**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.