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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Exact Formulas of the KPZ Fixed Point and Directed Landscape
KPZ不动点 定向景观 精确公式
2023/4/18
In the past twenty years, there have been huge developments in the study of the Kardar-Parisi-Zhang (KPZ) universality class, which is a broad class of physical and probabilistic models including one-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic mixed Siegel-Weil formulas and modular forms of arithmetic divisors
算术混合 西格尔-威尔公式 算术除数 模形式
2023/5/5
The classical Siegel–Weil formula relates theta series to Eisenstein series and its arithmetic version is central in Kudla's program. I will discuss arithmetic mixed Siegel-Weil formulas. I will focus...
GIAMBELLI AND DEGENERACY LOCUS FORMULAS FOR CLASSICAL G/P SPACES
LOCUS FORMULAS GIAMBELLI
2015/12/17
Let G be a classical complex Lie group, P any parabolic subgroup
of G, and X = G/P the corresponding homogeneous space, which parametrizes
(isotropic) partial flags of subspaces of a fix...
DOUBLE THETA POLYNOMIALS AND EQUIVARIANT GIAMBELLI FORMULAS
EQUIVARIANT GIAMBELLI FORMULAS DOUBLE THETA POLYNOMIALS
2015/12/17
We use Young’s raising operators to introduce and study double
theta polynomials, which specialize to both the theta polynomials of Buch,
Kresch, and Tamvakis, and to double (or factorial) Schur S-p...
DOUBLE ETA POLYNOMIALS AND EQUIVARIANT GIAMBELLI FORMULAS
DOUBLE ETA POLYNOMIALS EQUIVARIANT GIAMBELLI FORMULAS
2015/12/17
We use Young’s raising operators to introduce and study double
eta polynomials, which are an even orthogonal analogue of Wilson’s double
theta polynomials. Our double eta polynomials give Giambelli ...
HEIGHT FORMULAS FOR HOMOGENEOUS VARIETIES
HOMOGENEOUS VARIETIES Differential and integral calculus
2015/12/17
We use classicalSchubert calculus to evaluate the integral formula
of Kaiser and Kohler [KK] for the Faltings height of certain homogeneous
varieties in terms of combinatorial data, and verify thei...
Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a
permutation.
Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
Fulton's universal Schubert polynomials give cohomology formulas
for a class of degeneracy loci, which generalize Schubert varieties. The Ktheoretic quiver formula of Buch expresses the structure she...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
2015/12/17
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
GIAMBELLI, PIERI, AND TABLEAU FORMULAS VIA RAISING OPERATORS
GIAMBELLI PIERI TABLEAU FORMULAS
2015/12/17
We give a direct proof of the equivalence between the Giambelli
and Pieri type formulas for Hall-Littlewood functions using Young’s raising operators, parallel to joint work with Buch and Kresch for ...
QUANTUM GIAMBELLI FORMULAS FOR ISOTROPIC GRASSMANNIANS
ISOTROPIC GRASSMANNIANS Vector space
2015/12/17
Let X be a symplectic or odd orthogonal Grassmannian which
parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas ...
Formulas for the force dipole interaction of surface line defects in homoepitaxy
Formulas for the force surface line defects homoepitaxy
2015/10/16
Using asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between line defects (steps) of the same sign that form pertur...
One-dimensional model of interacting-step fluctuations on vicinal surfaces:Analytical formulas and kinetic Monte Carlo simulations
One-dimensional model interacting-step fluctuations vicinal surfaces Analytical formulas kinetic Monte Carlo simulations
2015/10/16
We study analytically and numerically a one-dimensional model of interacting line defects steps fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for appr...
Data compression and definability of types in stable and dependent formulas
Data compression formulas
2015/9/28
Data compression and definability of types in stable and dependent formulas.