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)
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. arXiv preprint (2022)
4. On some properties of birational derived splinters. arXiv preprint (2022)
3. Appendix to Direct summands of klt singularities (authored by Ziquan Zhuang). arXiv preprint (2022)
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. arXiv preprint (2022)
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), 297-308

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:

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: April 2024.