bio  website  ma.utexas.edu/users/… 

location  Austin, TX  
age  
visits  member for  5 years, 1 month 
seen  16 hours ago  
stats  profile views  1,814 
Postdoc at UT Austin.
3h

awarded  Good Answer 
Aug
8 
comment 
How algebraic is the holonomy map?
@David Roberts: I think the holonomy map is almost never a submersion. The exponential map is not an open map, even for compact Lie groups e.g. $SU(2)$, (see math.stackexchange.com/questions/301504/…), and not surjective in general for noncompact Lie groups (e.g. $SL_2(\mathbb C)$). 
Aug
4 
comment 
Semisimple monoidal category with duals
An even simpler example: $1 \otimes 1 \simeq 1$, and $1$ is self dual. 
Jul
20 
awarded  Yearling 
Jun
21 
comment 
Representation Theory of $U(N)$
@André: Fair point! I started to write a more detailed answer, then remembered that I had other things to do... probably this answer should have been a comment. 
Jun
20 
answered  Representation Theory of $U(N)$ 
Jun
18 
answered  Equivariant Derived Category 
Jun
1 
awarded  Popular Question 
May
3 
comment 
Characterizations of regular holonomic Dmodules
Have you looked in Bjork's book? I think most of this stuff is there. 
Apr
9 
awarded  Nice Answer 
Mar
7 
answered  Relations between functors in a recollement 
Mar
6 
comment 
Relations between functors in a recollement
Note that if you have a recollement with the property that $i_R q_L = 0 = i_L q_R$, then the category $\mathbb D$ splits as an orthogonal sum of $\mathbb D^0$ and $\mathbb D^1$; i.e. there are no Homs in either direction. This is certainly not the case for sheaves on a locally closed decomposition of a space... 
Mar
6 
comment 
Relations between functors in a recollement
Maybe I am getting confused here, but it is not true that $j^\ast i_\ast = 0$ (where $i$ is the open embedding and $j$ is the closed complement  opposite to my usual convention!). For example if you take the direct image of the constant sheaf under the open embedding $i:\mathbb R  \{0\} \hookrightarrow \mathbb R$, then the stalk $j^\ast i_\ast \mathbb Z_{\mathbb R  \{0\}}$ is 2dimensional. Similarly, $j^!i_!$ is not zero in general. 
Nov
22 
comment 
Is there a cotangent bundle of a stable $\infty$category?
You may complain that this is more like the tangent bundle than the cotangent, but I think some kind of Koszul duality should relate sheaves on this odd tangent bundle with sheaves on the cotangent bundle (at least up to shifts by 2). 
Nov
22 
comment 
Is there a cotangent bundle of a stable $\infty$category?
Not sure if this is relevant or not, but the categorical Hochschild homology (CHH) of a monoidal category seems to be a reasonable candidate for part 1 (no idea about part 2). By CHH I mean the category $\mathcal C \otimes{\mathcal C \times \mathcal C^{op}} \mathcal C$ associated to a monoidal category $(\mathcal C, \otimes)$. In the case $\mathcal C = QC(X)$, for X a scheme $CHH(\mathcal C) = QC(LX)$, where $LX = X\times_{X\times X} X$ is the derived loopspace (by a result of BenZviFrancisNadler). The derived loopspace is the same as the odd tangent complex by HKR. 
Sep
24 
awarded  Autobiographer 
Sep
2 
awarded  Revival 
Jul
20 
awarded  Yearling 
Jul
6 
awarded  Enlightened 
Jul
2 
awarded  Curious 