eCHT: Quadratic curve counting (Fall 2024)

• Lectures: M, 10-11am EST
• Office hours: W, 10-11am EST
• Instructors: Thomas Brazelton and Sabrina Pauli
• eCHT Link
• Syllabus

Talk list

Date	Speaker	Talk title	Topics
Sept. 9th	Thomas Brazelton and Sabrina Pauli	Overview	Classical interpolation, broad ideas for the course
Sept. 16th	Avik Chakravarty	Quantum cohomology and Gromov-Witten classes	Stacks, virtual fundamental classes
Sept. 28th		Expert office hours with Jim Bryan
Sept. 23th	Michael Zeng	Quantum cohomology and Gromov-Witten classes II	Quantum cohomology and Kontsevich's recursive formula for $N_d$
Sept. 25th		Expert office hours with Mark Shoemaker
Sept. 30th	Anna Viergever	Interpolation over $\mathbb{R}$	Interpolation over the reals, Degtyarev and Kharlamov's computations for cubics. Welschinger invariants for real rational curves on the plane
Oct. 2nd		Expert office hours with Frank Sottile
Oct. 7th	Andrés Jaramillo Puentes	Welschinger invariants	Symplectic manifolds and $J$-holomorphic curves, Welschinger invariants more generally
Oct. 9th		Expert office hours with Xujia Chen
Oct. 14th	Ruoxi Li	Welschinger invariants via open Gromov-Witten invariants	Open Gromov-Witten invariants, Spin/Pin structures, relation to Welschinger invariants.
Oct. 21st	Felix Röhrle	$\mathbb{A}^1$-enumerative geometry	Grothendieck-Witt rings, traces and norms, $\mathbb{A}^1$-Euler numbers, the $\mathbb{A}^1$-degree
Oct. 23rd		Expert office hours with Stephen McKean
Oct. 28th	Lukas Bröring	Global and local $\mathbb{A}^1$-degrees	Relative orientations of maps of varieties, computations for local and global $\mathbb{A}^1$-degrees
Nov. 4th	Jesse Pajwani	KLSW part I	The moduli space $\overline{\mathcal{M}_{0,n}}(\mathbb{P}^2,d)$, the evaluation map, and its twists
Nov. 6th		Expert office hours with Jake Solomon
Nov. 11th	Gabriela Guzmán	KLSW part II	Relative orientations of the evaluation map in characteristic zero and positive characteristic
Nov. 18th	Candace Bethea	KLSW part III	Levine's quadratically enriched Welschinger invariants agreeing with the local degree of the avluation map, and the main theorem of KLSW
Nov. 25th	Nathan Tiggemann	Tropical correspondence theorems	Tropical plane curves and dual subdivisions, Mikhalkin's correspondence theorem over the complex and real numbers, quadratically enriched tropical correspondence

More stuff

Some small values of $N_d$ and $W_d$: