Geometria Generalitzada

Self-crossing stable generalized complex structures
Aldo Witte (U Hamburg)
Dia: 19/02/2026
Hora: 14:00
Lloc: Teams (online)

Web: GENTLE

Resum: The first example of a manifold which admits a generalized complex structure, but neither a complex or symplectic structure was $3\mathbb{C}P2\#\overline{19 \mathbb{C}P2}$ which was constructed by Cavalcanti and Gualtieri. This structure is a very special example of a GC structure called stable: It has symplectic type outside of a codimension-two embedded submanifold where it has complex type.

Afterwards many more examples where constructed by several authors, many of these manifolds appear as connected sums. However, none of the GC structures on these manifolds appeared via a connected sum procedure. We will remedy this by introducing the notion of a self-crossing stable generalized complex structure: A generalisation of stable generalized complex structures which now degenerate on an immersed submanifold with transverse self-crossings. We will obtain a connected sum procedure for these structures, and a procedure which smoothens the immersed submanifold into an embedded one. In this manner we recover many of the existing examples in the literature as well as some new ones.

If time permits we will also study the relation with toric geometry and T-duality. Joint work with Gil Cavalcanti and Ralph Klaasse.

Join: https://teams.microsoft.com/meet/38114669707998?p=tvlUUlIxx3kpb9Iiqi
Meeting ID: 381 146 697 079 98, Passcode: 6DL2Zk33

Models Estocàstics i Deterministes

Blowup Phenomena in Nonlinear Parabolic Stochastic Partial Differential Equations
Mohammud Foondun (University of Strathclyde)
Dia: 19/02/2026
Hora: 15:00
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Grup de Topologia Algebràica

Resum: We investigate blowup behavior in a class of nonlinear parabolic stochastic partial differential equations driven by space–time noise. Under suitable growth and regularity assumptions on the drift and diffusion terms, we discuss conditions that lead to almost sure blow-up of solutions in arbitrarily small time.

Modelos dinámicos para sistemas territoriales: integración de información satelital y prospectiva: Aplicaciones al uso del suelo y sectores productivos en la Región de Aysén
Gerard Olivar-Tost (Universidad Católica del Maule, Xile)
Dia: 05/02/2026
Hora: 15:00
Lloc: Dpt Matematiques, Seminari Planta 3 (C1/366)

Resum: Esta charla presenta un enfoque de modelamiento matemático dinámico para el análisis prospectivo de sistemas territoriales, basado en la integración de información proveniente de imágenes satelitales con herramientas de la teoría de sistemas dinámicos. El trabajo se fundamenta en la formulación de modelos mediante sistemas de ecuaciones diferenciales ordinarias que describen la evolución temporal del uso del suelo y su interacción con variables productivas, ambientales y antrópicas.

La información derivada de la observación de la Tierra —como clasificaciones de cobertura y uso del suelo, índices espectrales y variables climáticas, incluyendo la cobertura nival— se incorpora al modelamiento como variables de estado, forzantes externas o parámetros dinámicos. Estos modelos, formulados inicialmente de manera determinista, se extienden de forma natural para incluir componentes estocásticas que permiten representar la variabilidad ambiental y la incertidumbre asociada a los procesos territoriales.

A través de estudios de caso vinculados a sectores económicos relevantes de la Región de Aysén, tales como sistemas agro-ganaderos y el manejo de ecosistemas naturales, se muestra cómo este enfoque permite construir escenarios prospectivos, analizar trayectorias futuras del uso del suelo y evaluar el impacto de distintas estrategias de manejo y políticas territoriales. El seminario enfatiza el rol del modelamiento dinámico como puente entre los datos satelitales y la toma de decisiones informada en planificación territorial y desarrollo sostenible.

Teoria d'Anells

On the space of Sylvester rank functions
Simone Virili (UAB)
Dia: 16/02/2026
Hora: 11:30
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Laboratori d'Interaccions entre Geometria, Àlgebra i Topologia

Resum: Given a ring R, let P(R) be the space of Sylvester rank functions on the category of finitely presented modules mod-R. Recall that P(R) can also be described as the space of normalized additive functions on the Abelianization Ab(R), which is the category of finitely presented objects in the additive functor category [R-mod,Ab]. Compared to mod-R, the category Ab(R) has a much richer structure, which can be used for the study of P(R). In this talk we will discuss two such applications: for the first one we will describe the space Pex(R) of exact rank functions in terms of effaceable functors, while for the second we will describe the irreducible discrete rank functions using the topology of the Ziegler spectrum. As a concrete application, we will give a complete description of the space P(R) when R is a Dedekind domain with a polynomial identity.