Topic 1: Normal partial tilting modules, exceptional subcategories and (generalized) non-crossing partitions
Plenary speakers:
Prof. 陈小伍, University of University of Science and Technology of China
Abstract:
The aim is to introduce the work of Ingalls-Thomas (2009) and Igusa-Schiffler-Thomas (2010) on the combinatorial classification of exceptional subcategories of the module category over a path algebra. We mention two survey papers: Krause (2012) and Ringel (2015). There are two “classical and important, but somehow forgotten” notions in the representation theory of artin algebras, which are fully emphasized in Ringel (2015), normal modules and exceptional subcategories.
References:
1. C. Ingalls, H. Thomas: Noncrossing partitions and representations of quivers, Compo. Math. 145 (2009). 1533-1562.
2. K. Igusa, R. Schiffler, Exceptional sequences and clusters, J. Algebra 323 (8) (2010), 2183-2202; with an appendix joint with H. Thomas.
3. H. Krause, Report on locally finite triangulated categories, J. K-Theory 9 (2012), 421-458.
4. C.M. Ringel, The Catalan combinatorics of the hereditary artin algebras, arXiv: 1502.06553, 2015.
Topic 2: Representation theory of Geigle-Lenzing complete intersections
Plenary speakers:
常文, 清华大学数学科学系, 博士生
陈健敏, 厦门大学数学科学学院, 副教授
阮诗佺, 清华大学数学中心. 博士后
Abstract:
The aim of this lecture is to introduce Geigle-Lenzing complete intersections and Geigle-Lenzing projective spaces, given by M. Herschend, O. Iyama, H. Minamoto and S. Oppermann [HIMO]. A Geigle-Lenzing (GL) complete intersection is a certain graded commutative ring R, whereas a Geigle-Lenzing (GL) projective space X is a higher dimensional analog of a weighted projective line introduced by Geigle and Lenzing. During this lecture, we will mainly talk about the tilting theory and higher dimensional Auslander-Reiten theory in both of the stable category of Cohen-Macaulay representations over R and the category of coherent sheaves over X.
References:
[HIMO] M. Herschend, O. Iyama, H. Minamoto and S. Oppermann. Representation theory of Geigle-Lenzing complete intersections. arXiv: 1409.0668vl [math. RT]
[I] O.Iyama. Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories. Advances in Mathematics, 210 (2007), no. 1: 22-50.
Topic 3: Double affine Hecke algebra
Plenary speakers:
刘守民, Shandong University
马晓光, Tsinghua University
Abstract:
In this course, we will give an introduction to the theory of Cherednik algebras, in particular, the rational Cherednik algebras. We will begin with the root system, and then define the Cherednik algebra. Then we will give several different types of degenerations of the Cherednik algebras including the rational degeneration. In the end, we will give an overview about the representation theory of rational Cherednik algebras.
References:
Pavel Etingof and Xiaoguang Ma. Lecture notes on Cherednik algebras.