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Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing
(2013-10-08)
We defined a new type of open Gromov-Witten invariants on hyperK\"aher manifolds with holomorphic
Compact Generation of the Category of D-Modules on the Stack of G-Bundles on a Curve
(2013)
The goal of the paper is to show that the (derived) category of D-modules on the stack \(Bun_G(X)\) is compactly generated. Here X is a smooth complete curve, and G is a reductive group. The problem is that \(Bun_G(X)\) ...
Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
(2013-10-08)
Suppose $f,g_1,\cdots,g_p$ are holomorphic functions over $\Omega\subset\cxC^n$. Then there raises a natural question: when can we find holomorphic functions $h_1,\cdots,h_p$ such that $f=\sum g_jh_j$? The celebrated Skoda ...
On Some Finiteness Questions for Algebraic Stacks
(Springer Science + Business Media, 2013)
We prove that under a certain mild hypothesis, the DG category of D-modules on a quasi-compact algebraic stack is compactly generated. We also show that under the same hypothesis, the functor of global sections on the DG ...
Knots which Behave Like the Prime Numbers
(Oxford University Press (OUP), 2013)
This paper establishes a version of the Chebotarev density theorem in which number fields are replaced by 3-manifolds.
Ind-Coherent Sheaves
(Independent University of Moscow, 2013)
We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial ...
Analysis of Some PDEs over Manifolds
(2013-02-14)
In this dissertation I discuss and investigate the analytic aspect of several elliptic and parabolic partial differential equations arising from Rimannian and complex geometry, including the generalized Ricci flow, Gaussian ...
The effect of one additional driver mutation on tumor progression
(Blackwell Publishing Ltd, 2013)
Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting ...
On Extractors and Exposure-Resilient Functions for Sublogarithmic Entropy
(Wiley-Blackwell, 2013)
We study resilient functions and exposure-resilient functions in the low-entropy regime. A resilient function (a.k.a. deterministic extractor for oblivious bit-fixing sources) maps any distribution on n -bit strings in ...
Lookahead Strategies for Sequential Monte Carlo
(Institute of Mathematical Statistics, 2013)
Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess ...