El objetivo del coloquio es la difusión de las matemáticas y de sus aplicaciones. Está dirigido
a un público matemático general (¡se incentiva la participación de estudiantes de pregrado!).
En una charla del coloquio usualmente se presentan de manera accesible resultados recientes
en un área de investigación o se da una perspectiva general de un tema matemático de interés.
Viernes, 14 de agosto de 2026
Juanita Duque-Rocero
University of Groningen
Ecuaciones diofánticas y grupos triangulares
📍 Salón C-207🕐 11:00
En esta charla, estudiaremos métodos de la geometría aritmética utilizados para resolver ecuaciones diofánticas. Nos centraremos, en particular, en ecuaciones de Fermat generalizado y en la manera en que los grupos triangulares aparecen de forma natural en su estudio. Explicaremos cómo estas conexiones permiten traducir preguntas sobre soluciones racionales en problemas geométricos y aritméticos sobre curvas algebraicas.
Viernes, 21 de agosto de 2026
David Sher
DePaul University
Pólya's conjecture in spectral geometry
📍 Salón LL-002🕐 11:00
Consider the eigenvalues of the Laplacian on a domain in Euclidean space, with either Dirichlet or Neumann boundary conditions. In the 1950s, George Pólya conjectured that these eigenvalues obey a striking inequality, which holds uniformly for all domains and all eigenvalues. Pólya himself quickly proved the inequality... but only for domains which tile Euclidean space. The general conjecture has remained open, even for simple non-tiling domains such as the ball. In this talk, I will explain the conjecture and then discuss recent progress, including a proof in the case of Euclidean balls. This work is joint with Nikolay Filonov (St. Petersburg State U., Russia), Michael Levitin (U. of Reading, UK), and Iosif Polterovich (U. de Montreal, Canada).
Martes, 25 de agosto de 2026
Serhii Miroshnichenko
University of the Fraser Valley
Where Does the Centroid Go? Balancing Shadows and Slices of Convex Bodies
📍 Salón C-205🕐 13:00
The centroid is a fundamental notion of center: it represents the center of mass in mechanics, the mean in probability and statistics, and a basic descriptor in data analysis and imaging. This talk asks what happens to the centroid when a high-dimensional convex body is viewed through a lower-dimensional slice or shadow. Surprisingly, neither operation generally preserves it.
We present three sharp results. Sections through the centroid satisfy an optimal bound on their imbalance; the projection of a centroid and the centroid of the projection differ by at most about 20.2% of the relevant width; and, in sufficiently high dimensions, a body may have only one central hyperplane section sharing its centroid. The emphasis will be on the geometric ideas behind these results, including first moments, concavity, symmetrization, and spherical transforms.