SUSTech-Nagoya workshop on Quantum Science 2022

Dates and Place

• Dates: May 31 (Tue) - June 3 (Fri), 2022.
• Style: The presentation and free discussion will be delivered by Zoom.
• Organizing committee: Masahito Hayashi (Chair, SUSTech/Nagoya Univ.),
  Hiroaki Kanno (Nagoya Univ.), Liang Kong (SUSTech), Shintarou Yanagida (Nagoya Univ.).
• Contact: sustechnagoya2022 [at] gmail.com

Registration

For the participation, please mail to sustechnagoya2022 [at] gmail.com
with the following information: your name, affiliation and e-mail address.
We will send Zoom addresses later.

KouShare/YouTube live streaming

Talks will be streamed by KouShare and YouTube.

• KouShare site
• YouTube
  5/31(Tue) AM, 5/31(Tue) PM.
  6/01(Wed) AM, 6/01(Wed) PM.
  6/02(Thu) AM, 6/02(Thu) PM.
  6/03(Fri) AM. 6/03(Fri) PM.

Time table

Program

• 5/31 (Tue)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Shinichiroh Matsuo (Graduate School of Mathematics, Nagoya University)
    Analytic indices in lattice gauge theory and their continuous limits slide
    We will consider the continuous limit of the analytic index of Wilson-Dirac operators in lattice gauge theory, and prove, as a corollary, the lattice index theorem.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Rongge Xu (School of Science, Westlake University)
    Categorical descriptions of 1-dimensional gapped phases with abelian onsite symmetries slide
    In this talk, I will show that the observables in 1d gapped phases with abelian onsite symmetries form enriched fusion categories. These categorical descriptions also provide us an existing classification result and shed light on a unified definition of all quantum phases. This work is done together with Zhi-Hao Zhang.
    The talk is based on the paper arXiv:2205.09656.
  • 10:50-11:10 (CST) 11:50-12:10 (JST)
    Holiverse Yang (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    An Introduction to mathematical theory of gapless edge of 2d topological orders slide
    We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e. a unitary fusion category) as a special case. Therefore, we obtain a unified mathematical description and a classification of both gapped and chiral gapless edges of a given 2d topological order. Our theory also implies that all chiral gapless edges can be obtained from a so-called topological Wick rotations. This fact leads us to propose, at the end of this work, a surprising correspondence between gapped and gapless phases in all dimensions.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Liang Kong (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    2D rational CFT's and categories slide
    In this talk, I will review some categorical aspects of 2D rational conformal field theories (CFT), and show how the categorical language leads to the mathematical description of the category of 2D rational CFT's.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    An-Si Bai (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    2-categorical interpretation of the Reconstruction Theorem for Weak Hopf Algebras slide
    Weak Hopf algebras (WHAs) have wide applications in the studies of quantum field theory, subfactor and topological order. One of the basic theorem of WHAs, the Reconstruction theorem (due to T. Hayashi), states that one can obtain a WHA from each pair (C,F:C->BiMod(R)), where C is a finite tensor category, F is a tensor functor and R is a separable algebra; Conversely, each WHA gives rise to such a pair. The appearance of R or BiMod(R) may seem ad hoc to many; In this talk I interpret this theorem as a special case of 2-categorical theorem, where R or BiMod(R) do not explicitly appear. This is based on a joint work with Zhi-Hao Zhang on understanding the algebraic structures in Kitaev-Kong (2012).
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Shintarou Yanagida (Graduate School of Mathematics, Nagoya University)
    Introduction to Macdonald polynomials as quantum integrable systems slide
    I will give a brief introduction to the theory of Macdonald polynomials, emphasizing the viewpoint of quantum integrable systems. A plan of the talk is:
    1. Schur, Jack and Macdonald polynomials of type A
    2. Relation to quantum integrable systems
    3. Macdonald polynomials associated to affine root systems
  • 15:40-16:00 (CST) 16:40-17:00 (JST)
    Zhi-Hao Zhang (Mathematics of Chinese Academy of Sciences, School of Mathematical Sciences, USTC & Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Enriched categories and their centers slide
    The notion of an enriched (fusion) category naturally appears in the study of the mathematical theory of topological orders. In this talk, I will introduce a symmetric monoidal 2-category of enriched categories with arbitrary background categories. Then the notion of an enriched (braided or symmetric) monoidal category can be defined as an E_n-algebra in this 2-category. Finally I will introduce the notion of a center and compute the center of an enriched (monoidal or braided monoidal) category.
    This is a joint work with Liang Kong, Wei Yuan and Hao Zheng, "Enriched monoidal categories I: centers", arXiv:2104.03121.
• 6/01 (Wed)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Qin Li (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Deformation quantization and Holomorphic differential operators slide
    Toeplitz operators on Kahler manifolds associate smooth functions to operators on Hilbert spaces $H^0(X,L^k)$. However, there composition only gives a formal deformation quantization by considering the asymptotic as $k \to \infty$. In this talk, I will describe a method of Fedosov to quantize a subclass of smooth functions to holomorphic differential operators on these Hilbert spaces. This gives a strong version of quantization since it gives rise to a non-formal deformation of the classical commutative multiplication.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Kohei Yamaguchi (Graduate School of Mathematics, Nagoya University)
    Macdonald-Koornwinder polynomials as multivariate q-orthogonal functions slide
    The family of Macdonald-Koornwinder polynomials is a multivariate $q$-orthogonal functions associated to the affine root system $C^\vee C$, having the quantum parameter $q$ and five extra parameters $t,a,b,c,d$ which are the most among the families of Macdonald polynomials. In this short talk, I will explain that this family is a multivariate analogue of the Askey-Wilson polynomials, one of the "master" $q$-hypergeometric orthogonal polynomials. I will also explain my recent study [1] on explicit formulas of product of the polynomials, and a collaboration [2] with my advisor Shintarou Yanagida on specializing parameters to relate Macdonald polynomials of other affine root systems.
    [1] K. Yamaguchi, "A Littlewood-Richardson rule for Koornwinder polynomials", arXiv:2009.13963; to appear in J. Algebraic Combinatorics.
    [2] K. Yamaguchi, S. Yanagida, "Specializing Koornwinder polynomials to Macdonald polynomials of type B,C,D and BC", arXiv:2105.00936.
  • 10:50-11:10 (CST) 11:50-12:10 (JST)
    Yuya Takahashi (Graduate School of Mathematics, Nagoya University)
    The moduli space of spatial polygons and geometric quantization slide
    The moduli space of spatial polygons is known as a symplectic manifold equipped with both Kahler and real polarizations. In this talk, we will construct morphisms of operads $\mathsf{f}_{Kah}$ and $\mathsf{f}_{re}$ by using the quantum Hilbert spaces $\mathcal{H}_{Kah}$ and $\mathcal{H}_{re}$ associated to the Kahler and real polarizations respectively. Moreover, we will relate the two morphisms $\mathsf{f}_{Kah}$ and $\mathsf{f}_{re}$, and prove the equality $\dim \mathcal{H}_{Kah} = \dim \mathcal{H}_{re}$ in general setting. This operadic framework is regarded as a development of the recurrence relation method by Kamiyama (2000) for proving $\dim \mathcal{H}_{Kah} = \dim \mathcal{H}_{re}$ in a special case.
    The talk is based on 2107.09412.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Hiroaki Kanno (Graduate School of Mathematics, Nagoya University)
    Non-Kerov deformation of the Macdonald polynomials slide
    The Macdonald polynomials (functions) are one of the most interesting classes of special functions in the representation theory. They are symmetric polynomials labeled by the partitions (Young diagrams) and enjoy the bi-spectral duality suggesting the existence of what we call "mother function". From the viewpoint of integrable system, the Macdonald functions are of trigonometric type. In our attempt at generalizing them to be of elliptic type, we arrived at the possibility of non-Kerov deformation. In my talk I will review Kerov and non-Kerov deformations of the Macdonald polynomials.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Panupong Cheewaphutthisakun (Graduate School of Mathematics, Nagoya University)
    MacMahon KZ equation for quantum toroidal $\mathfrak{gl}_1$ algebra slide
    In this talk, I will explain how to derive a generalized Knizhnik-Zamolodchikov (KZ) equation for the correlation function of the intertwiners of the MacMahon representations of quantum toroidal $\mathfrak{gl}_1$ algebra. Then, I will solve the equation and explain how we can regard the solution of the MacMahon KZ equation as a generalization of the Nekrasov factor, which is a fundamental quantity in five-dimensional supersymmetric gauge theories.
    This talk is based on the paper P. Cheewaphutthisakun, and H. Kanno, "MacMahon KZ equation for Ding-Iohara-Miki algebra”, J. High Energy Phys., 2021, no. 4 (2021), 1-47; arXiv:2101.01420.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Kazuhiko Minami (Graduate School of Mathematics, Nagoya University)
    Algebraic generalization of Jordan-Wigner transformation and its applications slide
    A new fermionization formula is introduced [1] in which series of solvable Hamiltonians and a transformation that diagonalize them are obtained simultaneously from a series of operators $\{\eta_j\}$ that satisfy specific commutation relations. The Jordan-Wigner transformation is a special case of this method.
    The two-dimensional Ising model with periodic interactions, the one-dimensional XY model with period 2, the transverse Ising chain, and other composite quantum spin chains, are diagonalized through this formula [1]. An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge $c=m/2$, where m is an integer [2].
    The fermionization formula is generalized to two-dimensional systems, and the two-dimensional Jordan-Wigner transformation appear as a special case. The honeycomb lattice Kitaev model ${\cal H}_{K}$ with two kind of Wen-Toric-code four-body interactions ${\cal H}_{WT}$ is investigated exactly and the ground state phase diagram is obtained. Six kind of three-body interactions are also considered. The model ${\cal H}_{K}+{\cal H}_{WT}$ is symmetric in four-dimensional interaction space, and the anyon excitations appear in each phase [3].
    It is also derived that operators that are composed of $\{\eta_j\}$, or its $n$-state clock generalizations, generate the Onsager algebra, which was introduced in the original solution of the rectangular Ising model, and appears in some integrable models [4].
    [1] Kazuhiko Minami, J. Phys. Soc. Jpn. 85, 024003 (2016).
    Solvable Hamiltonians and fermionization transformations obtained from operators satisfying specific commutation relations.
    [2] Kazuhiko Minami, Nucl. Phys. B, 925 (2017) 144-160.
    Infinite number of solvable spin chains, with cluster state, and with central charge c=m/2.
    [3] Kazuhiko Minami, Nucl. Phys. B, 939 (2019) 465-484.
    Honeycomb lattice Kitaev model with Wen-Toric-code interactions, and anyon excitations.
    [4] Kazuhiko Minami, Nucl. Phys. B 973, 115599 (2021).
    Onsager algebra and algebraic generalization of Jordan-Wigner transformation.
  • 15:40-16:00 (CST) 16:40-17:00 (JST)
    Hao Xu (Mathematisches Institut, Georg-August Universität Göttingen)
    Higher representation theory of finite group slide
    The classical representation theory of finite group is well-known for its simplicity and elegance. In recent years, people find natural categorifications of these structures when studying tensor categories. A nice parallel is obtained, which we shall call as the higher representation theory of finite group. In this talk, we will review basics of classical representation theory of finite group, introduce various categorified structures and present a classification result for simple 2-representations.
• 6/02 (Thu)
  • 9:30-10:10 (CST) 10:30-11:10 (JST)
    Dong Yang (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Distributed private randomness distillation slide
    We initiate the study of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent bits (ibits), which are bipartite states that contain ideal private randomness for each party, and motivate the natural set of the allowed free operations. As the main tool of our analysis, we introduce Virtual Quantum State Merging (VQSM), which is essentially the flip side of Quantum State Merging, without the communication. We focus on the bipartite case and find the rate regions achievable in different settings. Surprisingly, it turns out that local noise can boost randomness extraction. As a consequence of our analysis, we resolve a long-standing problem by giving an operational interpretation for the reverse coherent information capacity in terms of the number of private random bits obtained by sending quantum states from one honest party (server) to another one (client) via an eavesdropped quantum channel.
    Based on joint work PRL 123, 170501 (2019) with Karol Horodecki and Andreas Winter.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Baichu Yu (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    A Brief Introduction on Information Causality slide
    Quantum theory differs from classical theory by the fact that the space of states is a vector space. It would be desirable to know which principles underlie this structure. Instead of recovering the whole of quantum theory, a series of works have tried to find principles that single out the set of quantum correlations.
    In this talk I will make a brief introduction to information causality (IC), which is one of the first principles that have been invoked to bound the set of quantum correlations. I will also introduce several properties that imply IC, and some relevant unsolved questions.
    References:
    [1] Pawłowski M, Paterek T, Kaszlikowski D, et al., "Information causality as a physical principle[J]." Nature, 2009, 461(7267): 1101-1104.
    [2] Barnum H, Barrett J, Clark L O, et al., "Entropy and information causality in general probabilistic theories [J]." New Journal of Physics, 2010, 12(3): 033024.
    [3] Allcock J, Brunner N, Pawlowski M, et al., "Recovering part of the boundary between quantum and nonquantum correlations from information causality[J]." Physical Review A, 2009, 80(4): 040103.
  • 10:50-11:10 (CST) 11:50-12:10 (JST)
    Aditya Nema (Graduate School of Informatics, Nagoya University)
    One-shot multiparty local purity distillation slide
    One of the most fundamental resources for any quantum communication protocol is local pure states. In this work we obtain one-shot achievable bounds on the rates for distilling local pure states from a given mixed state. In a bipartite setting wherein the two parties, Alice and Bob, distill local pure states from a shared arbitrary quantum state, the aforementioned purity distillation problem can also be connected with the problem of distilling one-sided common randomness. Devetak (PR-A, 2005), characterized the optimal rate for distilling local purity in an asymptotic iid setting, where Alice and Bob are given access to many identical copies of a bipartite quantum state and to unlimited use of a dephasing channel from Alice to Bob. Further Krovi and Devetak (PR-A, 2007) extended this result to the scenario where the number of channel uses from Alice to Bob is finite. We first generalize Devetak’s bipartite local purity distillation to the one-shot setting, where Alice and Bob have access to only one copy of a mixed state. This involves translating the key technical asymptotic iid lemmas in Devetak’s work to the one-shot setting which is. In particular we use a new one-shot measurement compression lemma (in Chakraborty et al. arXiv:2203.16157) for this purpose. We can extend our one-shot result in a straightforward way to achieve the known asymptotic iid rate. In fact, we extend Devetak’s original protocol to the achievable one-shot rates for the tripartite scenario, that is, when three parties, Alice, Bob and Charlie have access to a tripartite state and Alice uses two dephasing channels from Alice to Bob and Alice to Charlie respectively, for local purity distillation for all the three parties. Along the way we prove a distributed source compression protocol with one sender and two receivers where the receiver’s have quantum side information.
    This is joint work with Sayantan Chakraborty and Francesco Buscemi and soon to be uploaded on arXiv.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Francesco Buscemi (Graduate School of Infomatics, Nagoya University)
    The theory of quantum statistical comparisons: a brief overview slide
    The theory of statistical comparisons, pioneered by David Blackwell between the 1940s and the 1950s, extends the idea of majorization from pairs of probability distributions to more general objects, like statistical experiments, discrete noisy channels, and matrices. In the past decade, various "quantum comparisons" (i.e., statistical comparisons between quantum states, quantum channels, etc.) have been introduced and studied, in particular in connection with quantum resource theories, of which they constitute a fundamental pillar. In this talk I will briefly recount some of my works toward the establishment of the theory of quantum statistical comparisons and its application in some areas of interest for quantum information theory and quantum foundations.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    
  Jiawei Wu (Department of Physics, Tsinghua University)
  A private dense coding framework slide
  We formulated the framework of private dense coding to realize quantum secure direct communication. This framework starts with general preshared states between Alice, Bob and Eve. Alice is allowed to apply a unitary operation from a group to encode her message and send her states to Bob. Bob applies measurement on the joint states of the received one and his own. The security is guaranteed for the worst scenario, in which Eve can intercept the states sent by Alice. We provide a concrete protocol as a case of our framework and give the upper bound of information leakage in the finite-length setting. The private dense coding framework is applicable in various protocols and provides a convenient tool for the security analysis.
  This talk is based on arXiv:2112.115113.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Harumichi Nishimura (Graduate School of Informatics, Nagoya University)
    Power of Distributed Quantum Merlin-Arthur Proofs slide
    Merlin-Arthur (MA) proof systems are computationally efficient verification systems based on NP-type one-way communication. In MA proof systems, an unlimitedly powerful party, Merlin, sends a message called a certificate to a party, Arthur, who has a polynomial-time computer, and Arthur verifies whether a given input is a yes-input for a yes/no-answer problem using the certificate. Distributed versions of MA proof systems have been studied extensively also in distributed computing, where Arthur is not a single party but many parties who are considered as the nodes in a network.
    In this talk, I present the notion of the distributed version of quantum Merlin-Arthur proof (QMA) systems, where Merlin sends a quantum certificate to the nodes in the network which may use quantum communication. I report the power of quantum certificates in the distributed QMA proof systems, and several open problems. The talk is based on Ref. [1].
    [1] P. Fraigniaud, F. Le Gall, H. Nishimura, A. Paz, Quantum proofs for replicated data,
    Leibniz International Proceedings in Informatics, 185, article no. 28 (2021); arXiv:2002.10018.
• 6/03 (Fri)
  • 9:30-10:10 (CST) 10:30-11:10 (JST)
    Francois Le Gall (Graduate School of Mathematics, Nagoya University)
    Dequantizing the Quantum Singular Value Transformation slide
    The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we investigate the hardness of classically simulating the QSVT. A recent result by Chia, Gilyén, Li, Lin, Tang and Wang (STOC 2020) showed that the QSVT can be efficiently "dequantized" for low-rank matrices, and discussed its implication to quantum machine learning. In this work, motivated by establishing the superiority of quantum algorithms for quantum chemistry and making progress on the quantum PCP conjecture, we focus on the other main class of matrices considered in applications of the QSVT, sparse matrices.
    We first show how to efficiently "dequantize", with arbitrarily small constant precision, the QSVT associated with a low-degree polynomial. We apply this technique to design classical algorithms that estimate, with constant precision, the singular values of a sparse matrix. We show in particular that a central computational problem considered by quantum algorithms for quantum chemistry (estimating the ground state energy of a local Hamiltonian when given, as an additional input, a state sufficiently close to the ground state) can be solved efficiently with constant precision on a classical computer. As a complementary result, we prove that with inverse-polynomial precision, the same problem becomes BQP-complete. This gives theoretical evidence for the superiority of quantum algorithms for chemistry, and strongly suggests that said superiority stems from the improved precision achievable in the quantum setting. We also discuss how this dequantization technique may help make progress on the central quantum PCP conjecture.
    This talk is based on arXiv:2111.09079.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Yongsheng Yao (Institute for Advanced Study in Mathematics, School of Mathematics, Harbin Institute of Technology)
    The Tight Exponent Analysis for Quantum Privacy Amplification slide
    The privacy amplification against quantum side information is a vital step in the Quantum Key Distribution which ensure that both parties of communication can share a pair of uniform secret key independent of the adversary. In this talk, I will introduce some recent progress on the reliability of the privacy amplification, i.e., the exponent of the asymptotic decreasing of the leaked information. Specifically, we derive an upper bound for the reliability which complement a earlier lower bound established by Hayashi, and the two bounds match when the rate of randomness extraction is above a critical value. Thus, we determined the exact security exponent for the case of high rate.
    This talk is based on arXiv 2111.01075.
  • 10:50-11:10 (CST) 11:50-12:10 (JST)
    Hayato Arai (Graduate School of Mathematics, Nagoya University)
    Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure slide
    An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose reasonable postulate about local systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure is valid. To examine this issue, we introduce pseudo standard entanglement structure as a structure of quantum composite system under natural assumptions based on the repeatability of measurement processing and the existence of approximations of all standard states. Surprisingly, there exist infinitely many pseudo standard entanglement structures different from the standard entanglement structure. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure.
    The talk is based on arXiv:2203.07968.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Masahito Hayashi (Shenzhen Institute for Quantum Science and Engineering, SUSTech / Graduate School of Mathematics, Nagoya University)
    Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory slide
    We formulate em algorithm in the framework of Bregman divergence, which is a general problem setting of information geometry. That is, we address the minimization problem of the Bregman divergence between an exponential subfamily and a mixture subfamily in a Bregman divergence system. Then, we show the convergence and its speed under several conditions.
    We apply this algorithm to rate distortion and its variants including the quantum setting, and show the usefulness of our general algorithm. In fact, existing applications of Arimoto-Blahut algorithm to rate distortion theory make the optimization of the weighted sum of the mutual information and the cost function by using the Lagrange multiplier. However, in the rate distortion theory, it is needed to minimize the mutual information under the constant constraint for the cost function. Our algorithm directly solves this minimization. In addition, we have numerically checked the convergence speed of our algorithm in the case of rate distortion problem.
    This paper was posted as arXiv:2201.02447.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Chun-Yu Bai (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Strong fusion 2-categories are grouplike slide
    It's a conjecture that first introduced by Tian Lan, Liang Kong, Xiao-Gang Wen. A fusion category is a finite semisimple monoidal category in which the unit object is indecomposable, equivalently has trivial endomorphism algebra. There are two natural categorifications of this notion: a fusion 2-category is a finite semisimple monoidal 2-category in which the unit object is indecomposable, and a strongly fusion 2-category is one in which the unit object has trivial endomorphism algebra. As I will explain in this talk, fusion 2-categories are extremely rich, with a seemingly-wild classification, whereas strongly-fusion 2-category are very simple: they are essentially just finite groups. Based on the work of Theo Johnson-Freyd and Matthew Yu.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Stavros Garoufalidis (SUSTech International Center for Mathematics)
    The Jones polynomial of a knot: the birth of quantum topology slide
    I will give a gentle survey of the Jones polynomial of a knot, which gave birth to quantum topology. I will discuss examples as well as unsolved questions connecting this knot polynomial to many areas of research in mathematics and physics.
  • 15:40-16:00 (CST) 16:40-17:00 (JST)
    Jiaheng Zhao (the Academy of Mathematics and System Sciences, Chinese Academy of Sciences)
    Generalized Eilenberg-Watts Calculus and 1d condensation theory slide
    In this talk I will develop a kind of Eilenberg-Watts calculus for module categories over finite tensor categories. To do this I will introduce the notion of module ends(coends). Then I will apply these mathematical notions to the condensation theory of 1-dimensional topological order. In particular, I will explain the geometric construction of the 1d condensation algebra.

Last update 2022/06/10.