bio  website  people.virginia.edu/~btw4e 

location  Charlottesville, VA  
age  33  
visits  member for  5 years, 9 months 
seen  yesterday  
stats  profile views  18,730 
I'm an Assistant Professor at the University of Virginia. My interests are geometric representation theory, knot homology and categorification.
2d

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Characteristic Cycles and Nearby Cycles
I don't think I can answer Q2 precisely, but my understanding is that this is usual connection between filtrations and deformations using Rees modules. That is, I think that Ginzburg's $L_0$ is the Rees module of the Vfiltration (suitably interpreted). 
2d

revised 
Characteristic Cycles and Nearby Cycles
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Jul 23 
answered  Do IwahoriHecke algebras come from cohomology classes? 
Jul 22 
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Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a “kernel” of the first Chern class?
This is explained on Wikipedia: en.wikipedia.org/wiki/Néron–Severi_group 
Jul 14 
answered  What are the “tensorclosed” object of the BGG category $\mathcal{O}$ of a semisimple Lie algebra $\mathfrak{g}$? 
Jul 13 
awarded  Enlightened 
Jul 13 
awarded  Nice Answer 
Jul 7 
awarded  Popular Question 
Jul 3 
answered  JacobsonMorozov theorem 
Jul 3 
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JacobsonMorozov theorem
@YCor Can you describe how you get $PSL_2$ in $PGL_4$? That nilpotent has a Jordan block of length 2 in the adjoint representation, which shouldn't be possible if it were the $E$ in a $PSL_2$ representation. 
Jul 1 
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Is every weight of an integrable highest weight module in the Tits cone?
That is false in all types: you have to be in the same coset of the root lattice as the highest weight. With that proviso, I think it's true. Again, induct on the number of times you've had to subtract positive roots. If the weight $\mu$ isn't dominant, then its conjugate which is dominant will reduce this number, and have the same weight multiplicity. Once it's dominant, I think one should be able to find a simple root such that $\mu+\alpha_i$ is in the polytope (I don't have a slick explanation, but the picture looks right in my head). $E_i$ is injective here, so by induction, QED. 
Jun 30 
revised 
Is every weight of an integrable highest weight module in the Tits cone?
edited body 
Jun 30 
answered  Picard group of a quotient of a group by its maximal parabolic subgroup 
Jun 30 
answered  Is every weight of an integrable highest weight module in the Tits cone? 
Jun 24 
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Understanding the Weyl Character Formula
@VítTuček No, there are really no maps. Think about $\mathfrak{sl}_2$. You have the Verma $M(n)$ and the Verma $M(n2)$. The space $Hom(M(n2),M(n)$ is 1d if $n$ is an integer with $n\geq 1$, and 0 dimensional otherwise. 
Jun 23 
answered  Understanding the Weyl Character Formula 
Jun 23 
revised 
Understanding the Weyl Character Formula
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Jun 16 
answered  Ext groups in the equivariant derived category 
Jun 15 
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Closed orientable 4manifold with $H^1(M;\Bbb Z_2)=\Bbb Z_2$ and nonzero cup product $H^1\times H^1\to H^2$
Any closed manifold has nonzero cup product by Poincare duality. So $S^1\times S^2$ satisfies your criteria. 
Jun 11 
answered  Do the support sets of subspaces give the representable matroids? 