bio  website  people.virginia.edu/~btw4e 

location  Charlottesville, VA  
age  33  
visits  member for  5 years, 11 months 
seen  1 hour ago  
stats  profile views  18,924 
I'm an Assistant Professor at the University of Virginia. My interests are geometric representation theory, knot homology and categorification.
2d

awarded  Disciplined 
Aug
24 
comment 
Deceptive linear algebra problem
@user Seems unlikely; the important property evenly spaces powers have is that their orthogonal is easily described. 
Aug
23 
answered  Decomposition and valuation rings 
Aug
19 
revised 
Eigenvectors and partitions of graphs
appended answer 79937 as supplemental 
Aug
16 
comment 
Will a tilting sheaf over Z which is a generator over Q be a generator modulo every prime?
@Dracula Clarified in the question. 
Aug
16 
revised 
Will a tilting sheaf over Z which is a generator over Q be a generator modulo every prime?
added 104 characters in body 
Aug
15 
comment 
Will a tilting sheaf over Z which is a generator over Q be a generator modulo every prime?
Sorry, I don't really follow. It seems like your argument gets a generator after inverting finitely many primes; my question was precisely whether it's really necessary to actually invert those primes. Did I miss something? 
Aug
15 
comment 
Will a tilting sheaf over Z which is a generator over Q be a generator modulo every prime?
@WillSawin I did say "basically", but I believe this is true. By 3.3 in Kaledin, $F$ is a generator if a particular object in the derived category of coherent sheaves is trivial; generation over $\mathbb{Q}$ is that this sheaf is torsion, which is the same as saying that it is trivial after base change to $\mathbb{F}_p$ for sufficiently large $p$. 
Aug
15 
asked  Will a tilting sheaf over Z which is a generator over Q be a generator modulo every prime? 
Aug
10 
answered  Projective normality of cones over projectively normal varieties 
Aug
10 
comment 
Varieties with an ample vector bundle mapping to their tangent bundle
@J.C.Ottem Thanks for the clarification. If Grassmannians don't work, it seems hard to imagine anything else would. 
Aug
9 
comment 
Varieties with an ample vector bundle mapping to their tangent bundle
I honestly don't understand the definitions well enough to be sure, but other Grassmannians seem like a good target; their tangent bundles are the tensor product of two bundles which I think are ample. 
Aug
9 
comment 
Irreducible representations of $S_n$ inside the ring of symmetric polynomials
I know that construction very well, but it's not a construction of an irreducible representation. It's a way of understanding their Grothendieck group. 
Aug
9 
comment 
Irreducible representations of $S_n$ inside the ring of symmetric polynomials
The first construction you list isn't in symmetric polynomials, and the second construction you list isn't a construction of an irreducible representation. 
Aug
3 
answered  The weird projection from SO(2n)/B to maximal isotropic grassmannian 
Aug
2 
revised 
Deceptive linear algebra problem
added 5 characters in body 
Aug
2 
comment 
How algebraic is the holonomy map?
It's a Laurent polynomial connection! You're right that it doesn't completely kill things, but it was meant as an illustration of how "solve a differential equation" is an extremely nonpolynomial operation. 
Aug
2 
revised 
Can the projective line be provided with a ring structure?
added 277 characters in body 
Aug
2 
answered  Can the projective line be provided with a ring structure? 
Aug
2 
comment 
How algebraic is the holonomy map?
I don't know the general answer, but would guess no. Think about the connection on $\mathbb{C}^\times$ with covariant derivative $\frac{\partial}{\partial x}a/x$. This has holonomy around the circle given by $e^a$, which is about as transcendental as it gets. In general, anything that involves solving a differential equation (as holonomy does) is really bad news for staying algebraic. 