24,211 reputation
469161
bio website people.virginia.edu/~btw4e
location Charlottesville, VA
age 33
visits member for 5 years, 11 months
seen 1 hour ago

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 non-polynomial 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.