个人简介：

冯惠涛，南开大学陈省身数学所教授、博士生导师、副所长，重庆理工大学兼职讲座教授。1963年6月出生于内蒙古五原县。1983年大学本科毕业于内蒙古大学数学系，1990年在南开大学数学系获理学硕士学位，研究方向为李群与微分几何，1997年在中科院数学所获理学博士学位，研究方向为微分几何。

冯惠涛教授主要从事流形上的几何与拓扑的研究，特别是Atiyah-Singer指标理论及其应用的研究，近年来主要关注和研究Atiyah-Singer指标理论在Finsler几何中的应用,已取得了一系列重要的研究成果。

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承担的主要项目：

[1] Atiyah-Singer指标理论及其应用，国家自然科学基金重点项目，2020.01-2024.12，260万，主持。

[2]微分几何，国家自然科学基金创新群体项目，2007.01-2015.12，（三期共9年），个人名下近100万，研究骨干；

[3] Finsler度量的曲率性质与ample全纯向量丛，国家自然科学基金面上项目，2016.01-2019.12，53.6万，主持；

[4]非交换指标定理和非交换留数的研究，国家自然科学基金面上项目，2018.01-2021.12，个人名下7万，第一参加人；

[5]指标定理,椭圆亏格,非交换留数和热核，国家自然科学基金面上项目，2013.01-2016.12，个人名下8万，第一参加人，；

[6]流形上的整体不变量，国家自然科学面上项目，2003.01-2005.12，10万，主持。

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代表性成果：

专著:

张伟平, 冯惠涛. 流形上的几何与分析, 北京: 高等教育出版社, 2022.1. (ISBN 978-7-04-056366-5)

论文:

[1] 冯惠涛，具有双不变拟Riemann度量的Lie群, 内蒙古大学学报（自然科学版），Vol.23, No.2(1992), 144-147.

[2] 包俊东，冯惠涛，一类二阶非线性中立型泛函微分方程的振动性，内蒙古大学学报（自然科学版），Vol.24,  No.2(1993), 126-130.

[3] Huitao Feng and Enli Guo, A super-twisted Dirac operator and Novikov inequalities, Science in China(Series A), Vol. 43, No. 5,(2000), 470-480.

[4] Huitao Feng and Enli Guo, Novikov-type inequalities for vector fields with non-degenerate zero points, Pacific Journal of Mathematics, Vol. 201, No.1(2001), 107-120.

[5] Huitao Feng, Wenchuan Hu, Weiping Zhang,  A family quantization formula for symplectic manifolds with boundary, Science in China (Series A), Vol. 44, No. 5(2001), 599-609.

[6] Huitao Feng and Enli Guo , A Hopf index theorem for a real vector bundle, Chin. Ann. of Math., 23B:4(2002), 507-518.

[7] Huitao Feng, 关于非交换陈特征的一个注记， 数学学报（中文版）46卷1期（2003), 57-64.

[8] Huitao Feng, Holomorphic equivariant cohomology via a transversal holomorphic vector field, International Journal of Math. V.14, No.5 (2003) ,499-514.

[9] Huitao Feng and Xiannan Ma, Transversal holomorphic section and localization of analytic torsion，Pacific J.Math. 219(2) (2005), 255-270.

[10] Huitao Feng and Binxia Zhang, The existence of Riemannian metrics with positive scalar curvature over complex complete intersections, 数学进展, Vol.36, No.1(2007), 47-50.

[11] Huitao Feng, G_{5,2}的同调群，重庆工学院学报，Vol. 21(2007), 1-6.

[12] Huitao Feng, Guangbo Xu, Weiping Zhang, Real embeddings, eta-invariants and Chern-Simons currents, Pure and Applied Mathematics Quarterly, Vol.5, No.3(2009), Special Issue: In honor of Friedrich Hirzebruch, Part 2 of 2, 1113-1137.

[13] Huitao Feng, Weiping Li, Weiping Zhang, A Poincaré-Hopf type formula for Chern character numbers, Math. Z.269.,401-410(2011).

[14] 陈旭，冯惠涛，联系于实向量丛一对截面的Poincare-Hopf型公式，西南大学学报（自然科学版），Vol.34, No. 4, (2012), 113-117

[15] Huitao Feng, Ming Li, Adiabatic limit and connections in Finsler geometry,  Commun. Anal. Geom, Vol. 21, No. 3 (2013), 607-624.

[16] Huitao Feng, Kefeng Liu, Xueyuan Wan, Chern forms of holomorphic Finsler vector bundles and some applications, International Journal of Math. Vol.27, No.4 (2016) 1650030(22 pages).

[17] Huitao Feng, Kefeng Liu, Xueyuan Wan, A Donaldson type functional on a holomorphic Finsler vector bundle, Math. Ann., 369, no. 3-4 (2017), 997–1019.

[18] Huitao Feng, Kefeng Liu, Xueyuan Wan, Compact K\"{a}hler manifolds with positive orthogonal bisectional curvature, Math. Res. Lett. , 24, no. 3 (2017), 767–780.

[19] Huitao Feng, Kefeng Liu, Xueyuan Wan, Geodesic-Einstein metrics and nonlinear stabilities,  Trans. AMS., 371, no. 11(2019), 8029–8049.

[20] Huitao Feng, Kefeng Liu, Xueyuan Wan, Complex Finsler vector bundles with positive Kobayashi curvature, Math. Res. Lett. , 27, no. 5 (2020), 1325–1339.

[21] Huitao Feng, Weiping Zhang, Flat vector bundles and open coverings, Differential Equations on Manifolds and Mathematical Physics, Dedicated to the Memory of Boris Sternin, Trends in Mathematics, Birkhäuser, 2021, pp. 142-155.

[22] Huitao Feng, Ming Li, A note on generalizations of the Gauss-Bonnet-Chern formula in Finsler geometry, Proceedings of the 22nd International Workshop on Differential Geometry of Submanifolds in Symmetric Spaces & the 17th RIRCM-OCAMI Joint Differential Geometry Workshop, 85-95, 2019.

[23] Huitao Feng, Yuhua Han, Ming Li, An equivalence theorem of a class of Minkowski norms and its applications. Sci. China Math.(Series A), Vol. 64, No. 7(2021), 1429-1446.

[24] Huitao Feng, Ming Li, Superconnections and An Intrinsic Gauss-Bonnet-Chern Formula for Finsler Manifolds, arXiv:1607.06611v3. 2021.

[25] Xiang Liu, Huitao Feng, Jie Wu and Kelin Xia, Persistent spectral hypergraph based machine learning (PSH-ML) for protein-ligand binding affinity prediction, Briefings in Bioinformatics, 00(00), 2021, 1–12.