**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. Will be expanded soon.

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!

**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:** January 2024.