# Cesar Hilario

**Institutional email:** Cesar.Hilario@hhu.de

**Permanent email:** cesar.hilario.pm@gmail.com
**Address:** Universitätstraße 1, 40225 Düsseldorf

**Office:** 25.22.02.39

I am a postdoc in the working group of Stefan Schröer at Heinrich-Heine Universität Düsseldorf.
I received my PhD in March 2022 from IMPA, where I was advised by Karl-Otto Stöhr.
Before that, I was an undergraduate student at Universidad Nacional de Ingeniería in Lima, Peru.

I work on algebraic geometry in positive characteristic.
I am interested in regular curves that become non-regular after base change, and especially in their connection to fibrations by singular curves in positive characteristic.
Among the tools I like to use is the theory of non-conservative function fields.

### Research

- Turning non-smooth points into rational points, 2024.
Arxiv.
- Fibrations by plane quartic curves with a canonical moving singularity (with Karl-Otto Stöhr), 2023.
Arxiv.
- Generalizations of quasielliptic curves (with Stefan Schröer).
*Épijournal Géom. Algébrique* 7 (2023), Art. 23, 31 pp.
Arxiv.
- On regular but non-smooth integral curves (with Karl-Otto Stöhr), 2022.
Arxiv.

### Talks

Miniworkshop on Algebraic Geometry, Phillips University of Marburg. November 2023.

Developments in Modern Mathematics: a WiMGo conference, University of Göttingen. September 2023.

Early Number Theory Researchers Workshop 2023, Bielefeld University. August 2023.

Seminar of Algebra, University of Gröningen. May 2023.

Graduate Students Colloquium, IMPA. March 2023.

Workshop 2240, University of Wuppertal. November 2022.

Seminar of Algebraic Geometry, Hanoi Institute of Mathematics (online). July 2022.

Oberseminar Algebraic Geometry, HHU Düsseldorf. June 2022.

38 movimientos, PUCP. September 2021.

Oberseminar Algebraic Geometry, HHU Düsseldorf (online). May 2021.

American Graduate Student Algebraic Geometry Seminar (online). April 2021.

Seminar of mathematics, PUCP (online). April 2021.

Segundo Congreso Internacional Multidisciplinario, Universidad Nacional de Ingeniería (online). March 2021.

Seminar of algebra, IMPA (online). January 2021.

Brazilian Algebraic Geometry Seminar (online). September 2020.

MPS Conference on Higher Dimensional Geometry 2020: Rationality, Simons Foundation (online). July 2020.

Graduate Students Coloquium, IMPA. May 2019.

Seminar of Algebra, IMCA. April 2019.

### Seminars

In 2021, during the covid pandemic, I co-organized a virtual Student Algebraic Geometry Seminar at IMPA.
### Miscellaneous

My undergraduate dissertation (in Spanish) on the Generalized Nash Equilibrium Problem.