**Links to Recent Papers by Participants that are Related to the Project, with names of project members in boldface. (Links to posters are at the bottom of this page, as well as links to articles that refer to the project.)**

[44] **Yunxiang Ren**, Universal skein theory for group actions, arXiv:1903.02012

[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, Comm. Math. Phys. 366 (2019), 865--894.

[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), 2497–2502.

[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 Project.These 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

**Links to Articles that Refer to the Project.**

[3] Peter Reuell, Picture Perfect Approach to Science, Harvard Gazette, January 24, 2018.

[2] Daniel S. Silver, The New Language of Mathematics, American Scientist, 105:6 (2017), 365.

[1] Peter Reuell, Making Math More Lego Like, Harvard Gazette, March 2, 2017.