Research Interests

My research interest lies in representation theory and is motivated by the connection between algebraic groups and combinatorics. My work delves into the intricate interplay among the maximal torus, the Borel groups acting on Schubert and spherical varieties and their associated combinatorial structures. Lately I’ve been investigating the shellability of symmetric spaces via their Bruhat orders posets. Also, I am keenly interested in topics related to algebraic coding theory.

Publications and Preprints

1. Lexicographic shellability of sects (with Aram Bingham-submitted)
2. Nearly toric Schubert varieties and Dyck paths (with Mahir Can-submitted)

Invited Talks

1. Shellability of symmetric spaces and Bruhat orders. SIAM TX-LA, University of Louisiana at Lafayette, LA, USA, Nov 3-5, 2023.
2. Enumerating spherical Dyck paths and smooth nearly toric varieties. DiscreteMath, Universidad Nacional, Bogotá D.C., Colombia, Oct 9, 2023.
3. Spherical partition Schubert varieties and Dyck paths. SRAC, NOLA, USA, March 24-26, 2023.
4. Dyck paths and nearly toric Schubert varieties. JMM, Boston, USA, January 4-7, 2023.
5. Ding and Schubert varieties. SMM, Universidad De Guadalajara, Jalisco, México (virtual-Mini-Plática).
6. Contar nos hace la vida más fácil. COCITEI, Oaxaca, México (virtual-slides).
7. \(Q_p\) Spaces on Hyperbolic Riemann Surfaces. Encuentro de Sociedades de Matemáticas Colombiana y Mexicana, Universidad del Norte, Colombia (slides).

Contributed Talks

1. Nearly toric Schubert varieties and Dyck paths. \(13^{th}\) Southeastern Lie Theory Workshop, Raleigh, NC, USA, May 12-14, 2023 (slides).
2. Dyck paths and nearly toric Schubert varieties. CombinaTexas, College Station, Texas, USA, April 22-23, 2023.
3. Ding and Schubert Varieties. Graduate Student Colloquium at Tulane university, USA (slides).
4. A naive Introduction to Affine Schemes. Graduate Student Colloquium at Tulane university, USA (slides).
5. From Differential Geometry to Lie Theory. Graduate Student Colloquium at Tulane university, USA (virtual-slides).
6. Manifolds and their applications. Graduate Seminar at IPN, México (slides).

Posters

1. Lexicographic shellability of sects. CAAC , LACIM (UQAM), Montreal, Canada, Jan 26–28, 2024 (poster).
2. Spherical Dyck paths. Permutation Pattern, University of Burgundy, Dijon, France , July 3–7, 2023 (poster).
3. Spherical partition Schubert varieties and Dyck paths. SLAM, University of North Texas, March 4–5, 2023.
4. Spherical partition Schubert varieties. PRIMA congress, Vancouver, Canada, December 4-9, 2022.