저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plucker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

https://www.springer.com/productFlyer_978-0-387-22356-8.pdf?SGWID=0-0-1297-34952457-0

Combinatorial Commutative Algebra

Groupes et algébres de lie

Let G be an inner form of a general linear group over a non-archimedean local field. We prove that the local Langlands correspondence for G preserves depths. We also show that the local Langlands correspondence for inner forms of special linear groups preserves the depths of essentially tame Langlands parameters.

Progress in Mathematics

Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these integrals from the standard descendent potential (for any target X). We use virtual localization and classical degeneracy calculations to find trigonometric closed form solutions for special Hodge integrals over the moduli space of pointed curves. These formulas are applied to two computations in Gromov-Witten theory for Calabi-Yau 3-folds. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g. The genus g, degree 0 Gromov-Witten invariant is calculated (in agreement with recent string theoretic calculations of Gopakumar-Vafa and Marino-Moore). Finally, with Zagier's help, our Hodge integral formulas imply a general genus prediction of the punctual Virasoro constraints applied to the projective line.

Hodge integrals and Gromov-Witten theory

1 Department of Mathematics, University of Stockholm, S-10691, Stockholm, Sweden (e-mail: teke@matematik.su.se) 2 Higher College of Mathematics, Independent University of Moscow and Institute for System Research RAS, Moscow, Russia (e-mail: lando@mccme.ru) 3 Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden (e-mail: mshapiro@math.kth.se) 4 Department of Mathematics and Department of Computer Science, University of Haifa, Haifa 31905, Israel (e-mail: alek@mathcs.haifa.ac.il)

https://www-users.math.umn.edu/~reiner/Classes/Math8680Fall2014Papers/EkedahlLandoShapiroVainshtein.pdf

Hurwitz numbers and intersections on moduli spaces of curves

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Canonical models of surfaces of general type in positive characteristic

This article is concerned with developing a formalism for complexes of l-adic sheaves instead of just for the sheaves themselves as was done in [SGA5:Exp.V]. The need for such a generalisation has become apparent from the theory of perverse sheaves, which by their definition are complexes of l-adic sheaves. When trying to carry through such an extension one is immediately faced with two problems. On the one hand it is clear already from the case of l-adic sheaves that — contrary to the case of torsion sheaves — one is not dealing with actual sheaves but rather inverse systems of sheaves. On the other hand one wants to pretend that one is dealing with sheaves and not some more abstract objects.

On The Adic Formalism

In this paper we find an explicit formula for the number of topologically different ramified coverings C → CP1 (C is a compact Riemann surface of genus g) with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.

On Hurwitz numbers and Hodge integrals

We introduce a Grothendieck group of algebraic stacks (with affine stabilisers) analogous to the Grothendieck group of algebraic varieties. We then identify it with a certain localisation of the Grothendieck group of algebraic varieties. Several invariants of elements in this group are discussed. The most important is an extension of the Euler characteristic (of cohomology with compact support) but in characteristic zero we introduce invariants which are able to distinguish between classes with the same Euler characteristic. These invariants are actually defined on the completed localised Grothendieck ring of varieties used in motivic integration. In particular we show that there are $\PSL_n$-torsors of varieties whose class in the completed localised Grothendieck ring of varieties is not the product of the class of the base and the class of $\PSL_n$.

Torsten Ekedahl

Papers

Hurwitz numbers and intersections on moduli spaces of curves

Canonical models of surfaces of general type in positive characteristic

On The Adic Formalism

On Hurwitz numbers and Hodge integrals

The Grothendieck group of algebraic stacks