visit to U Oregon.

It is very useful to consider singular Soergel module.

Question: is crossing the same as merge then split?

What is $x_1, x_2$? Consider $Fl(0,1,2)$, the complete flag in $\C^2$

In a 2-category, there are more directions to make a line segment into a circle. There are the monoidal direction, the 1-categorical direction. And, there are the omp

Consider 4 strands, full twists. (Closed) Bott-Samuelson variety, stusts to utustu, where s t u are the $s_1, \cdots, s_3$. The two movies gives equivalent morphisms of Bott-Samelson module, which is equivalent to total merge, and total split. Not true if you start from other positions. Can you use geometry to explain why?

Consider the finite Hecke algebra. We have the commutative algebra YJM, and the center Z. $$ Z \into YJM \into H_{fin} $$

There are categorification of finite Hecke algebra, into finite Hecke category. $$ Z \into YJM \into H_{fin} $$