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Minimal Model Program with scaling and adjunction theory
Quasi polarized pairs Adjunction Theory Minimal Model Program with scaling
2011/9/20
Abstract: Let (X,L) be a quasi polarized pairs, i.e. X is a normal complex projective variety and L is a nef and big line bundle on it. We study, up to birational equivalence, the positivity (nefness)...
Abstract: We construct an inverse system of unstable Vassiliev spectral sequences on the spaces of plumbers' knots, which model the homotopy type of the space of long knots, and show that the limit of...
Localization in Gromov-Witten Theory and Orbifold Gromov-Witten Theory
Gromov-Witten invariants toric varieties virtual localization orbifold Gromov-Witten invariants toric DM stacks
2011/9/19
Abstract: In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mum...
Applications of Derandomization Theory in Coding
Derandomization theory randomness extractors pseudorandomness wiretap channels group testing error-correcting codes
2011/10/9
Abstract: Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial...
The Local Structure of Compactified Jacobians: Deformation Theory
Compactified Jacobian compactified Picard scheme nodal curve torsion-free sheaf
2011/9/16
Abstract: This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ri...
On the passage from atomistic systems to nonlinear elasticity theory
nonlinear elasticity theory Analysis of PDEs
2011/9/16
Abstract: We derive continuum limits of atomistic models in the realm of nonlinear elasticity theory rigorously as the interatomic distances tend to zero. In particular we obtain an integral functiona...
Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian Processes
tail asymptotic Laplace method self-similar processes Gaussian processes locally stationary processes
2011/9/15
Abstract: We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome bu...
Dissimilarity maps on trees and the representation theory of $GL_n(\C)$
Dissimilarity maps trees the representation theory Algebraic Geometry
2011/9/14
Abstract: We revisit the representation theory in type $A$used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a di...
Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
Standard Monomial Theory for desingularized Richardson varieties in the flag variety GL(n)/B
Standard Monomial Theory Richardson varieties Algebraic Geometry
2011/9/14
Abstract: We consider a desingularization Gamma of a Richardson variety X_w^v=X_w \cap X^v in the flag variety Fl(n)=GL(n)/B, obtained as a fibre of a projection from a certain Bott-Samelson variety Z...
Conformal field theory and a new geometry
Conformal field theory D-branes vertex operator algebra stringy algebraic geometry
2011/9/14
Abstract: This paper is a review of open-closed rational conformal field theory (CFT) via the theory of vertex operator algebras (VOAs), together with a proposal of a new geometry based on CFTs and D-...
Some thoughts on Le Cam's statistical decision theory
likelihood ratios randomized estimators Skorohod-Dudley almost-sure representation Le Cam's statistical decision theory
2011/9/15
Abstract: The paper contains some musings about the abstractions introduced by Lucien Le Cam into the asymptotic theory of statistical inference and decision theory. A short, self-contained proof of a...
Smith theory and geometric Hecke algebras
Smith theory geometric Hecke algebras Representation Theory
2011/9/15
Abstract: In 1960 Borel proved a "localization" result relating the rational cohomology of a topological space X to the rational cohomology of the fixed points for a torus action on X. This result and...
Character formul?and GKRS multiplets in equivariant K-theory
Character formul?GKRS multiplets equivariant K-theory
2011/9/14
Abstract: Let $G$ be a compact Lie group, $H$ a closed subgroup of maximal rank and $X$ a topological $G$-space. We obtain a variety of results concerning the structure of the $H$-equivariant K-ring $...
Regularity of Schramm-Loewner Evolutions, annular crossings, and rough path theory
Schramm-Loewner Evolutions annular crossings rough path theory
2011/9/14
Abstract: When studying stochastic processes, it is often fruitful to have an understanding of several different notions of regularity. One such notion is the optimal H\"older exponent obtainable unde...