【报告摘要】  Projective spaces are among the most fundamental examples of algebraic varieties. A variety is called rational if it is birationally equivalent to projective space, and unirational if it admits a dominant rational map from projective space. This gives rise to two classical questions in algebraic geometry: Which varieties are rational or unirational? Is every unirational variety necessarily rational? These problems have shaped the development of algebraic geometry for over a century. While they are fully resolved for algebraic curves, their analogues for differential algebraic curves—one-dimensional solution sets of algebraic differential equations—remain open. In this talk, we present recent advances in this direction, bridging differential algebra and birational geometry.

 

【报告人简介】 李伟，中国科学院数学与系统科学研究院副研究员。研究方向为微分代数几何、应用模型论。主持国家自然科学基金委优秀青年基金；曾获国际计算机协会(ACM)SIGSAM/ISSAC杰出论文奖、吴文俊计算机数学青年学者奖等。研究工作主要发表在Found. Comput. Math.，Trans. Amer. Math. Soc.， J. London Math. Soc.， J. Algebra等期刊。