From March to May 2025, the Shenzhen International Center for Mathematics at the Southern University of Science and Technology (SUSTech) in Shenzhen successfully hosted the Shenzhen Thematic Program “Representation Theory” series of international conferences, covering three major themes: quantum groups, vertex algebras, and the representation of Lie algebras. Hundreds of scholars from around the world participated in the conferences, engaging in academic exchanges and delivering numerous research presentations that collectively advanced both the theoretical depth and disciplinary development of representation theory.
International Workshop "Quantum Groups in Shenzhen"
Group photo of participants at the International Workshop "Quantum Groups in Shenzhen" (March 23-27, 2025, Shenzhen)
Held from March 23 to 27, 2025, the International Workshop "Quantum Groups in Shenzhen" centered on the theory and applications of quantum groups. The event featured dozens of invited academic presentations by renowned scholars. Nicolai Reshetikhin, recipient of the Weyl-Wigner Award and one of the founders of quantum group theory, systematically elucidated the connection between dimer models on toric periodic graphs and the Ising model in his lecture. Prof. Evgeny Mukhin proposed a novel method for constructing irreducible modules of quantum affine sl(2), with his team introducing vertex operator algebra techniques to successfully construct integrable system models on infinite-dimensional Hilbert spaces. Prof. Ruibin Zhang revealed dimension mutation properties of the quantum G₂ invariant ring. Prof. Hiroyuki Yamane achieved a rigorous mathematical definition of UqD(1)(2,1;α) by developing the Drinfeld double construction for generalized quantum groups. Prof. Adriano Moura defined strongly real modules and demonstrated methods for constructing examples based on the concept of reality-determining subgraphs, derived from results providing sufficient conditions for a module to be real. Prof. Olivier Mathieu proposed a conjecture concerning dimensional components of multivariate free Jordan algebras J(D) and provided theoretical explanations with collaborators using Ext groups in the representation category of TKK algebras. Scholars including Duncan Laurie, Hao Chang, Hongdi Huang, Naihong Hu, Venkatesh Rajendran, Xiaomeng Xu, Xingpeng Liu, and Yunnan Li also delivered specialized reports in the field. The workshop introduced new tools for research into quantum integrable systems and statistical physics models, with over ten keynote presentations fostering interdisciplinary integration of quantum group theory with physics and geometry.
International Workshop "Vertex Algebras in Shenzhen"
Group photo of participants at the International Workshop "Vertex Algebras in Shenzhen" (April 20-26, 2025, Shenzhen)
Held from April 20 to 26, 2025, the International Workshop "Vertex Algebras in Shenzhen" explored the theory and applications of vertex algebras from multiple perspectives. Prof. Tomoyuki Arakawa, the primary organizer, proposed a conjecture in his opening lecture concerning the equivalence between the category of weight modules of affine Kac-Moody algebras and the unrolled small quantum group, presenting a proof for sp(2n) at the −1/2 admissible level. Prof. Dražen Adamović, the member of the list of most cited scientists for general mathematics (2020-2023), constructed a family of quasi-lisse vertex algebras closely related to SL(2) chiral differential operator algebras, demonstrated the isomorphism between the C3 and Deligne series vertex algebras, and established correspondences with affine W-algebras of types F4 and E8. Prof. Qing Wang constructed the Q-graded structure of osp(1|2) admissible-level vertex operator superalgebras and proved the semisimplicity of their weak module categories. Prof. Naihuan Jing advanced the Drinfeld realization of twisted quantum extended affine algebras, revealing deep connections between deformations of extended affine Lie algebras of nullity 2 and quantum torus algebras, as well as solutions to the Yang-Baxter equation. Prof. Libor Křižka developed computational methods for the associated varieties of non-admissible-level simple affine vertex algebras. Prof. David Ridout uncovered physical links between psl(2|2) superalgebras and superconformal field theory. Distinguished scholars including Christopher Raymond, Justine Fasquel, Jinwei Yang, Hao Zhang, Shigenori Nakatsuka, Simon Wood, Xuanzhong Dai, and Yevhen Makedonskyi delivered forward-looking presentations, offering innovative and practically valuable research insights. The workshop promoted the integration of vertex algebras with quantum groups, supersymmetric physics, and geometric representation theory, providing new directions for exploring complex structures like the Yang-Baxter equation and chiral differential operators.
International Workshop "Representation of Lie Algebras in Shenzhen"
Keynote presentation session at the International Workshop "Representation of Lie Algebras in Shenzhen" (May 25-31, 2025, Shenzhen)
Held from May 25 to 31, 2025, the International Workshop "Representation of Lie Algebras in Shenzhen" delved into core topics including the structure of Lie algebras, representation theory, geometry, and topology. Distinguished Reasearch Professor Daniel K. Nakano introduced the general category O defined for any quasireductive Lie superalgebra, clarifying that the complexity of modules in category O is finite and establishing an explicit upper bound. Chair Professor Xuhua He examined the relationship between conjugacy classes and irreducible representations of finite groups, analyzing the cocenter of Hecke algebras. Prof. David Hernandez explained that the Grothendieck ring of the category O for shifted quantum affine algebras possesses a cluster algebra structure. Prof. Kevin Coulembier investigated the behavior of specific tensor ideals in the representation categories of cyclic groups in positive characteristic and in the tilting module categories of quantum groups. Prof. Yongchang Zhu defined beta-gamma systems and b-c systems for modular groups. Prof. Haisheng Li demonstrated natural connections between deformed Virasoro algebras and certain infinite-dimensional Clifford algebras. Prof. Abdenacer Makhlouf introduced the concept of Poisson superbialgebras, expanding the representation theory related to Lie superbialgebras. Prof. Shun-Jen Cheng established equivalences between module categories of finite W-algebras and W-superalgebras. Prof. Michael Lau explored weight modules of sl(2)-graded Lie algebras arising from unit Jordan algebras. Prof. Kailash Misra studied the multiplicities of maximal dominant weights for affine Lie algebras. Prof. Alistair Savage investigated connections between quantum symmetric pairs and HOMFLYPT modules. Prof. Euiyong Park presented a new crystal theory for quantum twisted automorphisms. Prof. Boujemaa Agrebaoui studied the structure of solenoidal Virasoro algebras and explored their Harish-Chandra modules and super analogs. Prominent scholars including Arik Wilbert, Ben Webster, Chun-Ju Lai, Jonathan Nilsson, Kaveh Mousavand, Kei Yuen Chan, Olivier Mathieu, Samuel Lopes, and Xabier García-Martínez delivered in-depth and engaging presentations, covering a wide range of cutting-edge research directions and providing rich academic insights. The conference not only advanced research in Lie algebras and their representation theory but also created opportunities for collaboration among scholars in related fields.
By hosting this series of conferences, the Shenzhen International Center for Mathematics not only provides a platform for global scholars to engage in in-depth dialogues but also fosters the development of cross-regional and interdisciplinary collaborative networks, thereby strengthening the theoretical connections between representation theory and related fields, such as physics and geometry.
Contributed by: Shenzhen International Center for Mathematics