Shiji Lyu
Email: slyu [at] uic [dot] edu
Greetings! I am a Research Assitant Professor (postdoc) at UIC. I obtained my PhD from Princeton University. My advisor was Professor János Kollár. I obtained my B.Sc. at Peking University.
I am interested in commutative algebra and algebraic geometry, especially singularities in positive and mixed characteristics.
Papers and preprints:
7. Formal lifting of dualizing complexes and consequences. arXiv preprint (2023). To appear, Nagoya Math. J.
6. (In preparation) Uniform bounds in excellent rings and applications to semicontinuity. Draft (2023)
5. The gamma-construction and permanence properties of the (relative) F-rational signature. J. Algebra 659 (2024), pp.434-450. DOI arXiv
4. On some properties of birational derived splinters. arXiv preprint (2022). To appear, Michigan Math. J.
3. Appendix to Direct summands of klt singularities (authored by Ziquan Zhuang). arXiv preprint (2022). To appear, Invent. Math..
2. The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero, coauthored with Takumi Murayama. arXiv preprint (2022)
1. Permanence properties of splinters via ultrapower. Michigan Math. J. Advance Publication (2024), pp.1-8. DOI arXiv
0. Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs.
V. Roshan Joseph, Dianpeng Wang, Li Gu, Shiji Lyu, and Rui Tuo. Technometrics 61:3 (2019), pp.297-308. DOI
Notes:
Some results I discovered myself and found interesting.
1. A characterization of Noetherian local rings. A local ring is Noetherian if and only if its maximal ideal is finitely generated, and every finitely generated ideal of the ring is a finite intersection of finitely generated primary ideals. Let me know if you find a different proof than mine!
2. If a morphism of finite type schemes over a field is injective as a map of sets, then it is radicial over a dense open of the source. Proof.
Academic visits:
March 2024
Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain
Conference and seminar talks:
November 2024
Commutative algebra and algebraic geometry seminar, City University of New York, online
October 2024
Special Session on Singularities in Commutative Algebra (20-minutes talk), AMS Fall Eastern Sectional Meeting, SUNY, Albany, New York
October 2023
Algebraic geometry seminar, Northwestern University, Evanston, Illinois
September 2023
Deparment Colloquium, University of Illinois Chicago, Chicago, Illinois
May 2023
FRG special month in algebraic geometry (short-talk), University of Michigan, Ann Arbor, Michigan
March 2023
Algebraic geometry seminar, Stanford University, Stanford, California
Algebraic geometry seminar, Princeton University, Princeton, New Jersey
January 2023
Algebraic geometry seminar, University of Tokyo, Shibuya, Tokyo
October 2022
Commutative algebra seminar, University of Illinois Chicago, Chicago, Illinois
September 2022
Commutative algebra seminar, University of Utah, Salt Lake City, Utah
Algebraic geometry seminar, Purdue University, West Lafayette, Indiana
Commutative algebra seminar, University of Michigan, online
June 2022
Algebraic Geometry and Singularities Learning Workshop & Conference (mini-talk), University of Washington, Seattle, Washington
March 2022
Southern Regional Algebra Conference 2022, Georgia College & State University, Milledgeville, Georgia
Last updated: September 2024.