Higher Structures in China IV

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Recently, higher categories have appeared in many aspects of mathematics. Higher Structures in China is a series of conferences aimed at bringing together international and Chinese mathematicians in various intersecting areas of research to facilitate the exchange ideas and further the development of applications of higher structures in their respective fields.

This is the fourth conference of the series, and it will be held at the Mathematics School & Institute of LanZhou University, LanZhou, GanSu Province, from August 14-16, 2013. The first, the second, and the third conference Higher Structures in China, Higher Structures in China II, Higher Structures in China III were held in October 2010, August 2011, and August 2012, respectively.

The program will include mini-courses and expository and research talks by participants. We hope to also provide ample opportunities for participants to interact informally to explore common interests and to generate ideas for future collaboration. (Click here for more pictures).

Contents

Organizers

  • Li Guo(Rutgers University at Newark, Lanzhou University): liguo@rutgers.edu
  • Yanfeng Luo (Lanzhou University)
  • Weiwei Pan (St. Mary's)
  • Yunhe Sheng (Jilin University): ysheng888(at)gmail.com, +86-150-4405-4878
  • Chenchang Zhu (Universität Göttingen)

Speakers

  • John Baez, minicourse speaker
  • Chengming Bai
  • Xiaojun Chen
  • Zhuo Chen
  • J.-P. Curien, minicourse speaker
  • Chongying Dong, minicourse speaker
  • Frederic Fauvet
  • Changchang Xi
  • Marco Zambon

Program

The scientific program starts on Wednesday, August 14th, and ends on Friday, August 16th. August 17th-August 19, free discussion.


Spans and the Categorified Heisenberg Algebra

Heisenberg reinvented matrices while discovering quantum mechanics, and the algebra generated by annihilation and creation operators obeying the canonical commutation relations was named after him. It turns out that matrices arise naturally from 'spans', where a span between two objects is just a third object with maps to both those two. In terms of spans, the canonical commutation relations have a simple combinatorial interpretation. More recently, Khovanov introduced a 'categorified' Heisenberg algebra, where the canonical commutation relations hold only up to isomorphism, and these isomorphisms obey new relations of their own. The meaning of these new relations was initially rather mysterious. However, Jeffrey Morton and Jamie Vicary have shown that these, too, have a nice interpretation in terms of spans. We can begin to formalize this using the work of Alex Hoffnung and Mike Stay, who have shown that spans of groupoids are morphisms in a symmetric monoidal bicategory.



Pierre-Louis Curien: Higher-dimensional rewriting and applications to coherent presentations of Artin groups

I shall present recent works of Stéphane Gaussent, Yves Guiraud, Philippe Malbos, Samuel Mimram, that develop of theory of rewriting systems extended to higher dimensions, in the setting of polygraphs, which can be seen as presentation of higher (stict) categories. I will present applications to the study of Artin groups.



Chongying Dong: Quantum dimesions and quantum Galosi theory.


Abstract: In this mini course we will discuss the follwoing topics: (1) Vertex operator algebras and automorphic groups, (2) The quantum dimensions of modules for vertex operator algebras, including the properties of quantum dimensions and the possible values of the quantum dimensions, (3) The Galois theory for vertex operator algebras with finite automorphism group actions.


Schedule

Schedule for Wednesday 14 Aug

08:50 - 09:00 REGISTRATION and PHOTO
Chair Li Guo
09:00 - 09:50 John Baez Spans and the Categorified Heisenberg Algebra I
10:00 - 10:50 Chongying Dong Quantum dimensions and quantum Galois theory I
11:10 - 12:00 J.-P. Curien Higher-dimensional rewriting and applications to coherent presentations of Artin groups I
12:00-14:30 LUNCH BREAK
Chair Zhangju Liu
14:30 - 15:20 Changchang Xi Higher dimensional tilting modules
15:40 - 16:30 Frédéric Fauvet Algebraic structures and operations on Moulds
16:50 - 17:50 Question session
18:00 - ??? Banquet

Schedule for Thursday 15 Aug

Chair Chenchang Zhu
08:30- 09:20 John Baez Spans and the Categorified Heisenberg Algebra II
09:40 - 10:30 Chongying Dong Quantum dimensions and quantum Galois theory II
10:50 - 11:40 J.-P. Curien Higher-dimensional rewriting and applications to coherent presentations of Artin groups II
12:00 - 14:30 LUNCH BREAK
Chair Yunhe Sheng
14:30 - 15:20 Chengming Bai Classical Yang-Baxter equations and related algebraic structures
15:40-16:30 Zhuo Chen From Atiyah Classes to Homotopy Leibniz Algebras
16:50 - 17:40 Xiaojun Chen Noncommutative Poisson structures and their applications toCalabi-Yau categories
18:00 Dinner

Schedule for Friday 16 Aug

Chair Weiwei Pan
08:30- 09:20 John Baez Spans and the Categorified Heisenberg Algebra III
09:40 - 10:30 Chongying Dong Quantum dimensions and quantum Galois theory III
10:50 - 11:40 J.-P. Curien Higher-dimensional rewriting and applications to coherent presentations of Artin groups III
12:00 - 14:00 LUNCH BREAK
Chair Yanfeng Luo
14:00 - 14:50 Marco Zambon Multisymplectic manifolds, moment maps and conserved quantities.
15:00 - 15:50 Jun Pei Splitting and Replicating of Operads
17:55 - ??? depart

Registration

The registration is closed.

Sponsors

Higher Structures in China IV is sponsored by the Department of Mahematics, LanZhou University, the Mathematics School & Institute of Jilin University, Changchun, China and the Courant Research Center, Georg-August-Universität Göttingen.

Accommodation

All participants will be housed in Tsuiying Hotel (萃英大酒店).

Getting to Lanzhou

The city of Lanzhou is the capital of Gansu Province. Lanzhou Zhongchuan Airport is an airport serving Lanzhou. It is located 67 kilometers (42 mi) north of downtown Lanzhou. The airport and LZU is connected by shuttle bus service, which takes some 1 hour and costs 30 CNY.

Airport Shuttle

  • Shuttle from Airport to LZU: Lanzhou Airport → Lanzhou Eastern Hotel 兰州机场 → 东方大酒店
    • Time: from the first flight to the last flight 从首班飞机到末班飞机
  • Shuttle from LZU to Airport: CAAC ticketing office → Lanzhou Airport 民航售票处(近兰州大学,兰州锦江阳光大酒店对面)→ 兰州机场
    • Time: 06:00 -- 19:00 (every hour on the hour 每个整点一班)

For more information see 更详细机场巴士信息请见 this page (in Chinese).

Railway station

Lanzhou railway station is 1.5 km away from Lanzhou University. Take bus Line 1, Line 16 or Line 127 from the railway station and get off at the stop Panxuan Lu. 火车站到兰州大学约1.5公里,乘1路、16路、127路公交经两站在盘旋路站(校门北侧30米)下车即可。

Google Map

A Google interactive map with airport, shuttle,hotel, railway station.

Participants

  • Yanhui Bi (Nanchang Hangkong University)
  • Du Li (Goettingen University)
  • Honglei Lang (Peking University)
  • Zhangju Liu (Beijing University)
  • Li Ren (SiChuan University)
  • Xiaomeng Xu (Geneva University)
  • Zhujun Zheng (South China Uni. of Technology)
  • Deshou Zhong (China Youth Uni. for Political Sciences)
  • Shuyun Zhou (青海民大)
  • Jiangang tang (新疆伊犁师院)
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