Algebra, combinatorics, and mathematical computer science

在代数几何和表示论中有许多重要的对象(“三角范畴”)，它们的结构通常非常复杂，因此很难直接研究。我计划通过连接到更好理解的主题来研究它们，比如对称性(用更专业的语言来说，是“根系”和“Weyl群”)。相反，我也希望在简单的(“组合”)环境中出现的一些现象，可以通过三角范畴的解释来解释。到目前为止，这两个数学领域之间可能的联系还没有得到足够的重视，所以现在是进行这一研究计划的理想时机。

There are many important objects in algebraic geometry and representation theory ("triangulated categories") whose structure is typically very complicated, and which are therefore difficult to study directly. I plan to study them by drawing connections to better-understood topics, such as symmetry (in more technical language, "root systems" and "Weyl groups"). Conversely, I also hope that some phenomena arising in the simple ("combinatorial") settings, may be explained by interpreting them in terms of triangulated categories. The possible connections between these two areas of mathematics have so far received insufficient attention, so now is an ideal time to pursue this research program.