Upcoming talk:

Title: On b-Whittaker functions

Speaker: Tianqing Zhu （Graduate of YMSC, Tsinghua University）
Time: 11-08 15:00-17:00
Venue: Shuanqging Building C546

Abstract:  

I shall introduce the concept of b-Whittaker functions in the Coxeter-Toda integrable system and its connection with the positive representations

Past talks:

Title: Cluster realization of from quantum character varieties

Speaker: Tianqing Zhu （Graduate of YMSC, Tsinghua University）
Time: 11-01 15:00-17:00
Venue: Shuanqging Building C546

Abstract:

In this talk I will introduce the work of G. Schrader and A. Shapiro in which they construct an algebra monomorphism of the quantum group into a quantum -cluster algebra associated to the moduli space of framed -local systems on a marked punctured disk.

Title: Tensor product decomposition of positive representations of quantum modular double of sl_2(\mathbb{R})

Speaker: Dimitry Solovyev （Graduate of YMSC, Tsinghua University）
Time: 10-25 15:00-17:00
Venue: Shuanqging Building C546

Abstract: In this talk we will finish discussing Clebsch-Gordan and Racah-Wigner coefficients for discrete series of irreducible representations of U_q(sl_2). Then we use similar approach to derive Clebsch-Gordan and Racah-Wigner coefficients for positive representations of the modular double U_{q\tilde{q}}(sl_2(\mathbb{R})). 

Title: quantum group and representation theory 

Speaker: Dimitry Solovyev （Graduate of YMSC, Tsinghua University）
Time: 10-18 15:00-17:00
Venue: Shuanqging Building C546

Abstract: I will give a brief introduction to quantum groups and their representation theory with the emphasis on applications to integrable systems. If time permits, I will talk about positive representations and their Clebsch-Gordan coefficients and Racah-Wigner coefficients in the case of U_q(sl_2). 

Title: Representation of quantum cluster variety II 

Speaker: Tianqing Zhu （Graduate of YMSC, Tsinghua University）
Time: 10-13 15:00-17:00
Venue: Shuanqging Building C546

Abstract: I will talk about how to construct the representation of quantum cluster variety, as an application, I will show how to relate it to the positive representation of U_{q}(sl_2). 

Title: quantum cluster variety, an introduction
Speaker: Tianqing Zhu （Graduate of YMSC, Tsinghua University）
Time: 9-27 15:00-17:00
Venue: Shuanqging Building C546
Abstract：In this talk, I will introduce the concept of quantum cluster variety, quantum dilogarithm and the centre of the quantum cluster variety. 

Title: Introduction to quantum cluster variety.
Speaker: Chao Shen（Graduate of Department of Mathematical Sciences, Tsinghua University） & Tianqing Zhu （Graduate of YMSC, Tsinghua University）
Time: 9-13 15:00-17:00
Venue: Shuanqging Building C546
Abstract: We will briefly recall the definitions of cluster algebras, cluster varieties,quantum cluster varieties and related concepts.