学术报告题目与摘要

1. 报告人：樊赵兵，哈尔滨工程大学

题目：i-quantum groups and their geometric approach

摘要：i-quantum groups are generalization of ordinary quantum groups. Generalizing various works of quantum groups to i-setting is so called i-program. In this talk, I will introduce recent developments on the i-program. In particular, several different geometric approaches to i-quantum groups are introduced, including perverse sheaves on double flag varieties, equivariant K-theory on Steinberg varieties and i-quiver varieties.

2. 报告人：高楠，上海大学

题目：A functorial approach to monomorphism categories for species

摘要：We investigate abstract versions of the monomorphism category as studied by Ringel and Schmidmeier. We prove that analogues of the kernel and cokernel functor send almost split sequences over the path algebra and the preprojective algebra to split or almost split sequences in the monomorphism category. This is based on the joint work with Julian Kuelshammer, Chrysostomos Psaroudakis and Sondre Kvamme.

3. 报告人：耿圣飞，四川大学

题目：A characterization  of cluster categories of canonical algebras

摘要：Let (Q,W) be a Jacobian-finite quiver with non-degenerate potential, C=C_ (Q,W) be the corresponding generalized cluster category defined by Amiot. If there is a cluster-tilting object T in C such that End_C(T) is isomorphic to a cluster-tilted algebra arising from some weighted projective line X with X having at most three weights or X is of tubular type, it is proved that C is triangulated equivalent to the cluster category C_X associated with X. Moreover, for any weighted projective line X with at most three weights, we show there is an acyclic quiver Q and a terminal  kQ-module M, such that C_X is triangulated equivalent to the stable 2-Calabi-Yau category associated to M defined by Geiss-Lelecrc-Schroer. As an application, we  get that the corresponding cluster algebra A_X is finitely generated and the cluster monomials of A_X form a linearly independent family. This is joint work with Changjian Fu.

4. 报告人：胡维，北京师范大学

题目：Derived equivalences from quiver construction

摘要：In this talk, shall discuss how to get derived equivalences from quiver constructions. This includes gluing vertices, unifying arrows, etc.

5. 报告人：林记，阜阳师范大学

题目： 广义Frobenius范畴与modified Ringel-Hall代数  

摘要：我们定义广义Frobenius范畴，它特别地包含Frobenius范畴和遗传正合范畴的有界或周期的复形范畴。我们首先给出它的导出范畴的概念，然后定义相应的modified Ringel-Hall代数。该modified Ringel-Hall代数是Bridgeland关于投射对象的复形的Hall代数、Gorsky关于Frobenius范畴的半导出Hall代数、以及我们之前关于遗传abel范畴的复形范畴的modified Ringel-Hall代数的统一。我们的主要结果是利用广义Frobenius范畴的导出范畴给出了相应modified Ringel-Hall代数的一组基。这是与彭联刚教授合作的工作。

6. 报告人：卢明，四川大学

题目：Geometric realization of i-quantum groups

摘要： A quantum symmetric pair consists of a quantum group and its coideal subalgebra (called an i-quantum group). A quantum group can be viewed as an example of i-quantum groups associated to symmetric pairs of diagonal type. In recent years, several fundamental constructions (such as canonical bases, R-matrices) for quantum groups have been generalized to the setting of i-quantum groups. In our recent work with W. Wang, we obtained a Hall algebraic realization of i-quantum groups, generalizing the construction of Bridgeland. 

In this talk, we provide a geometric construction of the universal i-quantum groups and their dual canonical bases" with positivity, via the quantum Grothendieck rings of Nakajima-Keller-Scherotzke quiver varieties. It can also be viewed as a generalization of Qin's geometric realization of quantum groups.

This is joint work with Weiqiang Wang.

 7. 报告人：邱宇，清华大学

题目：Global dimension of triangulated categories and q-deformation of

stability conditions

摘要：Motivated by Ikeda-Qiu's q-deformation of Bridgeland stability conditions, we study the global dimension function gl.dim on the space Stab of stability conditions of a triangulated category D. The inf of gl.dim should be considered as the global dimension for D. We calculate such inf for Dynkin quivers and explain how gl.dim shed lights on contractibility of Stab.

8. 报告人：周宇，清华大学

题目：Torsion theories and derived equivalences

摘要：Associated to a torsion pair in an abelian category A, there is an abelian category B, the so-called Happel-Reiten-Smalo tilting. I will give necessary and sufficient conditions on the torsion pair such that there is an equivalence from D^b(B) to D^b(A). This is based on joint work with Xiao-Wu Chen and Zhe Han.

9. 报告人：朱彬，清华大学

题目：Cluster tilting theory in extriangulated categories

摘要：TBA.