Theory – 4/6

09:30 – 10:30 LectureFedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 4/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

BramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 3/6

12:00 – 13:30 Lunch13:30 – 14:30 Lecture

Johannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 4/6

14:30 – 15:30 LectureFedele Lizzi (Unina)Noncommutative Geometry and Field Theory – 5/6

15:30 – 16:00 Coffee Break16:00 – 17:00 Lecture

Nathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 4/6

17:00 – 18:00 Training and group activities, leisure time18:00 – 18:30 Shuttles departure from ICISE to Seagull Hotel19:00 – 20:30 Dinner

Wednesday, July 19, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

Fedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 5/6

09:30 – 10:30 LectureBramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 4/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Seminar

YoshiakiMaeda (TFC)Noncommutative one-sheeted hyperboloids via deformation quantization

12:00 – 13:30 Lunch13:30 – 19:00 Free Afternoon19:00 – 20:30 Dinner

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Thursday, July 20, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

BramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 5/6

09:30 – 10:30 LectureNathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 5/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Fedor Sukochev (UNSW)Introduction to Noncommutative Analysis and Integration – 6/6

12:00 – 13:30 Lunch13:30 – 14:30 Lecture

Johannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 5/6

14:30 – 15:30 LectureFedele Lizzi (Unina)Noncommutative Geometry and Field Theory – 6/6

15:30 – 16:00 Coffee Break16:00 – 17:00 Training and group activities, leisure time17:00 – 18:30 Free time (round trip to the hotel)18:30 – 22:00 Conference Dinner (at ICISE)

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Friday, July 21, 201707:45 – 08:00 Shuttles departure from Seagull Hotel to ICISE08:30 – 09:30 Lecture

BramMesland (Universitaet Bonn)Unbounded KK-theory in Noncommutative Geometry and Physics – 6/6

09:30 – 10:30 LectureNathan Brownlowe (USyd)Equilibrium states on operator-algebraic dynamical systems – 6/6

10:30 – 11:00 Coffee Break11:00 – 12:00 Lecture

Johannes Kellendonk (ICJ)Noncommutative Topology and Topological Quantization – 6/6

12:00 – 13:30 Lunch13:30 – 14:30 Seminar

Paolo Bertozzini (TU)Higher C∗-categories – Towards Categorified NCG

14:30 – 15:30 Seminar15:30 – 16:00 Coffee Break16:00 – 18:00 Informal discussion between participants and lecturers18:00 – 18:30 Shuttles departure from ICISE to Seagull Hotel19:00 – 20:30 Dinner

Saturday, July 22, 2017 — Departure of Participants

Shuttles to Airport

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Lectures

Unbounded KK-theory in Noncommutative Geometry and Physics

Bram Mesland, Universitaet Bonn, Germany.We will give an introduction to the unbounded picture ofKK-theory. The constructive Kasparov product, which

can be viewed as a type of noncommutative fibration compatible with index theory, will play a central role. Thecourse will introduce the main aspects of this product, as well as examples from hyperbolic dynamical systems,quantum groups and the factorisation of Dirac operators on principal bundles. Special attention will be given tothe type III setting. This presents mathematical challenges to unify the analytic and algebraic aspects of unboundedKK-theory.

Lecture 1  – Dirac operator on a compact manifold, twisting by a connectionLecture 2  – Spectral triples, K-cycles, index pairingLecture 3  – KK-theory, relation to K-theory and K-homology, existence of the Kasparov productLecture 4  – Unbounded Kasparov productLecture 5  – Construction of spectral tripes on noncommutative C∗-algebras, gauge transformationsLecture 6  – Examples: theta deformations, crossed products from conformal group actions, Cuntz algebras

Equilibrium states on operator-algebraic dynamical systems

Nathan Brownlowe, School of Mathematics and Statistics, University of Sydney, Australia.Equilibrium states, or KMS states, are mathematical objects used to describe quantummechanical systems when

in equilibrium. We will model quantum mechanical systems with operator-algebraic dynamical systems, whichconsist of an action (representing time evolution) of the real line on aC∗-algebra (representing the observable of thesystem). Wewill start with some background onC∗-algebras and states onC∗-algebras, before looking at the physicalmotivation behind the KMS condition. We will spend the second half of the course looking at recent work on theKMS-state structure of various C∗-algebras, including directed graph C∗-algebras and Noncommutative solenoids.

Noncommutative Geometry and Field Theory

Patrizia Vitale and Fedele Lizzi, Department of Physics, University of Naples Federico II, Italy.Some of the applications of noncommutative geometry and noncommutative spaces to physics will be introduced

and some of the relevant examples will be discussed in detail. In particular gauge theory on noncommutative spaces,and spectral action and the applications to the standard model of particles physics. The course will be self-containedand the relevant mathematical tools and relevant physics concepts will be introduced.

Lecture 1  – Noncommutative spaces, physical origins, mathematical foundations (F. Lizzi).Lecture 2  – Short introduction to gauge theory. Derivation based differential calculus for noncommutative

associative algebras (P. Vitale).Lecture 3  – Noncommutative gauge theory I (Moyal space-time) (P. Vitale).Lecture 4  – Noncommutative gauge theory II (Lie algebra type non-commutativity) (P. Vitale).Lecture 5  – The standard model of fundamental interactions as an almost commutative geometry (F. Lizzi).Lecture 6  – The spectral action confronts “real physics” (F. Lizzi).

Introduction to Noncommutative Analysis and Integration

Fedor Sukochev, School of Mathematics and Statistics, University of New South Wales, Sydney, Australia.In NCG, the singular (Dixmier) traces have become an indispensable tool. These traces are defined via dilation

invariant extended limits on the space of bounded measurable functions. We will discuss in details the formulaerelating Dixmier traces and zeta-function residues and underlying concepts of NC integration theory with respectto such traces. These formulae are established under various additional conditions on these extended limits.

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Formal and non-formal Quantization and Index Theorems

Ryszard Nest, Department of Mathematical Sciences, Copenhagen, Denmark.Deformation quantization produces a lot of interesting examples of “noncommutative spaces”. After an intro-

duction to deformation quantization and some formality theorems, this lecture will focus on some algebraic indextheorems, on the algebras of pseudodifferential and Fourier integral operators, and finally on geometric quantizationand its relation to physics and representation theory, especially in a NCG-approach to LoopQuantum Gravity.

Noncommutative Topology and TopologicalQuantization

Johannes Kellendonk, Institut Camille Jordan, Université Claude Bernard, Lyon, France.In quantum physics, noncommutative topology is one of the most successful tools to describe topological quan-

tization in presence of disorder. In particular, it allows to identify some topological invariants. This lecture is anintroduction to noncommutative topology with applications to topological quantization. It will address operatorK-theory, cyclic cohomology, K-homology, Quantum Hall Effect, classification of topological insulators…

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Seminars

Paolo Bertozzini (TU), Tambon Khlong Nung, Khlongluang, ThailandHigherC∗-categories – Towards Categorified NCGJuly, 21, 13:30 – 14:30

We review some tentative steps towards a (horizontal and vertical) categorification of non-commutative geometry,starting for now only at the “topological level”, with the description of suitable notions of “strict higherC∗-categories”.C∗-categories were introduced long ago by John E.Roberts and, despite the quite remarkable developments in higher

category theory (that has recently evolved along lines closer to classical higher homotopy)… still no satisfactory notionof n −C∗-category (for n > 2) has been produced and no marriage between “higher” categories and operator algebrashas been in sight.We propose a possible (and questionable) solution to the problem and also suggest some physical areas (relational

quantum physics, quantum cybernetics), where higher C∗-categories might find natural application.

Yoshiaki Maeda (TFC), Midori-ku Yokohama-shi, JapanNoncommutative one-sheeted hyperboloids via deformation quantizationJuly, 19, 11:00 – 12:00

In this talk, we exhibit the non-formal star-exponential of the Lie group SL(2,R) realized geometrically on thecurvature contraction of its one-sheeted hyperboloid orbits endowed with its natural non-formal star-product. It isdone by a direct resolution of the defining equation of the star-exponential and produces an expression with Besselfunctions. This yields a continuous group homomorphism from SL(2,R) into the von Neumann algebra of multipliersof the Hilbert algebra associated to this natural star-product. As an application, we prove a new identity on Besselfunctions. This is the joint work with Axel de Goursac and Pierre Bieliavsky, which is still in progress.

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Posters

Arkadiusz Bochniak (WFAIS UJ), Kraków, PolandBraided Hopf algebras from twisting

This poster is based on joint work with A. Sitarz [1]. For a complex parameter q, the algebra A(SUq(2)) was shownto be a braided Hopf algebra in some braided tensor category [2]. Our original motivation was to construct braideddifferential calculi on this algebra. We show that there is a class of Hopf algebras forwhich, using the general frameworkof twisting, one can construct their braided versions. In particular, the Hopf algebras of SUq(n) and the quantum doubletorus belong to this class. Furthermore, the twisting can also be applied to the (co-,bi-)modules over the braidable Hopfalgebras, and permits us to consider braided differential calculi.References:[1] A. Bochniak, A. Sitarz. Braided Hopf algebras from twisting. arXiv:1701.01106.[2] P. Kasprzak, R. Meyer, S. Roy, S.L. Woronowicz. Braided quantum SU (2) groups, J. Noncommut. Geom. 10, p.

1161-1125 (2016)

Hideki Inoue (NU), Nagoya, JapanIndex theorem in scattering theory: the case ∞ = ∞ !

Gihyun Lee (SNU), Seoul, Korea, Republic ofConformal Distributions and Pseudodifferential Calculus on Noncommutative Tori

In this poster we shall present a detailed account on the pseudodifferential calculus on noncommutative tori [1].This calculus turns out to be very useful (see, e.g., [2]), but its analytic aspect hasn’t been studied well in any literature.The aim of this poster is to fulfill this deficiency. This is joint work with Hyun-su Ha and Raphaël Ponge.References:

[1] A. Connes, C*-algèbres et géométrie différentielle. C.R. Acad. Sc. Paris, t. 290, Série A, 599-604, 1980.[2] A. Connes, P. Tretkoff, The Gauss-Bonnet theorem for the noncommutative two torus. Noncommutative geometry,

arithmetic, and related topics, pp. 141–158, Johns Hopkins Univ. Press, Baltimore, MD, 2011.

TomaszMiller (WUT), Warsaw, PolandCausal relation in noncommutative spacetimes

Einstein’s causality is one of the fundamental principles underlying modern physical theories. Whereas it is readilyimplemented in classical physics founded on Lorentzian geometry, its status in quantum theory has long been contro-versial. On the mathematical side, the classical causal structure is a certain binary relation on the set events, i.e. pointsof spacetime. But in the quantum world the very notion of a point-like event becomes blurred and it is widely believedthat the causal structure would also be afflicted with uncertainty.

However, together with my colleagues M. Eckstein and N. Franco, we have developed a rigorous framework, inwhich the causal structure remains rigid, although the events themselves become nonlocal. The idea, founded on theoperational viewpoint on physics compelling us to exchange the classical spacetime for the space of states of someabstract algebra of observables, is incarnated with a Lorentzian version of noncommutative geometry à la Connes. Theexplanation of the basic concepts of our formalismwill be followed by an illustrative example of an almost-commutativespacetime, which, moreover, sheds a new light on the peculiar properties of massive fermions.References:

[1] N. Franco and M. Eckstein, An algebraic formulation of causality for noncommutative geometry. ClassicalQuantGrav, 30(13):135007, 2013.[2] M. Eckstein and T. Miller, Causality for nonlocal phenomena. Ann. Henri Poincaré. Published online 13 March

2017.[3] M. Eckstein, N. Franco, and T. Miller, Noncommutative geometry of Zitterbewegung. Phys Rev D, 95:061701,

2017.

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Semiu Oladipupo Oladejo (GSU), Gombe, NigeriaJoin reducible, Meet Irreducible and Complete Equivalence Set In FiniteQuantum Syatems

In this work, join and meet algebraic structure which exists in non-near-linear finite geometry is discussed. Lines innon-near-linear finite geometry were decomposed as products of lines in near-linear finite geometry and the existenceof lattice between any pair of near-linear finite geometryZpi for q a divisor of d and between a subsystems of a finitequantum systems with variables in Zd and its subsystems with variables in Zpi was confirmed. A duality betweenfloor and roof in a phase space of a finite quantum system is shown using examples. A bijection between the set ofsubgeometry and finite geometry from the subsets of the set of divisors of d and set of subsystems of a finite quantumsystem and a finite system from the subsets of the set of divisors of d is established.References:[1] A. Vourdas, Rep. Prog. Phys. 67, 1 (2004)[2] M. Shalaby, A. Vourdas, J. Phys. A45, 052001 (2012)[3] S.O. Oladejo,C.Lei, and A. Vourdas, J. Phys. A: Math. Theor. 47 485204 (2014)

Thomas Scheckter (UNSW), Sydney, AustraliaVilenkin Systems in Noncommutative Lp Spaces

Vilenkin groups are a natural generalisation of the Walsh group, and have been extensively studied in the context ofclassical harmonic analysis. We consider the Vilenkin-Fourier transformation acting upon noncommutative Lp spacesassociated to the hyperfinite type I I1 factor R, and study weak type inequalities for the partial summation operators.The structure of the Vilenkin groups induces a natural filtration on the factor R, and so we also investigate noncom-

mutative martingale spaces corresponding to this filtration.

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Participants

M. Ayaz Ahmad — Tabuk Portal University, Tabuk, Saudi ArabiaMuhammad Ardhi Khalif — Universitas Islam Negeri Walisongo, Semarang, IndonesiaParatat Bejrakarbum —Thammasat University, Pathumthani, ThailandPaolo Bertozzini — Thammasat University, Tambon Khlong Nung, Khlongluang, ThailandHoa Binh —Quy Nhon University, Quy Nhon, Viet NamArkadiusz Bochniak — Fac. of Physics, Astronomy and Appl. Comp. Science of Jagiellonian Univ. and Copernicus Center, Kraków, PolandAxel Boldt — Metropolitan State University, Saint Paul, MN, USA, Saint Paul, United StatesNathan Brownlowe — The University of Sydney, Camperdown, AustraliaHao Bui — Quy Nhon University, Quy Nhon, Viet NamClarisson Rizzie Canlubo — Institute of Mathematics, University of the Philippines-Diliman, Quezon City, PhilippinesAlesandro Carotenuto — Scuola Internazionale Superiore di Studi Avanzati, Trieste, ItalyJuancho Collera — University of the Philippines Baguio, Baguio, PhilippinesLê Công Trình — Quy Nhon University, Thành phốQui Nhơn, Viet NamDuong Dinh — Korea Advanced Institute of Science and Technology, Daejeon, Korea, Republic ofKen Joffaniel Gonzales — Inst. of Math., Univ. of the Philippines - Diliman, Quezon City, PhilippinesHyunsu Ha — Seoul National University, Seoul, Korea, Republic ofLuu Hiep — Quy Nhơn University, Quy Nhon, Viet NamLe Hoang Anh — Hanoi National University of Education, Ha Noi, Viet NamHideki Inoue — Graduate school of mathematics, Nagoya, JapanJohannes Kellendonk — Institut Camille Jordan, Villeurbanne, FranceTam Lam — University of Quynhon, Qui Nhơn, Viet NamMai Dũng Lê — Hanoi National University of Education, Hà Nội, Viet NamHieu LeThanh — Quy Nhon University, Binh Dinh, Viet NamGihyun Lee — Seoul National University, Seoul, Korea, Republic ofHeon Lee — Seoul National University, Seoul, Korea, Republic ofHojun Lee — Seoul National University, Seoul, Korea, Republic ofFedele Lizzi — Università di Napoli Federico II, Napoli, ItalyYoshiakiMaeda — Tohoku Forum for Creativity, Midori-ku Yokohama-shi, JapanThierry Masson — Centre de Physique Théorique, Marseille, FranceBramMesland — Universitaet Bonn, Bonn, GermanyTomaszMiller — Warsaw University of Technology, Warsaw, PolandKunal Krishna Mukherjee — Indian Institute of Technology Madras, Chennai, IndiaRyszard Nest — Copenhagen University, Copenhagen, DenmarkĐào Ngọc Hân —Quy Nhon University, Quy Nhon, Viet NamDung NguyenThi Phuong — Banking Academy, Hanoi, Viet NamStéphanie Nivoche — Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7351, Nice, FranceSemiu Oladipupo Oladejo — Gombe State University, Gombe, Nigeria, Gombe, NigeriaVipul Pandey — Banaras Hindu University, Varanasi, IndiaBenjamin Passer — Technion-Israel Institute of Technology, Haifa, IsraelIssan Patri — Chennai Mathematical Institute, Chennai, IndiaChatchai Puttirungroj —Thammasat University, Khlong Luang, ThailandThomas Scheckter — University of New South Wales, Sydney, AustraliaByungchang So — Seoul National University, Gwanak-gu, Korea, Republic ofFedor Sukochev — University of New South Wales, Sydney, AustraliaDinhThanh Duc — University of Quynhon, Thành phốQui Nhơn, Viet NamRoland Triay — Centre de Physique Théorique, Aix Marseille Université, Marseille, FranceBac Trong Nguyen — University of Economics and Business Administration, Thái Nguyên, Viet NamHien Van — Hue University of Education, Hue, Viet NamPatrizia Vitale — Università di Napoli Federico II, Napoli, ItalyApimook Watcharangkool — National Astronomical Research Institute of Thailand, Chiang Mai, Thailand

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Conference Secretariat

Christian BareilleIsabelle Cossin

Vera De Sa VarandaAimie Fong

Maryvonne JoguetNguyễn Thị LợiHo Thi Thao LyTrần Thị Hải Liên

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