杨东 - 南京大学

个人简介

主要课程线性代数、箭图表示、三角范畴与微分分次范畴 Professor Department of Mathematics, Nanjing University Hankou Road 22, Gulou district, Nanjing 210093, P.R.China Teaching 2018 Autumn: Probability and Statistics 2018 Spring: Linear Algebra, Quiver representations 2017 Autumn: Linear Algebra 2017 Spring: Triangulated categories and differential graded categories 2016 Autumn: Linear Algebra 2016 Spring: Quiver representations 2015 Autumn: Linear Algebra 2015 Spring: Triangulated categories and differential graded categories 2014 Autumn: Linear Algebra 2014 Spring: Linear Algebra Relative singularity categories II: DG models, joint with Martin Kalck, arXiv:1803.08192. Discreteness of silting objects and t-structures in triangulated categories, joint with Takahide Adachi and Yuya Mizuno, to appear in Proc. Lond. Math. Soc., arXiv:1708.08168. Examples of finite dimensional algebras which do not satisfy the derived Jordan—Hoelder property, joint with Qunhua Liu, arXiv:1704.00398. Quotients of triangulated categories and equivalences of Buchweitz, Orlov and Amiot—Guo—Keller, joint with Osamu Iyama, to appear in American Journal of Mathematics, arXiv:1702.04475. From simple-minded collections to silting objects via Koszul duality, joint with Hao Su, Algebra and Representation Theory, published online, doi:10.1007/s10468-018-9763-y, arXiv:1609.03767. Notes on seminar/conference talks Koszul algebras, slides (dvi-file), talk given in Leicester, May 2004. From triangulated categories to cluster algebras (after Palu), pdf-file, talk given in Bielefeld, July 2009. Recollements and singularity categories, pdf-file, talk given in Beijing, May 2011. Algebraic stratifications of derived module categories and derived simple algebras, pdf-file, talk given in Okayama, September 2011. Recollements generated by idempotents and application to singularity categories, pdf-file, talk given in Okayama, September 2011. Silting objects, t-structures, cluster-tilting objects and their mutations, arXiv:1302.6045, talk given in Bielefeld, August 2012 (ICRA XV). Hearts of t-structures: some examples, slides (pdf-file), talks given in Shanghai, July 2014, and in Hefei, October 2015. Algebraic stratifications and derived simplicity, slides (pdf-file), talk given in Sanya, August 2014 (ICRA XVI). A derived Jordan--Hoelder property, slides (pdf-file), talk given in Yangzhou, May 2016. The interplay between 2- and 3-CY categories, arXiv:1811.07553, talks given in Stuttgart, November 2011, and in Nagoya, May 2013. Silting t-structures, slides (pdf-file), talks given in Shanghai, October 2018.

研究领域

Derived categories of algebras: tilting theory, recollements, silting objects, t-structures Singularity categories, relative singularity categories Cluster categories and related, for example, Ginzburg dg algebras, mutation of quivers with potential. Hall algebras of abelian and triangulated categories Affine Schur algebras

近期论文

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2-Calabi-Yau范畴和3-Calabi-Yau范畴，中国科学: 数学 48, 1 (2018 )，doi/10.1360/N012018-00001. English version: arXiv:1811.07553 Silting reduction and Calabi--Yau reduction of triangulated categories, joint with Osamu Iyama, Trans. Amer. Math. Soc. 370 (2018), no. 11, 7861--7898. arXiv:1408.2678. Derived categories of graded gentle one-cycle algebras, joint with Martin Kalck, J Pure Appl Algebra 222 (2018), 3005-3035. arXiv:1611.01903. The derived category of an algebra with radical square zero, Comm. Alg. 46 (2018), no. 2, 727--739. arXiv:1612.05750. Recollements and stratifying ideals, joint with Lidia Angeleri Hügel, Steffen Koenig and Qunhua Liu, J. Alg. 484 (2017), 47—65. arXiv:1606.05992. Ladders of derived module categories, joint with Lidia Angeleri Hügel, Steffen Koenig and Qunhua Liu, J. Alg. 472 (2017), 15--66. arXiv:1310.3479. Stratifications of algebras with two simples, joint with Qunhua Liu, Forum Math. 28 (2016), no. 1, 175--188. arXiv:1310.3480. Relative singularity categories I: Auslander resolutions, joint with Martin Kalck, Adv. Math. 301 (2016), 973--1021. arXiv:1205.1008. Homotopy categories, Leavitt path algebras and Gorenstein projective modules, joint with Xiao-Wu Chen, Int. Math. Res. Not. IMRN 2015, no. 10, 2597--2633. arXiv:1301.0195. Intermediate co-t-structures, two-term silting objects, tau-tilting modules and torsion classes, joint with Peter Jørgensen and Osamu Iyama, Algebra and Number Theory 8 (2014), no. 10, 2413--2431. arXiv:1311.4891. Frobenius categories, Gorenstein algebras and rational surface singularities, joint with Osamu Iyama, Martin Kalck and Michael Wemyss, Compos. Math. 151 (2015), no. 3, 502--534. arXiv:1209.4215. Gluing silting objects, joint with Qunhua Liu and Jorge Vitória, Nagoya Math. J. 216 (2014), 117--151. arXiv:1206.4882. Silting objects, simple-minded collections, t-structures and co-t-structures for finite-dimensional algebras, joint with Steffen Koenig, Doc. Math. 19 (2014), 403--438. arXiv:1203.5657 (this incorporates arXiv:1011.3938). Ordered exchange graphs, joint with Thomas Brüstle, Advances in Representation Theory of Algebras, 135--193, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2013. arXiv:1302.6045. Sparseness of t-structures and negative Calabi--Yau dimension in triangulated categories generated by a spherical object, joint with Thorsten Holm and Peter Jørgensen, Bull. Lond. Math. Soc. 45 (2013), 120--130. arXiv:1108.2195 Blocks of group algebras are derived simple, joint with Qunhua Liu, Math. Z. 272 (2012), 913--920. arXiv:1104.0500 . Endomorphism algebras of maximal rigid objects in cluster tubes, Comm. Alg. 40 (2012), no. 12, 4347--4371. arXiv:1004.1303 The Ringel--Hall Lie algebra of a spherical object, joint with Changjian Fu, J. Lond. Math. Soc. (2) 85 (2012), 511--533. arXiv:1103.1241, correction. Stratifications of derived module categories, joint with Lidia Angeleri Hügel, Steffen Koenig and Qunhua Liu, C. R. Acad. Sci. Paris, Ser I 349 (2011), 1139--1144. Recollements from generalized tilting, Proc. Amer. Math. Soc. 140 (2012), 83--91. arXiv:1006.1227 Derived equivalences from mutation of quiver potentials, joint work with Bernhard Keller, Adv. Math. 226 (2011), 2118--2168. arXiv:0906.0761 The Hall algebra of a spherical object, joint work with Bernhard Keller and Guodong Zhou, J. Lond. Math. Soc. (2) 80 (2009), no. 3, 771--784. arXiv:0810.5546 Non-simply-laced clusters of finite type via Frobenius morphisms, Algebra Colloquium 16 (2009), no.1, 143--154. arXiv:math/0608114 On the affine Schur algebra of type $A$ II, Algebras and Representation Theory 12 (2009), no. 1, 63--75. arXiv:math/0609660 On the affine Schur algebra of type $A$, Comm. Alg. 37 (2009), no. 4, 1389--1419. arXiv:math/0609659 On defining ideals or subrings of Hall algebras (with an appendix by Andrew Hubery), Algebras and Representation Theory 10 (2007), no.6, 619--629. arXiv:math/0608677. Unramified extensions of quadratic fields, joint work with Wei Li, and Xianke Zhang, Prog. Nat. Sci. 18 (2008), no. 3, 323--324. Quadratic number fields with class numbers divisible by a prime q, joint work with Xianke Zhang, Tsinghua Science and Technology 9 (2004), no.4, 476-481.

学术兼职

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