The day after Presidents Day, 2/22/22, will be Monday Instruction.

# News Archive

## Monday Instruction

## Winter Opening Social

Join us on January 21st at 6pm for our Winter Opening Social! There will be pizza, games, and good company.

155 TMCB

## Colloquium: Stephen McKean (Duke University)

**Title:**Enumerative geometry beyond

**C**

**Abstract:**There are 27 lines on a cubic surface, 8 circles tangent to 3 given circles, and a single line through 2 points. For millennia, mathematicians have sought to count solutions to geometric problems. However, most theorems in enumerative geometry require one to work over an algebraically closed field (such as the complex numbers). Using the 27 lines on a cubic surface as a case study, I will discuss some history about enumerative geometry over non-algebraically closed fields. Time permitting, I will describe some recent results in enriched enumerative geometry, where one uses tools from motivic homotopy theory to give quadratic form-valued counts.

## Colloquium: Michael Griffin (BYU)

Title: AGM and Jellyfish Swarms of Elliptic Curves

Abstract: The classical AGM produces wonderful interdependent infinite sequences of arithmetic and geometric means with common limits. For finite fields with order 3 (mod 4), we introduce a finite field analogue of the classical AGM that spawns directed finite graphs instead of infinite sequences. The compilation of these graphs are reminiscent of a jellyfish swarm, as renderings of the connected components resemble jellyfish (i.e. tentacles connected to a bell head). Each jellyfish in this “swarm” is an isogeny graph of elliptic curves with isomorphic groups of Fq-points. This interpretation can be used to count the total number of such jellyfish in a swarm, as well as to give a description of the class numbers of Gauss, Hurwitz, and Kronecker which is akin to counting types of jellyfish in the swarm.