%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Nicholas Beaton at 2019-05-27 12:20:31 +1000 %% Saved with string encoding Unicode (UTF-8) @misc{C, Author = {Chepuri,S.}, Eprint = {1804.02059}, Eprinttype = {arxiv}, Title = {Plabic R-matrices}, Year = {2018}} @misc{P, Author = {Postnikov,A.}, Eprint = {math/0609764}, Eprinttype = {arxiv}, Title = {Total positivity, Grassmannians, and networks}, Year = {2006}} @inbook{N, Address = {Zurich}, Author = {Nakanishi,T.}, Chapter = {Periodicities in cluster algebras and dilogarithm identities}, Date-Added = {2018-11-14 11:02:25 -0600}, Date-Modified = {2018-11-14 11:07:01 -0600}, Editor = {Skowronski,A. and Yamagata,K.}, Pages = {407-- 443}, Publisher = {Eur. Math. Soc.}, Series = {EMS Ser. Congr. Rep.}, Title = {Representations of algebras and related topics}, Year = {2011}} @article{LP1, Author = {Lam,T. and Pylyavskyy,P.}, Date-Added = {2018-11-14 11:01:30 -0600}, Date-Modified = {2018-11-14 11:02:19 -0600}, Journal = {Selecta Math.}, Number = {173-235}, Title = {Crystals and total positivity on orientable surfaces}, Volume = {19}, Year = {2013}} @article{LP2, Author = {Lam,T. and Pylyavskyy,P.}, Date-Added = {2018-11-14 11:00:46 -0600}, Date-Modified = {2019-05-27 12:20:31 +1000}, Doi = {10.1016/j.aim.2012.03.012}, Journal = {Adv. Math.}, Number = {3}, Pages = {1222-1271}, Title = {Total positivity in loop groups, I: Whirls and curls}, Volume = {230}, Year = {2012}} @article{KW2, Author = {Kodama,Y. and Williams,L.}, Date-Added = {2018-11-14 10:59:53 -0600}, Date-Modified = {2019-05-27 12:20:01 +1000}, Doi = {10.1007/s00222-014-0506-3}, Journal = {Invent. Math.}, Number = {3}, Pages = {637-699}, Title = {KP solitons and total positivity for the Grassmannian}, Volume = {198}, Year = {2014}} @article{KW1, Author = {Kodama,Y. and Williams,L.}, Date-Added = {2018-11-14 10:59:00 -0600}, Date-Modified = {2019-05-27 12:19:29 +1000}, Doi = {10.1073/pnas.1102627108}, Journal = {Proc. Nat. Acad. Sci. USA}, Number = {22}, Pages = {8984-8989}, Title = {KP solitons, total positivity, and cluster algebras}, Volume = {108}, Year = {2011}} @article{KNY, Author = {Kajiwara,K. and Noumi,M. and Yamada,Y.}, Date-Added = {2018-11-14 10:57:58 -0600}, Date-Modified = {2018-11-14 10:58:57 -0600}, Journal = {Lett. Math. Phys.}, Number = {3}, Pages = {211-219}, Title = {Discrete Dynamical Systems with $W(A_{m-1}^{(1)}\times A_{n-1}^{(1)})$ Symmetry}, Volume = {60}, Year = {2002}} @article{KNO, Author = {Kashiwara,M. and Nakashima,T. and Okado,M.}, Date-Added = {2018-11-14 10:56:54 -0600}, Date-Modified = {2019-05-27 12:18:46 +1000}, Doi = {10.1090/s1088-4165-2010-00379-9}, Journal = {Represent. Theory}, Pages = {446-509}, Title = {Tropical $R$ maps and affine geometric crystals}, Volume = {14}, Year = {2010}} @misc{ILP, Author = {Inoue,R. and Lam,T. and Pylyavskyy,P.}, Eprint = {1607.00722}, Eprinttype = {arxiv}, Title = {On the cluster nature and quantization of geometric $R$-matrices}, Year = {2017}} @article{GS, Author = {Goncharov,A. and Shen,L.}, Date-Added = {2018-11-14 10:55:34 -0600}, Date-Modified = {2019-05-27 12:18:07 +1000}, Doi = {10.1016/j.aim.2017.06.017}, Journal = {Adv. Math.}, Pages = {225--348}, Title = {Donaldson-Thomas transformations of moduli spaces of G-local systems}, Volume = {327}, Year = {2017}} @article{GSV1, Author = {Gekhtman,M. and Shapiro,M. and Vainshtein,A.}, Date-Added = {2018-11-14 10:54:42 -0600}, Date-Modified = {2019-05-27 12:17:24 +1000}, Doi = {10.4171/jems/311}, Journal = {J. Europ. Math. Soc.}, Number = {2}, Pages = {541-570}, Title = {Poisson geometry of directed networks in an annulus}, Volume = {14}, Year = {2012}} @article{GSV2, Author = {Gekhtman,M. and Shapiro,M. and Vainshtein,A.}, Date-Added = {2018-11-14 10:53:45 -0600}, Date-Modified = {2019-05-27 12:16:50 +1000}, Doi = {10.1007/s11511-011-0063-1}, Journal = {Acta Math.}, Number = {2}, Pages = {245-310}, Title = {Generalized B{\"a}cklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective}, Volume = {206}, Year = {2011}} @book{GSVbook, Author = {Gekhtman,M. and Shapiro,M. and Vainshtein,A.}, Date-Added = {2018-11-14 10:52:28 -0600}, Date-Modified = {2019-05-27 12:16:19 +1000}, Publisher = {Amer. Math. Soc., Providence, PI}, Title = {Cluster Algebras and Poisson Geometry}, Year = {2010}} @article{FZ, Author = {Fomin,S. and Zelevinsky,A.}, Date-Added = {2018-11-14 10:50:58 -0600}, Date-Modified = {2019-05-27 12:15:42 +1000}, Doi = {10.1007/bf03024444}, Journal = {Math. Intelligencer}, Number = {1}, Pages = {23-33}, Title = {Total positivity: tests and parametrizations}, Volume = {22}, Year = {2000}} @article{FZ2, Author = {Fomin,S. and Zelevinsky,A.}, Date-Modified = {2019-05-27 12:16:08 +1000}, Doi = {10.1112/s0010437x06002521}, Journal = {Compos. Math.}, Number = {1}, Pages = {112-164}, Title = {Cluster algebras IV: coefficients}, Volume = {143}, Year = {2007}} @article{E, Author = {Etingof,P.}, Date-Added = {2018-11-14 10:50:02 -0600}, Date-Modified = {2018-11-14 10:50:53 -0600}, Journal = {Comm. Algebra}, Number = {4}, Pages = {1961-1973}, Title = {Geometric crystals and set-theoretical solutions to the quantum Yang-Baxter equation}, Volume = {31}, Year = {2003}} @article{CM, Author = {Curtis,E.B. and Ingerman,D. and Morrow,J.A.}, Date-Added = {2018-11-14 10:48:57 -0600}, Date-Modified = {2019-05-27 12:15:09 +1000}, Doi = {10.1016/s0024-3795(98)10087-3}, Journal = {Linear Algebra Appl.}, Number = {1-3}, Pages = {115-150}, Title = {Circular planar graphs and resistor networks}, Volume = {283}, Year = {1998}} @incollection{BK, Author = {Berenstein,A. and Kazhdan,D.}, Booktitle = {Visions in Mathematics}, Date-Added = {2018-11-14 10:35:51 -0600}, Date-Modified = {2019-05-27 12:14:04 +1000}, Editor = {Alon,N. and Bourgain,J. and Connes,A. and Gromov,M. and Milman,V.}, Pages = {188-236}, Publisher = {Birkh{\"a}user Basel}, Series = {Modern Birkh{\"a}user Classics}, Title = {Geometric and unipotent crystals}, Year = {2010}} @article{ALT, Author = {Alman, J. and Lian, C. and Tran, B.}, Date-Added = {2018-11-14 10:34:31 -0600}, Date-Modified = {2019-05-27 12:11:35 +1000}, Doi = {10.1016/j.jcta.2014.11.004}, Journal = {J. Combin. Theory Ser. A}, Pages = {58-101}, Title = {Circular planar electrical networks: Posets and positivity}, Volume = {132}, Year = {2015}} @book{ABCTPbook, Author = {Arkani-Hamed,N. and Bourjaily,J. and Cachazo,F. and Postnikov,A. and Trnka,J.}, Date-Added = {2018-11-14 10:32:32 -0600}, Date-Modified = {2019-05-27 12:13:05 +1000}, Publisher = {Cambridge University Press, Cambridge, UK}, Title = {Grassmannian Geometry of Scattering Amplitudes}, Year = {2016}} @article{ABCPT, Author = {Arkani-Hamed,N. and Bourjaily,J. and Cachazo,F. and Postnikov,A. and Trnka,J.}, Date-Added = {2018-11-14 10:21:36 -0600}, Date-Modified = {2019-05-27 12:12:35 +1000}, Doi = {10.1007/jhep06(2015)179 }, Journal = {J. of High Energy Phys.}, Pages = {179}, Title = {On-shell structures of MHV amplitudes beyond the planar limit}, Year = {2015}} @misc{ABCGPT, Author = {Arkani-Hamed,N. and Bourjaily,J. and Cachazo,F. and Goncharov,A. and Postnikov,A. and Trnka,J.}, Eprint = {1212.5605}, Eprinttype = {arXiv}, Title = {Scattering Amplitudes and the Positive Grassmannian}, Year = {2014}}