About me

¡Hola! My name is Juan Sebastian Numpaque Roa. I am from Bogotá, Colombia. Currently, I am a third year mathematics Ph.D. student working under the supervision of Prof. Peter B. Gothen. Besides my academic activities, I enjoy listening to music (I am a great fan of jazz) and reading while having a cup of Colombian coffee or a cold beer. I also very much like to walk, I believe this is a healthy and wonderful way of getting to know the local culture of a city.

Research

Research interests

I work on complex algebraic geometry with a focus on moduli spaces and geometric representation theory. More concretely, my mathematical interests (i.e. things I have been learning, thinking about or that I would like to learn) include:

Moduli of quiver representations and quiver bundles.

Vector bundles, Higgs bundles and their moduli.

Non-abelian Hodge Theory.

Construction of moduli spaces via gauge theory and GIT.

Stacky and arithmetic versions of the above.

Publications

(2022) With Nicolás Cardozo. Evaluation of Work Stealing Algorithms.
In: Gonzalez, E., Curiel, M., Moreno, A., Carrillo-Ramos, A., Páez, R., Flórez-Valencia, L. (eds) Advances in Computing. CCC 2021. Communications in Computer and Information Science, vol 1594. Springer, Cham.

Preprints

Theses

These are some written works, any mistake is my solely fault. Feel free to share with me any feedback, typos or improvements!

Academic activities

Here I share the seminars I have participated in and that I am organizing. Also you will find hand-written notes and slides for talks I have given (These are full of mistakes and inaccuracies. Please forgive me and send me your feedback). Finally, you will find information on some conferences I have and will attend.

Seminars

Since the first semester of 2024, my colleague Hamza Bakhouch and I have been running a reading group on Scheme theory.
In the first semester of 2023, Prof. João Nuno Mestre organized a reading group on Symplectic Geometry at Coimbra. Our main reference was Ana Cannas Da Silva's book. Some talks I contributed with, related to my research, were on the Moduli space of flat connections and Kähler manifolds and Hodge theory.

Talks

I gave a talk on the Hitchin Fibration in the Geometry seminar of CMUC-Universidade de Coimbra.
As part of the final exam of the course of Representation Theory that I followed on the first year of my Ph.D. I gave a talk on the Gabriel's theorem. I mainly followed the nice notes by Crawley-Boevey.
As part of the final exam of the course of Differential Geometry that I followed on the first year of my Ph.D. I gave a talk on the Moduli space of Elliptic curves.
As part of the final exam of the course of Character Varieties that I followed on my Master 2 in Paris, I gave a talk on the E-polynomial of the rank two character variety.

Future/Past conferences

(May 2025) TiME 2025 Summer School on Invariant Theory, Lie-Størmer Center, Tromsø, Norway.
(April 2025) Spring School "The Dynkin Classification", Ruhr Universität Bochum, Bochum, Germany.
(October 2024) MaPhyAG Workshop: Integrability, Geometry and QFT, Universidad Complutense de Madrid, Madrid, Spain.
(July 2024) 2nd Simons Math Summer Workshop: Moduli, Simons Center for Geometry and Physics, Stony Brook, United States of America.
(April 2024) Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany.
(December 2023) Moduli spaces of vector bundles and curves, Université de Cergy-Pontoise, Paris, France.
(October 2023) Vector bundles and combinatorial algebraic geometry, Goethe Universität Frankfurt am Main, Frankfurt, Germany. In this conference I contributed with a 5 minute mini-talk on my research entitled: "From Higgs to quiver bundles".

Teaching

Past courses

At the Department of Mathematics of Universidad de los Andes I was hired as a teaching assistant. I was in charge of running the exercise sessions (2H of class per week + Weekly quiz writing and grading + Exam overseeing and grading) for the following courses:

(2021-1) Two sessions of Linear Algebra

(2020-1) Two sessions of Linear Algebra

(2019-2) Vector Calculus and Mathematics for Economics and Business administration

(2019-1) Differential Calculus and Vector Calculus

(2018-1) Vector Calculus

(2017-2) Integral Calculus

Other Materials

During the COVID-19 pandemic, the Department of Mathematics of Universidad de los Andes focused on creating multimedia material that could support students through their learning process. My contribution to this project consisted in producing audiovisual material for the course of Vector Calculus.

E-mail:	js.numpaqueroa@gmail.com
Professional Address:	Centro de Matemática da Universidade do Porto
	Rua do Campo Alegre 687
	4169-007 Porto, Portugal