notes and talks

2024

1. 

   Intro to quasicategories

   2024

   Notes from a talk at the Floer homotopy theory spring school

   HTML PDF

2. 

   Introduction to Lagrangian torus fibrations and SYZ mirror symmetry

   2024

   Slides from a talk at the Differential Geometry seminar ran by Aleksander Doan at UCL, as well as the Junior Geometry seminar in Cambridge

   PDF

3. 

   Derived categories of cubic fourfolds

   2024

   Slides from a talk at the Derived Obsessed Graduate Students seminar

   HTML PDF

4. 

   Symplectic cohomology and spectra

   2024

   Slides from a talk on symplectic cohomology and Thomas Kragh’s paper on Viterbo’s map

   HTML PDF

5. 

   Mirror symmetry for cubic fourfolds

   2024

   Slides from a talk at Nick Sheridan’s seminar on HMS for Fanos

   HTML PDF

2024

1. 

   SYZ for hypersurfaces in toric varieties

   2024

   First year miniproject

   Abs PDF

   Notes on SYZ for hypersurfaces in toric varieties, following the paper by Auroux, Abouzaid and Katzarkov. Includes a summary of the construction and a worked out example: homological mirror symmetry for T^*S^2

2. 

   Derived categories and cubic fourfolds

   2024

   First year miniproject

   Abs PDF

   Joint miniproject on derived categories. I focused on cubic fourfolds and their Kuznetsov components. Included are some foundations and for example, the proof that the Kuznetsov component is CY2. I focus in particular on cubic fourfolds containing a plane and show they are associated to a twisted K3 surface. Also, I briefly discuss Addington-Thomas’ paper connecting the Hodge theoretic and derived categorical viewpoints.

2023

1. 

   Categorical symplectic topology of T^*S^n

   2023

   Abs PDF

   Part III essay I wrote under the supervision of Dr. Jack Smith. The content is about Fukaya categories, in particular those of cotangent bundles of spheres. I give an overview of Seidel’s paper on the topic.

2. 

   Notes on Geometry and Topology

   2023

   Abs PDF

   Big collection of notes I took during my master’s. Includes material on differential and algebraic geometry, algebraic topology, K-theory and complex manifolds. Beware of plenty of typos/mistakes.

2022

1. 

   The Hodge decomposition theorem

   2022

   Abs PDF

   Undergrad summer project where I learned about Hodge theory