About
This is a seminar organized by Zhengwei Liu, Linzhe Huang, Sebastien Palcoux, Yilong Wang and Jinsong Wu. The topics range in the broad area of quantum mathematics and physics, including but not limited to
- Topological Quantum Field Theory
- Tensor Categories
- Subfactor Theory
- Vertex Operator Algebras
- Quantum Information
- Quantum Computation
- Low-Dimensional Topology
- …
- Speaker:
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Yu-An Chen (陈昱安), Peking University
- Title:
- Operator algebra approach for topological Pauli stabilizer codes in two dimensions
- Time:
-
13:30 ~ 14:30
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
In this talk, I will discuss the operator algebra and computational algorithms for analyzing topological Pauli stabilizer codes in two spatial dimensions. These codes underpin the study of topological phases of matter and the design of quantum codes for fault-tolerant quantum computation. Building on the generalized Pauli stabilizer codes framework, I will present algorithms for extracting topological data such as anyon types, fusion rules, topological spins, and braiding statistics. I will also introduce methods for constructing gapped boundaries and defects through boundary anyon condensation. The algebraic approach, which utilizes matrix operations such as the Hermite and Smith normal forms, allows for efficient analysis and systematic construction of surface codes. Examples, including toric codes, color codes, and bivariate bicycle codes, illustrate the versatility of these methods in revealing new insights into the bulk and boundary topological properties of quantum codes. These results deepen our understanding of two-dimensional topological stabilizer codes and pave the way for practical designs of quantum error-correcting codes in fault-tolerant quantum computing.
Speaker Intro:
陈昱安，北京大学物理学院量子材料科学中心助理教授。2015 年 6 月毕业于美国麻省理工学院，获得数学、物理学学士学位；2020 年 6 月毕业于美国加州理工学院，获得物理学博士学位。曾任谷歌公司量子人工智能（Quantum AI）研究团队研究科学家。2020 年 9月至 2023 年 6 月期间，在美国马里兰大学帕克分校联合量子研究所（JQI）博士后研究员 。2023 年 7 月加入北京大学物理学院。2009年和2010年分别获第40届国际物理奥林匹克竞赛（IPhO）金牌和第51届国际数学奥林匹克竞赛铜牌。
- Speaker:
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Kenichi Shimizu, Shibaura Institute of Technology
- Title:
- Rigidity of the category of local modules
- Time:
-
14:30 ~ 15:30
(Beijing Time)
- Venue:
- A3-4-101
- Online:
- Zoom 637 734 0280 (BIMSA)
- Abstract:
- Given a commutative algebra \(A\) in a braided monoidal category \(C\), the category \(C_A^{loc}\) of local \(A\)-modules in \(C\) is defined as a certain full subcategory of the category of \(A\)-bimodules in \(C\). As has been pointed out by Pareigis, provided that \(C\) admits coequalizers and the tensor product of \(C\) preserves them, the category \(C_A^{loc}\) has a natural structure of a braided monoidal category inherited from that of \(C\). As it later turned out, the category of local modules is related to representations of an extension of a vertex operator algebra. We are therefore interested in knowing when the category of local modules has nice properties. In this talk, I will introduce a criterion for \(C_A^{loc}\) to be rigid monoidal. As an application, \(C_A^{loc}\) is a braided finite tensor category if \(C\) is a braided finite tensor category and the category of \(A\)-bimodules is a finite tensor category (or, equivalently, \(A\) is an indecomposable exact commutative algebra in \(C\)). If, in addition, \(C\) is non-degenerate and \(A\) is symmetric Frobenius, then \(C_A^{loc}\) is a modular tensor category in the sense of Lyubashenko. I will also discuss the Witt equivalence of non-degenerate braided finite tensor categories and relevant questions.
- Speaker:
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Haixing Zhu, Nanjing Forestry University
- Title:
- The computation on the Brauer group of a quasitriangular Hopf algebra
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
- Let (H, R) be a Hopf algebra H with the quasitriangular structure R (i.e., R-matrix). The Brauer group Br(H, R) of a quasitriangular Hopf algebra is the group of the equivalence classes of H-Azumaya algebras. It is also described as specific braided autoequivalences on the Drinfeld center of the category of H-modules. We will first describe the Drinfeld center of the representation category as the category of comodules over the braided Hopf algebra HR, which is deformed by R-matrix. This description helps us realize specific autoequivalences on the Drinfeld center by some quantum-commutative Galois objects. Then the group of these Galois objects is naturally related to the Brauer group Br(H, R), and actually appeared in an exact sequence of the Brauer group Br(H, R), which was constructed by Prof. Yinhuo Zhang. Next we will investigate how to construct / characterize these Galois objects, and mainly use Sweedler’s cohomology of the braided Hopf algebra HR to give its subgroup, and then get some information on Br(H, R).
- Speaker:
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Yuxuan Yang, Peking University
- Title:
- On the Volume Conjecture for hyperbolic Dehn-filled 3-manifolds along the twist knots
- Time:
-
16:00 ~ 17:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 293 812 9202 (BIMSA)
- Abstract:
- For a twist knot K_p’, let M be the closed 3-manifold obtained by doing (p, q) Dehn-filling along K_p’. In this article, we prove that Chen-Yang’s volume conjecture holds for sufficiently large |p| + |q| and |p’| for M. In the proof, we construct a new ideal triangulation of the Whitehead link complement which is different from Thurston’s triangulation. Our triangulation has led to some new discoveries regarding symmetry, including insights into “sister manifolds” as introduced by Hodgson, Meyerhoff, and Weeks. This work is a collaboration with Huabin Ge, Chuwen Wang, and Yunpeng Meng.
- Speaker:
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Robert McRae, Tsinghua university, YMSC
- Title:
- Commutative algebras in braided monoidal categories and rigidity
- Time:
-
16:30 ~ 17:30
(Beijing Time)
- Venue:
- A3-2a-302
- Online:
- Zoom 815 762 8413 (BIMSA)
- Abstract:
- I will discuss recent joint works with Thomas Creutzig, Kenichi Shimizu, Harshit Yadav, and Jinwei Yang. Let \(A\) be a commutative algebra in a braided monoidal category \(C\). For example, \(A\) could be a vertex operator algebra (VOA) extension of a VOA \(V\) in a category \(C\) of \(V\)-modules. First, assuming that \(C\) is a finite braided tensor category, I will discuss conditions under which the category \(C_A\) of \(A\)-modules in \(C\) and its subcategory \(C_A^{loc}\) of local modules inherit rigidity from \(C\). These conditions are based on criteria of Etingof and Ostrik for \(A\) to be an exact algebra in \(C\). As an application, we show that if a simple non-negative integer-graded vertex operator algebra \(A\) contains a strongly rational vertex operator subalgebra \(V\), then \(A\) is also strongly rational, without requiring the dimension of \(A\) in the modular tensor category of \(V\)-modules to be non-zero. Second, assuming that \(C\) is a Grothendieck-Verdier category (which means that \(C\) admits a weaker duality structure than rigidity), I will discuss conditions under which \(C\) inherits rigidity from \(C_A^{loc}\). These conditions are motivated by free field-like VOA extensions \(A\) of a vertex operator subalgebra \(V\) where \(A\) is often an indecomposable \(V\)-module. As an application, we show that the category of weight modules for the simple affine VOA of \(sl_2\) at any admissible level is rigid.
- Speaker:
-
JingCheng Dong (董井成), Nanjing University of Information Science and Technology
- Title:
- On perfect modualr categories of low dimension
- Time:
-
14:00 ~ 15:15
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
- In this talk, we prove that modular categories of Frobenius-Perron dimension \(p^2\)\(q^2\)\(r^2\)\(m\) are solvable, where \(p\),\(q\),\(r\) are distinct prime numbers, \(m\) is square-free with \(g\)\(c\)\(d\)(\(m\),\(p\)\(q\)\(r\))=1. As applications, we get that integral modular categories of Frobenius-Perron dimension less than 1800 are solvable, and hence integral perfect modular categories have Frobenius-Perron dimension greater than or equal to 1800. When the modular categories considered are weakly group-theoretical, we get some further results.
- Speaker:
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Bin Gui (归斌), Tsinghua university YMSC
- Title:
- From Segal’s sewing to pseudo-q-traces and back
- Time:
-
13:30 ~ 15:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
In 1990, Zhu proved that if V is a C2 cofinite rational VOA, then the q-traces of the vertex operators for modules of V span a modular-invariant space. These q-traces have a clear geometric meaning: they are special cases of Segal’s sewing construction (≈partial contractions for conformal blocks). However, if V is C2 cofinite but irrational, Miyamoto proved in 2004 that achieving modular invariance requires generalizing q-traces to pseudo-q-traces. At first glance, pseudo-q-traces do not appear to fit within Segal’s sewing framework. Did Segal miss something?
In this talk I will provide the answer: No. By suitably adjusting Segal’s sewing, we can achieve a geometric interpretation of pseudo-q-traces. Our interpretation enables us to prove a conjecture by Gainutdinov-Runkel relating the spaces of torus conformal blocks to the categorical data of V-modules. This is joint work with Hao Zhang.
Speaker Intro:
归斌现为清华大学丘成桐数学中心助理教授。本科毕业于上海交通大学。博士毕业于美国Vanderbilt University，师从Vaughan Jones。博士后工作于美国Rutgers University。
归斌的研究兴趣为顶点算子代数，以及与其相关的泛函分析与算子代数、张量范畴等问题。在顶点算子代数表示范畴的酉性（unitarity）方面、以及其与共形网（conformal nets）的表示范畴的等价性方面都首先做出系统性的研究。多篇论文发表于Communications in Mathematical Physics, Transactions of AMS, IMRN等期刊。
- Speaker:
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Liang Chang, Nankai University
- Title:
- Modular data of non-semisimple modular categories
- Time:
-
09:00 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
- Modular tensor categories are semisimple tensor categories with nondegenerated braiding, which have many applications in low dimensional topology and topological physics. Recently, the notion of modularity is extended to non-semisimple tensor category. In this talk, we will talk about the work to extend the well-understood theory of semisimple modular categories, such as the SL(2, Z)-representation and rank finiteness, to the non-semisimple case by using representations of factorizable ribbon Hopf algebras.
- Speaker:
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Francis Bonahon, University of Southern California & Michigan State University
- Title:
- Invisible SL_n-skeins
- Time:
-
09:00 ~ 10:30
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
- For a Lie group G, the G-skein module of a 3-dimensional manifold M is a fundamental object in Witten’s interpretation of quantum knot invariants in the framework of a topological quantum field theory. It depends on a parameter q and, when this parameter q is a root of unity, the G-skein module contains elements with a surprising “invisibility” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some of these invisible elements in the case of the special linear group SL_n. The construction is based on the very classical theory of symmetric polynomials in n variables.
- Speaker:
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Xingting Wang, Louisiana State University
- Title:
- Hopf algebras of dimension \(p^2\) in positive characteristic \(p\)
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom 242 742 6089 (BIMSA)
- Abstract:
- In characteristic zero, it is well-known that the only nonsemismiple Hopf algebras of dimension for a prime number are the Taft algebras. In this talk, we will discuss some recent work on Hopf algebras of dimension \(p^2\) in positive characteristic \(p\). It is joint work with Richard Ng.
- Speaker:
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Haimiao Chen (陈海苗), Beijing Technology and Business University
- Title:
- Torsion in the Kauffman bracket skein module of a knot exterior
- Time:
-
14:30 ~ 15:30
(Beijing Time)
- Venue:
- A3-4-312
- Online:
- 2427426089 (BIMSA)
- Abstract:
- For a compact oriented \(3\)-manifold \(M\), its Kauffman bracket skein module \(\mathcal{S}(M)\) is defined as the quotient of the free \(\mathbb{Z}[q^{\pm\frac{1}{2}}]\)-module generated by isotopy classes of framed links embedded in \(M\) by the submodule generated by skein relations. It was known in 1990s that \(\mathcal{S}(M)\) may admit torsion if \(M\) contains an essential sphere or torus. A problem in “Kirby’s list” asks whether \(\mathcal{S}(M)\) is free when \(M\) does not contains an essential sphere or torus. We show that \(\mathcal{S}(M)\) has infinitely many torsion elements when \(M\) is the exterior of the \((a_1/b_1,a_2/b_2,a_3/b_4,a_4/b_4)\) Montesinos knot with each \(b_i\ge 3\); in particular, \(\mathcal{S}(M)\) is not free. Using surgery we can construct closed hyperbolic \(3\)-manifolds \(N\) such that \(\beta_1(N)=0\) and \(\mathcal{S}(N)\) admits torsion.
- Speaker:
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Mainak Ghosh, BIMSA
- Title:
- Unitary connections and Q-systems
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
The standard invariant plays a major role in subfactor theory. In this talk, I will discuss a 2-categorical generalization of an axiomatization of the standard invariant and further discuss some algebraic structures associated to it.
References: arXiv:2211.03822, arXiv:2302.04921
- Speaker:
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Haonan Zhang (张浩楠), University of South Carolina
- Title:
- On the quantum KKL theorem and related inequalities
- Time:
-
14:00 ~ 15:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting 293 812 9202 (PASSWORD: BIMSA)
- Abstract:
- The KKL theorem is a fundamental result in Boolean analysis, stating that any Boolean function has an influential variable. Montanaro and Osborne proposed a quantum extension of Boolean functions. In this context, some classical results have been extended to the quantum setting, such as Talagrand’s \(L^1\)-\(L^2\) inequality. However, a quantum version of the KKL theorem seems to be missing, as conjectured by Montanaro and Osborne. In this talk, I will present an alternative answer to this question, saying that every balanced quantum Boolean function has a geometrically influential variable. This is based on joint work with Cambyse Rouzé (Inria) and Melchior Wirth (IST Austria).
- Speaker:
-
Siu-Hung Ng (吴少雄), Louisiana State University
- Title:
- Mining for modular data from congruence representations
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- Modular fusion categories (MFCs) arise naturally in many areas of mathematics and physics. Associated with an MFC is a pair of complex matrices, called modular data, which are arguably the most important invariants of an MFC. The modular data of an MFC generate some uncanonical congruence representations of SL(2,Z). In this talk, we will discuss how modular data could be reconstructed or discovered from congruence representations of SL(2,Z). The talk is based on a joint work with Eric Rowell, Zhenghan Wang and Xiao-Gang Wen.
- Links:
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- Speaker:
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Ce Shen (沈策), BIMSA
- Title:
- Fusion Rules of Edge Excitations in Topological Order
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom Meeting 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- We re-examine the issue of boundary excitations at topological boundaries or junction defects between different topological boundaries in nonchiral bosonic topological orders in 2+1 dimensions. Through physical reasoning, we derive a formula that connects the fusion rules of boundary excitations with the “half-linking” number between condensed anyons and confined boundary excitations. This formula serves as a direct analogue to the Verlinde formula. Additionally, we illustrate how these half-linking numbers can be calculated in specific Abelian and non-Abelian scenarios.
- Speaker:
-
Mo Huang, East China Normal University
- Title:
- 2-character theory of finite 2-groups
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301
- Online:
- Zoom Meeting 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- The character plays an important role in the representation theory of finite groups. In this talk, I will introduce the notion of 2-character of 2-representations of a finite 2-group G. The conjugation invariance implies that the 2-characters can be viewed as objects in the Drinfeld center $Z_1(VecG)4. I will also introduce a topological quantum field theory (TQFT) point of view on the 2-characters and show that they are Lagrangian algebras in \(Z_1(VecG)\). Finally, I will discuss the orthogonality of 2-characters, which categorifies the classical orthogonality of characters. This talk is based on arXiv: 2305.18151 and 2404.01162, joint with Hao Xu and Zhi-Hao Zhang.
- Speaker:
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Kun Zhou (周坤), BIMSA
- Title:
- Constructing modular tensor categories by using Hopf algebras
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- A modular tensor category is a non-degenerate ribbon finite tensor category. We will construct ribbon factorizable Hopf algebras whose representation categories are modular tensor categories. Specifically, we give some general construction methods of ribbon factorizable Hopf algebras. Then we use these methods to obtain a family of semisimple ribbon factorizable Hopf algebras and two families of non-semisimple ribbon factorizable Hopf algebras. The representation categories of the last two families are prime modular tensor categories, while the representation categories of first family are not prime modular tensor categories. Finally, we compared their representation categories with known modular tensor categories from ribbon factorizable Hopf algebras in some degree.
- Speaker:
-
Zhian Jia (贾治安), National University of Singapore
- Title:
- Weak Hopf symmetry behind the 2d topological phases
- Time:
-
17:00 ~ 18:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- Two-dimensional (2d) topological phases are characterized by a unitary modular tensor category (UMTC) along with the chiral central charge \(c_−\). For non-chiral topological phases, where \(c_−\) vanishes, the topological phase is fully described by a UMTC. There are two prominent classes of lattice models that realize 2d non-chiral topological phases: (i) Kitaev’s quantum double models and (ii) Levin and Wen’s string-net models. These two model classes are intimately related. This talk will present a generalization of Kitaev’s quantum double models to weak Hopf algebras, as well as a generalization of Levin-Wen string-net models to multifusion categories. We will establish an equivalence between these two broader classes of lattice models for non-chiral 2D topological phases. From the perspective of lattice gauge theory, we introduce weak Hopf gauge and charge symmetries. In particular, we elucidate the weak Hopf symmetry underlying the multifusion string-net models. Some interesting open problems related to these generalizations will also be highlighted.
- Speaker:
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Josse van Dobben de Bruyn, Technical University of Denmark
- Title:
- Asymmetric graphs with quantum symmetry
- Time:
-
17:00 ~ 18:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 518 868 7656 (PASSWORD: BIMSA)
- Abstract:
In this talk, I will present a sequence of graphs which have trivial (classical) automorphism group and non-trivial quantum automorphism group, which we believe to be the first known examples of any kind of classical space with this property. The construction is inspired by solution groups of binary linear systems, as defined by Cleve, Liu and Slofstra in 2015 in relation to certain non-local games in quantum information theory.
Reference: This talk is based on joint work with David E. Roberson (Technical University of Denmark) and Simon Schmidt (Ruhr University Bochum, Germany), arXiv:2311.04889.
Speaker Intro:
Josse van Dobben de Bruyn is a postdoctoral researcher at the Technical University of Denmark (DTU), working on interactions between graph theory, quantum groups, and quantum information theory. He obtained his PhD in algebraic combinatorics from Delft University of Technology in the Netherlands in 2023, supervised by Prof. dr. Dion Gijswijt.
- Speaker:
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Yuanhang Zhang (张远航), Jilin University
- Title:
- On commutators of quadratic operators
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
A bounded linear operator \(A\) is said to be quadratic if there is a polynomial \(p\) of degree \(2\) such that \(p(A)=0\). Square zero operators, involutions, and idempotents are all typical quadratic operators.
We will give characterizations of matrices could be expressed as commutators of two square zero matrices, and explain some related results about limits of commutators of two square zero operators acting on a complex, separable Hilbert space \(\mathcal{H}\).
We will also study the norm-closure of the set \(\mathfrak{C}_{\mathfrak{E}}\) of bounded linear operators acting on \(\mathcal{H}\) which may be expressed as the commutator of two idempotent operators. In particular, biquasitriangular operators belong to the norm-closure of \(\mathfrak{C}_{\mathfrak{E}}\) are fully charateriezed.
This talk is based on joint papers with Laurent Marcoux and Heydar Radjavi.
- Speaker:
-
Ping Zhong (钟平), University of Wyoming, US
- Title:
- Upgrading free convolution to non-normal random variables
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
The free probability theory is a probability theory of noncommutative random variables, where usual independence is replaced by free independence. It was initially designed to study longstanding problems about von Neumann algebras of free groups. It turns out to be an extremely powerful framework to study the universality laws in random matrix theory due to the groundbreaking work of Voiculescu. These limiting laws are encoded in abstract operators, called free random variables.
Brown measure is a sort of spectral measure for free random variables, not necessarily normal. I will report some recent progress on the Brown measure of the sum \(X+Y\) of two free random variables \(X\) and \(Y\), where \(Y\) has certain symmetry or explicit R-transform. The procedure relies on Hermitian reduction and subordination functions. The Brown measure results can predict the limit eigenvalue distribution of various full rank deformed random matrix models. The talk is based on my work on Brown measure of elliptic operators and joint works with Hari Bercovici, Serban Belinschi and Zhi Yin.
- Speaker:
-
Lian Wu (吴恋), Central South University (中南大学)
- Title:
- Noncommutative weak-\(L^\infty\) and BMO
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- Bennett, DeVore and Sharpley (Ann of Math. 113: 601-611, 1981) introduced the weak analogue of the space \(L^\infty\) and studied its relationship to the space of functions of bounded mean oscillation. The purpose of this paper is to continue this line of research in the context of functions on \(\R^d\) with values in a semifinite von Neumann algebra. As a by-product, this allows for the comparison of the \(BMO\) norms of an operator-valued function and its decreasing rearrangement. The argument rests on a new distributional estimate for noncommutative martingales invoking Cuculescu projections, which is of independent interest. The applications include related \(BMO\to wL^\infty\) inequalities for square functions and conditional square functions, as well as corresponding versions of Stein and dual Doob estimates, which are new even for classical martingales.
- Speaker:
-
Simeng Wang (王斯萌), Harbin Institute of Technology (哈尔滨工业大学)
- Title:
- Rigidity of some quantum group actions on classical compact spaces
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 BIMSA
- Online:
- Zoom Meeting: 242 742 6089 (PASSWORD: BIMSA)
- Abstract:
- We give a complete description of the actions by the free quantum permutation group \(S_N^+\) on compact topological spaces, and in particular prove that \(S_N^+\) cannot act ergodically on any nontrivial compact connected space, which was an open problem dating back to the related work of Goswami around 2010s. The proof is based on a combinatorial approach to the Tannaka-Krein duality for quantum group actions, and the method also applies to many other easy quantum groups. This is joint work with Amaury Freslon and Frank Taipe.
- Speaker:
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César Galindo, Universidad de los Andes, Bogotá, Colombia
- Title:
- Braided Zestings of Verlinde Modular Categories and Their Modular Data
- Time:
-
10:30 ~ 12:00
(Beijing Time)
- Venue:
- A3-3-301 北京雁栖湖应用数学研究院(BIMSA)
- Online:
- ZOOM 293 812 9202 (PASSWORD: BIMSA)
- Abstract:
In this talk, I will describe the construction known as ‘Zesting of Braided Fusion Categories’, a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. I will also present our work on classifying and constructing all possible braided zesting data for modular categories associated with quantum groups at roots of unity. We have produced closed formulas, based on the root system of the associated Lie algebra, for the modular data of these new modular categories.
Reference: This talk is based on the preprint https://arxiv.org/abs/2311.17255, a joint work with Giovanny Mora and Eric C. Rowell.
- Links:
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