**Links to Recent Papers by Participants that are Related to the Project (Links to posters are at the bottom of this page.)**

[43] **Arthur Jaffe and Zhengwei Liu**, Refelction Positivity for Levin-Wen models, arXiv:1901.10662

[42] **Zhengwei Liu**, **William Norledge**, and **Adrian Ocneanu**, The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations, arXiv:1901.03243

[41] Lu Li, **Kaifeng Bu**, and Zi-Wen Liu, Quantifying the resourse content of quantum channels: An operational approach, arXiv:1812.02572

[40] **Kaifeng Bu** and Dax Enshan Koh, Classical simulation of quantum circuits by half Gauss sums, arXiv:1812.00224

[39] **Fei Wei**, Arithmetic functions of natural numbers and its application,* *arXiv:1811.11000

[38] **Kaifeng Bu**, **Weichen Gu**, and **Arthur Jaffe**, Duality of graph invariants, arXiv:1810.08633

[37] **Fei Wei**, Disjointness of Möbius from asymptotically periodic functions, arXiv:1810.07360

[36] **Yunxiang Ren**, From skein theory to presentations for Thompson group, Journal of Algebra, 498(1) 2018, 178-196

[35] Ryuji Takagi, Bartosz Regula, **Kaifeng Bu**, Zi-Wen Liu, and Gerardo Adesso, Operational advantage of quantum resources in subchannel discrimination, arXiv:1809.01672. To appear in *Physical Review Letters.*

[34] Jordan Nikkel and **Yunxiang Ren**, On Jones Subgroup of R. Thompson's Group T, arXiv:1710.06972, *International Journal of Algebra and Computation,*** 28(5)** (2018), 877-903.

[33] **Kaifeng Bu**, **Arthur Jaffe**, **Zhengwei Liu** and **Jinsong Wu**, De Finetti Theorems for Braided Parafermions, arXiv:1805.05990

[32] **Zhengwei Liu** and **Jinsong Wu**, Antisymmetric Characters and Fourier Duality, arxiv:1805.04783

[31] **Zhengwei Liu** and **Jinsong Wu**, Extremal Pairs of Young’s Inequality for Kac Algebras, *Pacific Journal of Mathematics*, 295(1) (2018), 103-121.

[30] **Arthur Jaffe**, Reflection Positivity Then and Now, arXiv:1802.07880

[29] **William Norledge**, Singer cyclic lattices of type M, arXiv:1711.09332.

[28] **William Norledge**, Quotients of buildings by groups acting freely on chambers, arXiv: 1711.09330.

[27] **William Norledge**, Quotients of buildings as W-groupoids, arXiv:1710.06968.

[26] Keshab Chandra Bakshi, Sayan Das, **Zhengwei Liu**, and **Yunxiang Ren**, An angle between intermediate subfactors and its rigidity, arXiv:1710.00285, to appear in *Transactions of the AMS*.

[25] **Zhengwei Liu**, Scott Morrison, and David Penneys, Lifting shadings on symmetrically self-dual subfactor planar algebras, arXiv:1709.05023, to appear in *Contemporary Mathematics*.

[24] **Arthur Jaffe** and **Zhengwei Liu**, A Mathematical Picture Language Program, *Proceedings of the National Academy of Sciences* 115(1) (2018), 81–86.

[23] **Zhengwei Liu**, Quon Language: Surface Algebras and Fourier Duality, arXiv:1707.03995.

[22] **Chunlan Jiang**, **Zhengwei Liu,** and **Jinsong Wu**, Block maps and Fourier analysis, arXiv:1706.03551.

[21] **Zhengwei Liu** and Feng Xu, Jones-Wassermann subfactors for modular tensor categories, arXiv:1612:08573.

[20] Corey Jones, **Zhengwei Liu**, and **Yunxiang Ren**, Classification of Thurston-Relation Subfactor Planar Algebras, arXiv:1606.00779, to appear in *Quantum Topology*.

[19] **Arthur Jaffe**, **Zhengwei Liu**, and **Alex Wozniakowski**, Holographic Software for Quantum Networks, *Science China Mathematics* 61(4) (2018), 593-626.

[18] **Arthur Jaffe**, **Zhengwei Liu**, and **Alex Wozniakowski**, Qudit Isotopy, arXiv:1602.02671

[17] **Zhengwei Liu**, Yang-Baxter Relation Planar Algebras, arXiv:1507.06030

[16] **Chunlan Jiang**, **Zhengwei Liu**, and **Jinsong Wu**, Uncertainty principles for locally compact quantum groups, *Journal of Functional Analysis*,* ***270(1) **(2016), 264–311.

[15] **Zhengwei Liu** and David Penneys, The generator conjecture for 3* ^{G }*subfactor planar algebras.

*Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F.R. Jones' 60th Birthday.*344-366

[14] **Zhengwei Liu**, Simeng Wang, and **Jinsong Wu**, Young’s inequality for locally compact quantum groups. *Journal of Operator Theory,** ***77(1)**** **(2017), 109–131.

[13] **Zhengwei Liu** and **Jinsong Wu**, Uncertainty principle for Kac algebras, *Journal of Math**ematical Physics** ***58(5)**** **(2017), 052102.

[12] Dietmar Bisch, **Vaughan F. R. Jones**, and **Zhengwei Liu**, Singly generated planar algebras of small dimension, part III. arXiv:1410.2876, *Transactions of the AMS,** ***369(4) **(2017), 2461–2476.

[11] **Zhengwei Liu** and **Jinsong Wu**, The Noncommutative Fourier Transform: A survey, *Acta Mathematica Sinica Chinese Series,** *(In honor of the 75th birthday of Bingren Li) **60(1)**** **(2017), 69–80.

[10] **Zhengwei Liu**, and **Alex Wozniakowski,** and **Arthur Jaffe**, Quon 3D language for quantum informatio*n. **Proceedings of the National Academy of Sciences,** ***114(10) **(2017), 2947–2502.

[9] **Arthur Jaffe,** **Zhengwei Liu**, and **Alex Wozniakowski**, Constructive Simulation and Topological Design of Protocols, *New Journal of Physics*, **19**** **(2017), 063016.

[8] **Arthur Jaffe** and **Bas Janssens**, Reflection Positive Doubles, *Jour. Funct. Anal.*, **272 **(2017), 3506–3557.

[7] **Arthur Jaffe **and **Zhengwei Liu**, Planar Para Algebras, Reflection Positivity, *Commun. **Math. Phys.** ***352**** **(2017), 95–133.

[6] **Chunlan Jiang**, **Zhengwei Liu**, and **Jinsong Wu**, Noncommutative uncertainty principles, *Journal of Functional Analysis*, **270(1)**** **(2016), 264-311.

[5] **Arthur Jaffe** and **Bas Janssens**, Characterization of Reflection Positivity: Majoranas and Spins, *Commun. Math. Phys.*, **346(3)**** **(2016), 1021–1050.

[4] **Arthur Jaffe** and Fabio L. Pedrocchi, Reflection Positivity for Parafermions, *Comm. **Math. Phys.*, **337**** **(2015), 455–472.

[3] **Arthur Jaffe**, Stochastic Quantization, Reflection Positivity, and Quantum Fields, *J. Stat. **Physics*, **161**, (2015) 1–15.

[2] **Arthur Jaffe**, **Christian Jäkel**, and Roberto Martinez, Complex Classical Fields: an Example, *Journal of Functional Analysis** ***266**** **(2014), 1833–1881.

[1] **Arthur Jaffe** and Fabio L. Pedrocchi, Topological Order and Reflection Positivity, *Euro **Physics Letters** ***105**** **(2014), 40002.

**Links to Posters by Participants that are Related to the ProjectThese may be large files, which take some time to load.**

[4] **QIP 2019 January12, 2019 (Boulder, CO). Poster by Kaifeng Bu**

[3] **Harvard Physics Research Scholar Retreat September 12, 2018. Poster by Kaifeng Bu (Awarded first prize)**

[1] Harvard Physics Research Scholar Retreat September 28, 2017. Poster by William Norledge