2018年8月20日至2019年8月21日，我以访问学者身份在美国TEXAS TECH UNIVERSITY学习一年，本次访学由国家留学基金委员会资助。

本次访学期间的合作导师是LARS WINTHER CHRISTENSEN教授，LARS WINTHER CHRISTENSEN教授的研究方向是Applications of homological and homotopical algebra to ring theory。在访学的一年内，除了节假日，LARS WINTHER CHRISTENSEN教授每周与我讨论2-3次，每次2-3小时，主要研究相对同调代数中的前沿课题。具体来讲：

1. New characterizations of restricted injective dimensions for complexes.

We study the restricted injective dimensions of complexes. Some new characterizations of the restricted injective dimensions are obtained. In particular, it is shown that the restricted injective dimensions can be computed in terms of the restricted injective resolutions. As applications, we get some results on the behavior of the restricted injective dimensions under change of rings. In addition, a characterization of almost Cohen-Macaulay ring is obtained.

2. A Bass equality for Gorenstein injective dimension of modules finite over  homomorphisms

    The homological theory of modules over commutative noetherian rings comes out particularly elegant for finitely generated modules. One way to relax this finiteness condition---without sacrificing elegance---is to settle for finite generation over some noetherian, but otherwise arbitrary, extension ring. This theme has been systematically explored for at least fifteen years. As part of that effort, this short paper answers an open question in Gorenstein homological algebra.

3. A homological invariant based on Gorenstein flat cotorsion modules.

We study the Gorenstein flat cotorsion dimension for complexes over an associative ring, and we prove that it behaves as expected without any assumptions on the ring. Further, we prove that it is finite for every complex of finite Gorenstein flat dimension and that it is the same as the Gorenstein flat dimension for right coherent rings—the setting where Gorenstein flat dimension is known to behave as expected.    

4. 论文列表：

[1] Lars Winther Christensen, Dejun Wu, A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms, Arch. Math. https://doi.org/10.1007/s00013-019-01346-1, (2019). (SCI)

[2] Dejun Wu, New characterizations of restricted injective dimensions for complexes, Indian J. Pure and Appl. Math, to appear. (SCI)

[3] Lars Winther Christensen, Sergio Estrada, Li Liang, Peder Thompson, Dejun Wu, Gang Yang,  A homological invariant based on Gorenstein flat cotorsion modules. Submit.

访学心得：

来到德州理工大学（TTU）, 看见TTU的各种建筑和设施，确实是以人为本，真正感觉到了学校的主体是员工，感受到了深厚的人文气息。TTU在教辅方面也为员工提供了很多便利，例如学校到处都是可以坐下学习和看书的地方，充分满足员工随时随地的学习与休息。TTU校园科研气氛浓厚，校园设施齐全，教师也非常敬业，教师可以全身心的投入教学和科研工作。为激发大家的学习和科研兴趣，学校经常会举办一些研究兴趣活动，为吸引大家积极参加，还会提供免费的披萨和饮料等食品。TTU的图书馆不用任何证件就可以随时进入学习查阅，工作日24小时开放。美国大学教育宽进严出，和国内大学基本100%的毕业率差别很大。美国食物基本以方便快捷的冷食为主，烹饪也以炖煮和烘焙为主，日常很少花长时间准备餐食。在住宿方面，美国人一般享有更大的住房面积和现代化的设施。在出行交通方面，美国是名副其实的“车轮上的国家”，交通发达但公共交通设施发展落后，无车一族在美国生活很不便利。

访学归来本人最大的心得体会就是百闻不如一见，无论是生活阅历还是做学术科研，都要多去看看外面的世界，多和优秀的人交流，才能发现自己的不足，才能取长补短走得更远。访学期间，我也秉承永利集团奋进求是的校训，交流访学做到求真务实，回国后将继续以开放、严谨的态度专心学术科研，以饱满的热情和立德树人的原则投入教书育人工作。

吴德军副教授访学期间的留影：

在TTU正门口

在TTU图书馆

与Lars Christensen教授的合影