方复全科研成就科研领域方复全在微分与拓扑范畴解决了“四维流形到七维欧氏空间中的嵌入问题”，将Haefliger-Hirsch、吴文俊等人的工作中遗留下来多年悬而未决的重要公开问题画上句号

与人合作，证明了正曲率流形的π2有限性定理（同时独立得到的还有Petrunin-Tuschmann），被美国科学院院士Cheeger主编的权威综述报告列为有关领域有史以来九个主要定理之一，并被几何学家Berger写入历史性综述报告《二十世纪下半叶的黎曼几何》

与人合作，首次发现了Grove问题的反例，被中国国外专家作为牛津大学研究生教材丛书的重要内容，并以 “方-戎方法”冠名小节标题

与人合作，首次建立了Tits几何与一大类正曲率流形之间的联系，并得到了完整的拓扑分类

 承担项目开始时间截止时间项目名称资金来源1999年1月国家杰出青年科学基金国家自然科学基金委员会2010年1月2013年12月国家自然科学基金重点项目国家自然科学基金委员会2012年1月2014年12月教育部和创新团队发展计划-“几何分析”创新团队项目教育部北京市教委2015年1月2018年12月国家自然科学基金重点项目：低维流形的几何与拓扑国家自然科学基金委员会参考资料来源： 科研成果奖励2003年，方复全独立获得天津市自然科学奖一等奖

2004年，方复全获得天津市自然科学奖一等奖

 2014年，方复全独立获得国家自然科学奖二等奖

 论文著作据2020年3月首都师范大学官网显示，方复全在“Acta Math.", Invent. Math.”， “Journal of Differential Geometry”， “Topology”等数学杂志上发表五十余篇科研论文

 主要论著论文题目（书名）期刊（出版社）Tits geometry and positive curvatureActa MathematicaVolume 218, No. 1 (2017)The Second twisted Betti numbers and the convergence of collapsing Riemannian manifoldsInvent. Math. 150 (2002), no. 1, 61–109Non-negatively curved manifolds and Tits geometry第27届国际数学家大会45分钟报告（2014）Positive pinching, volume and second Betti numberGeom. Funct. Anal. 9 (1999), no. 4, 641–674.Curvature, diameter, homotopy groups, and cohomology ringsDuke Math. J. 107 (2001), no. 1, 135–158.Reflection groups in non-negative curvatureJ. Differential Geom. 102 (2016), no. 2, 179–205.An almost flat manifold with a cyclic or quaternionic holonomy group boundsJ. Differential Geom. 103 (2016), no. 2, 289–296.Embedding four manifolds in RTopology 33 (1994), no. 3, 447–454Topology of complete intersectionsComment. Math. Helv. 72 (1997), no. 3, 466–480.Smooth group actions on 4 -manifolds and Seiberg-Witten invariantsInternat. J. Math. 9 (1998), no. 8, 957–973.Non-singular solutions to the normalized Ricci flow equationMath. Ann. 340 (2008), no. 3, 647–674.Rank three geometry and positive curvatureComm. Anal. Geom. 24 (2016), no. 3, 487–520.The symmetric commutator homology of link towers and homotopy groups of 3-manifoldsCommun. Math. Stat. 3 (2015), no. 4, 497–526.Long term solutions of normalized Ricci flowDifferential geometry, 21–48, Adv. Lect. Math. (ALM), 22, Int. Press, Somerville, MA, 2012.Knots in Riemannian manifolds.Math. Z. 267 (2011), no. 1-2, 425–431Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7Math. Z. 266 (2010), no. 3, 719–746.Complete intersections with metrics of positive scalar curvatureC. R. Math. Acad. Sci. Paris 347 (2009), no. 13-14, 797–800.Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvatureAnn. Inst. Fourier (Grenoble) 59 (2009), no. 2, 563–573.Collapsed 5-manifolds with pinched positive sectional curvatureAdv. Math. 221 (2009), no. 3, 830–860.Maximum solutions of normalized Ricci flow on 4-manifoldsComm. Math. Phys. 283 (2008), no. 1, 1–24.Positive quaternionic K?hler manifolds and symmetry rank IIMath. Res. Lett. 15 (2008), no. 4, 641–651.Complete gradient shrinking Ricci solitons have finite topological typeC. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 653–656.Finite isometry groups of 4-manifolds with positive sectional curvatureMath. Z. 259 (2008), no. 3, 643–656.G 2 -manifolds and coassociative torus fibrationFront. Math. China 3 (2008), no. 1, 49–77.Perelman's λ -functional and Seiberg-Witten equationsFront. Math. China 2 (2007), no. 2, 191–210.K?hler manifolds with numerically effective Ricci class and maximal first Betti number are toriC. R. Math. Acad. Sci. Paris 342 (2006), no. 6, 411–416.A connectedness principle in the geometry of positive curvatureComm. Anal. Geom. 13 (2005), no. 4, 671–695.Complex immersions in K?hler manifolds of positive holomorphic k -Ricci curvatureTrans. Amer. Math. Soc. 357 (2005), no. 9, 3725–3738.Homeomorphism classification of positively curved manifolds with almost maximal symmetry rankMath. Ann. 332 (2005), no. 1, 81–101.Positive quaternionic K?hler manifolds and symmetry rankJ. Reine Angew. Math. 576 (2004), 149–165.Positively curved manifolds with maximal discrete symmetry rankAmer. J. Math. 126 (2004), no. 2, 227–245.Secondary Brown-Kervaire quadratic forms and π -manifoldsForum Math. 16 (2004), no. 4, 459–481.Index of Dirac operator and scalar curvature almost non-negative manifoldsAsian J. Math. 7 (2003), no. 1, 31–38.Kahler manifolds with almost non-negative bisectional curvature.Asian J. Math. 6 (2002), no. 3, 385–398.Positively curved 6-manifolds with simple symmetry groupsAn. Acad. Brasil. Ciênc. 74 (2002), no. 4, 589–597.Fixed points of discrete nilpotent group actions on SAnn. Inst. Fourier (Grenoble) 52 (2002), no. 4, 1075–1091.Orientable 4-manifolds topologically embed into RTopology 41 (2002), no. 5, 927–930.Smooth group actions on 4-manifolds and Seiberg-Witten theoryDifferential Geom. Appl. 14 (2001), no. 1, 1–14.Equifocal hypersurfaces in symmetric spacesChinese Ann. Math. Ser. B 21 (2000), no. 4, 473–478.Fixed point free circle actions and finiteness theoremsCommun. Contemp. Math. 2 (2000), no. 1, 75–86.Smooth structures on Σ×RTopology Appl. 99 (1999), no. 1, 123–131.Topology of Dupin hypersurfaces with six distinct principal curvaturesMath. Z. 231 (1999), no. 3, 533–555.On the topology of isoparametric hypersurfaces with four distinct principal curvaturesProc. Amer. Math. Soc. 127 (1999), no. 1, 259–264.Embedding 3 -manifolds and smooth structures of 4 -manifoldsTopology Appl. 76 (1997), no. 3, 249–259.Topological classification of complete intersectionsC. R. Acad. Sci. Paris Sér. I Math. 323 (1996), no. 7, 799–803.Embeddings of nonorientable 4 -manifolds in RTopology 35 (1996), no. 4, 835–844.Topological classification of 4 -dimensional complete intersectionsManuscripta Math. 90 (1996), no. 2, 139–147.Diffeomorphism type of certain 3 -connected closed smooth 12 -manifoldsNortheast. Math. J. 10 (1994), no. 3, 351–358.参考资料来源： 学术交流2014年，方复全获邀在第二十七届国际数学家大会做45分钟特邀报告

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