José Simental Rodríguez

I am a fifth year Ph.D. student at Northeastern University working under the supervision of Ivan Losev . Here is my CV

I am interested in representation theory. I have been working with Harish-Chandra bimodules over rational Cherednik algebras. These are analogous to the corresponding notion in Lie theory, although the methods and results turn out to be quite dissimilar. Presently, I am studying HC bimodules from the perspective of quantized symplectic resolutions.

During my Masters, advised by Sergio López-Permouth , I have worked with questions regarding relative injectivity of modules over a general (associative, with unit) ring. In particular, we found necessary and sufficient conditions for a class of modules to be the injectivity domain of a module. However, it has been a while since I don't think of this stuff.

For my bachelor's thesis at Universidad Nacional Autónoma de México (UNAM), done under the supervision of Michael Barot, I classified those 2-connected quivers whose path algebra arises as the endomorphism algebra of a module over the algebra of upper triangular n × n-matrices for some n . Here is a link to it. (110 pp, in Spanish)

*Following Latin American traditions, my last name is made of two components and it is "Simental Rodríguez". I normally use just 'Simental' to avoid confusions, and because I don't like my hyphenated last name.


In March 2015, I was course assistant at a Masterclass on Quantized Quiver Varieties given by Ivan Losev at QGM, Aarhus. As course assistant, I gave approximately 40% of the lectures. Here are videos of them.
I am on the job market. Here are my research statement and my teaching statement.

Papers

In preparation: Harish-Chandra bimodules for quantized quiver varieties.

[3] Harish-Chandra bimodules over rational Cherednik algebras. Submitted.   .pdf   arXiv

[2] (jt. wt. Joseph Mastromatteo, Chris Holston and Sergio López-Permouth) An alternative perspective on projectivity of modules. Glasg. Math. J. 57 (01) 2015, pp. 83-99.   .pdf   arXiv   journal

[1] (jt. wt. Sergio López-Permouth) Characterizing rings in terms of the extent of the extent of the injectivity and projectivity of their modules. J. Algebra 362 2012, pp. 56-69.   arxiv   journal

Not intended for publication: Harish-Chandra bimodules for quantizations of type A Kleinian singularities. After writing this paper, I found a much easier proof of the main result (which has a gap here in Prop. 5.2 anyways) that is now written in Section 5 of [3] above. However, some other results here may be of independent interest. .pdf


Expository texts.

D-modules on flag varieties and localization of g-modules. Notes for the MIT-NEU Graduate Seminar on Quantum Cohomology and Representation theory, Fall 2013.

Rational Cherednik algebras of type A. Notes for the MIT-NEU Graduate Seminar on Quantum Cohomology and Representation Theory, Spring 2014.

Cluster algebras and Quantum affine algebras. Notes for a talk given for the course "Cluster algebras", taught by Dylan Rupel, Spring 2014.

Introduction to type A categorical Kac-Moody actions. Notes for the MIT-NEU Graduate Seminar on Hecke algebras and Affine Hecke algebras. Fall 2014.

Introduction to Geometric Invariant Theory. Notes for the MIT-NEU Graduate Student Seminar on moduli of sheaves on K3 surfaces. Spring 2016.

Notes on Tannakian Categories. Notes for a talk given for the course "Differential equations and Quantum groups", taught by Valerio Toledano Laredo, Spring 2016.

D-modules and the Riemann-Hilbert correspondence. Notes for the MIT-NEU Graduate Student Seminar on Hodge Modules, Fall 2016.


Teaching.

Spring 2014. Math 1215: Mathematical thinking. Syllabus.   Student Evaluations.

Summer 2014. Math 1231: Calculus for Business and Economics. Syllabus.   Student Evaluations.

Fall 2015. Math 1215: Mathematical thinking. Syllabus   Student Evaluations.


With Simone Cecchini, I organized the Graduate Student Seminar at Northeastern during the semesters of Fall 2014 , Spring 2015, Fall 2015 and Spring 2016.
On the academic year 2015-2016, I served as the treasurer of the Mathematics Graduate Students Association.
Whenever I have time, I am a tutor at PieRSquared . This is a non-profit organization looking to provide free math tutoring in the community, with an emphasis on developing student confidence and competence in math for the purpose of encouraging broader academic and career choices for Boston's youth.