1 2021-05-14

2 2021-05-13

2.1 00:14

Questions: \(\pi_1(X)\) can be defined for schemes.

3 2021-05-12

3.1 10:28

See Serre’s uniformity conjecture.

3.2 20:46

Source: Frobenius exact symmetric tensor categories - Pavel Etingof. IAS Geometric/modular representation theory seminar. https://www.youtube.com/watch?v=7L06K7SL5qw

Link to Diagram

4 2021-05-11

4.1 12:48

What is an isocrystal?

What does it mean to be crystalline?

What is a symplectic basis?

What is the Mordell-Weil sieve?

How can one pass from p-adic solutions to rational solutions?

4.2 13:05

What is the conductor of an elliptic curve?

See Serre’s open image theorem.

4.3 13:11

What is inertia?

What is the cyclotomic character?

4.4 13:49

See Mazur’s Program B

4.5 14:11

See Goursat’s lemma in group theory.

5 2021-05-10

5.1 12:34

We haven’t been able to classify the rational points on \begin{align*}\[modular curves\end{align*} ]!

5.2 13:16

Reference: Kirsten Wickelgren, Colloquium Presentation: zeta functions and a quadratic enrichment. Rational Points and Galois Representations workshop

See \begin{align*}\[motivic homotopy\end{align*} ].

Link to Diagram

Link to Diagram

Link to Diagram

image_2021-05-10-13-36-13
image_2021-05-10-13-49-00
image_2021-05-10-13-56-27

5.3 16:35

Reference: Foling Zou, Nonabelian Poincare duality theorem and equivariant factorization homology of Thom spectra. MIT Topology Seminar.

image_2021-05-10-17-13-16

where \(R{\hbox{-}}\)line is the \(\infty{\hbox{-}}\)category of line bundles up to equivalence?

6 2021-05-08

6.1 22:55

Not every simplicial complex is a PL manifold:

image_2021-05-08-22-55-16

7 2021-05-06

7.1 11:15

Reference: Arpon Raksit - Hochschild homology and the derived de Rham complex revisited. https://www.youtube.com/watch?v=E84gVDm1kvM