Lecture Notes
Courses and Minicourses
Toric Varieties Course
These are the lecture notes from an LTCC graduate course I taught on toric varieties.
- Toric Varieties- Lecture 1 (PDF) Why study toric varieties, algebraic geometry background, algebraic tori
- Toric Varieties- Lecture 2 (PDF) Affine toric varieties, normality
- Toric Varieties- Lecture 3 (PDF) Fans, smooth toric varieties
- Toric Varieties- Lecture 4 (PDF) Separated toric varieties
- Toric Varieties- Lecture 5 (PDF) Orbit cone correspondence, morphisms of toric varieties, projective toric varieties
From Toric Varieties to Cluster Varieties Minicourse
These are the lecture notes for a minicourse I gave at Centro de Ciencias Matemáticas UNAM Campus Morelia on the path from the theory of toric varieties to an analogous theory for minimal models of cluster varieties.
Seminar Talks
Cluster Varieties Lecture
Slides from a talk on cluster varieties in the Symplectic Cut seminar.
Convexity in Tropical Spaces and Compactifications of Cluster Varieties talk
Slides from a talk given in the Bath Algebra, Geometry and Number Theory Seminar, based on joint work with Mandy Cheung and Alfredo Nájera Chávez.
Littlewood-Richardson Coefficients from Mirror Symmetry talk
Slides from a talk given in the Clusters and Geometry Seminar at Yale, based on my PhD thesis.
Grassmannians, Plabic Graphs, and Mirror Symmetry for Cluster Varieties talk
Slides from a talk given in the Fanosearch Group Seminar at Imperial College London, based on ongoing joint work with Lara Bossinger, Mandy Cheung, and Alfredo Nájera Chávez.
Toric Degenerations of Cluster Varieties talk
Slides from a talk given at the Tropical Geometry Meets Representation Theory II Workshop at the University of Leicester, based on joint work with Lara Bossinger, Juan Bosco Frías Medina, and Alfredo Nájera Chávez.