Science China Mathematics, ISSN 1674-7283, 11/2019, Volume 62, Issue 11, pp. 2409 - 2422

This is an expository article on the recent progress on the arithmetic fundamental lemma conjecture, based largely on Zhang (2019...

relative trace formula | Gross-Zagier formula | Mathematics | arithmetic fundamental lemma | 11G40 | Applications of Mathematics | arithmetic Gan-Gross-Prasad conjecture | 14G35 | 11F67

relative trace formula | Gross-Zagier formula | Mathematics | arithmetic fundamental lemma | 11G40 | Applications of Mathematics | arithmetic Gan-Gross-Prasad conjecture | 14G35 | 11F67

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2017, Volume 11, Issue 10, pp. 2425 - 2445

W. Zhang's arithmetic fundamental lemma (AFL) is a conjectural identity between the derivative of an orbital integral on a symmetric space with an arithmetic intersection number on a unitary Rapoport-Zink space...

Special cycles | Arithmetic fundamental lemmas | Arithmetic Gan–Gross–Prasad conjectures | Rapoport–Zink spaces | MATHEMATICS | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjectures | arithmetic fundamental lemmas

Special cycles | Arithmetic fundamental lemmas | Arithmetic Gan–Gross–Prasad conjectures | Rapoport–Zink spaces | MATHEMATICS | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjectures | arithmetic fundamental lemmas

Journal Article

02/2019, ISBN 9780691181387, 281

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical...

Mathematics | Combinatorial number theory

Mathematics | Combinatorial number theory

eBook

Compositio mathematica, ISSN 0010-437X, 10/2013, Volume 149, Issue 10, pp. 1631 - 1666

The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p...

arithmetic fundamental lemma | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjecture | MATHEMATICS | Mathematics | Arithmetic

arithmetic fundamental lemma | Rapoport-Zink spaces | special cycles | arithmetic Gan-Gross-Prasad conjecture | MATHEMATICS | Mathematics | Arithmetic

Journal Article

Annali di matematica pura ed applicata, ISSN 1618-1891, 2010, Volume 190, Issue 3, pp. 539 - 551

.... By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of...

Fundamental theorem of algebra | Functions of a hypercomplex variable | Quaternions | Octonions | Mathematics, general | 30G35 | 32A30 | Mathematics | 30C15 | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | FUNDAMENTAL THEOREM | ALGEBRA | SETS

Fundamental theorem of algebra | Functions of a hypercomplex variable | Quaternions | Octonions | Mathematics, general | 30G35 | 32A30 | Mathematics | 30C15 | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | FUNDAMENTAL THEOREM | ALGEBRA | SETS

Journal Article

Mathematische Zeitschrift, ISSN 1432-1823, 2007, Volume 258, Issue 2, pp. 395 - 406

We improve Margulis lemma for a compact connected Lie group G: there is a neighborhood U of the identity such that for any finite subgroup $$\Gamma\subset G$$ , $$U\cap \Gamma...

Mathematics, general | Mathematics | MATHEMATICS | MANIFOLDS | FUNDAMENTAL-GROUPS | SPACES | NONNEGATIVE CURVATURE

Mathematics, general | Mathematics | MATHEMATICS | MANIFOLDS | FUNDAMENTAL-GROUPS | SPACES | NONNEGATIVE CURVATURE

Journal Article

Canadian journal of mathematics, ISSN 0008-414X, 08/2018, Volume 70, Issue 4, pp. 898 - 924

In this paper, we prove the spherical fundamental lemma for metaplectic group $M{{p}_{2n}}$ based on the formalism of endoscopy theory by J...

Elliptic stable trace formula | Endoscopic group | Metaplectic group | Fundamental lemma | metaplectic group | endoscopic group | P-ADIC GROUPS | MATHEMATICS | elliptic stable trace formula | REPRESENTATIONS | THEOREM | REDUCTIVE GROUPS | fundamental lemma | TRACE FORMULA

Elliptic stable trace formula | Endoscopic group | Metaplectic group | Fundamental lemma | metaplectic group | endoscopic group | P-ADIC GROUPS | MATHEMATICS | elliptic stable trace formula | REPRESENTATIONS | THEOREM | REDUCTIVE GROUPS | fundamental lemma | TRACE FORMULA

Journal Article

Neutrosophic sets and systems, ISSN 2331-6055, 12/2019, Volume 30, pp. 44 - 69

... and Burnside’s lemma of NET group. We introduce NET orbits, stabilizers, conjugates and NET group action...

net group action; net orbit; net stabilizer; net conjugate; burnside’s lemma; net fixed points; the fundamental theorem about net group action

net group action; net orbit; net stabilizer; net conjugate; burnside’s lemma; net fixed points; the fundamental theorem about net group action

Journal Article

Mathematische Zeitschrift, ISSN 1432-1823, 2017, Volume 287, Issue 1-2, pp. 181 - 197

We prove that the arithmetic fundamental lemma conjecture (AFL) of Wei Zhang is equivalent to a similar conjecture, but for Lie algebras, in the case of non-degenerate intersection...

14G17 | Intersection product | Unitary Rapoport–Zink space | 11G18 | Mathematics, general | Mathematics | Arithmetic fundamental lemma | 14G40 | Orbital integral | MATHEMATICS | ENDOMORPHISMS | Unitary Rapoport-Zink space | Algebra

14G17 | Intersection product | Unitary Rapoport–Zink space | 11G18 | Mathematics, general | Mathematics | Arithmetic fundamental lemma | 14G40 | Orbital integral | MATHEMATICS | ENDOMORPHISMS | Unitary Rapoport-Zink space | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 05/2014, Volume 406, pp. 251 - 271

We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have κ...

Fundamental groups of graphs of groups | Systems of equations | Geometric and combinatorial group theory | k-Acylindricity | Algorithmic bounds | K-Acylindricity | MATHEMATICS | Algorithms | Mathematics - Group Theory

Fundamental groups of graphs of groups | Systems of equations | Geometric and combinatorial group theory | k-Acylindricity | Algorithmic bounds | K-Acylindricity | MATHEMATICS | Algorithms | Mathematics - Group Theory

Journal Article

Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 10/2019, Volume 2019, Issue 755, pp. 1 - 65

To every singular reduced projective curve one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on...

MATHEMATICS | BUNDLES | REPRESENTATIONS | THEOREM | MODULI SPACE | DUALITY | SPECTRAL CURVES | FUNDAMENTAL LEMMA | TRANSFORMS

MATHEMATICS | BUNDLES | REPRESENTATIONS | THEOREM | MODULI SPACE | DUALITY | SPECTRAL CURVES | FUNDAMENTAL LEMMA | TRANSFORMS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2017, Volume 369, Issue 8, pp. 5341 - 5402

To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which...

Locally planar singularities | Abel map | Compactified jacobians | MATHEMATICS | SCHEME | AUTODUALITY | BUNDLES | locally planar singularities | Compactified Jacobians | DUALITY | ABEL MAPS | FUNDAMENTAL LEMMA

Locally planar singularities | Abel map | Compactified jacobians | MATHEMATICS | SCHEME | AUTODUALITY | BUNDLES | locally planar singularities | Compactified Jacobians | DUALITY | ABEL MAPS | FUNDAMENTAL LEMMA

Journal Article

Algebraic Geometry, ISSN 2313-1691, 01/2018, Volume 5, Issue 1, pp. 77 - 113

.... In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a G-equivariant morphism f : X...

Luna's fundamental lemma | Diagonalizable groups | MATHEMATICS | FACTORIZATION | HOMOMORPHISMS | QUILLEN | diagonalizable groups | BIRATIONAL MAPS | TORIFICATION | HOMOLOGY | SCHEMES

Luna's fundamental lemma | Diagonalizable groups | MATHEMATICS | FACTORIZATION | HOMOMORPHISMS | QUILLEN | diagonalizable groups | BIRATIONAL MAPS | TORIFICATION | HOMOLOGY | SCHEMES

Journal Article

Advances in Differential Equations, ISSN 1079-9389, 11/2018, Volume 23, Issue 11-12, pp. 889 - 908

In the paper, we derive a fractional version of the Du BoisReymond lemma for a generalized Riemann-Liouville derivative...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | ORDER ALPHA | VARIATIONAL CALCULUS | TERMS | FORMULA | EULER-LAGRANGE EQUATIONS | DERIVATIVES | FUNDAMENTAL LEMMA

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | ORDER ALPHA | VARIATIONAL CALCULUS | TERMS | FORMULA | EULER-LAGRANGE EQUATIONS | DERIVATIVES | FUNDAMENTAL LEMMA

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6169 - 6212

This article gives a proof of the Langlands-Shelstad fundamental lemma for the spherical Hecke algebra for every unramified p-adic reductive group G in large positive characteristic...

MATHEMATICS | ENDOSCOPY | FUNDAMENTAL LEMMA

MATHEMATICS | ENDOSCOPY | FUNDAMENTAL LEMMA

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2016, Volume 438, Issue 1, pp. 274 - 284

A triple of commuting operators for which the closed tetrablock E‾ is a spectral set is called a tetrablock contraction or an E-contraction. The set E is...

Fundamental operators | Operator model | Tetrablock contraction | Canonical decomposition | MATHEMATICS | MATHEMATICS, APPLIED | SCHWARZ-LEMMA

Fundamental operators | Operator model | Tetrablock contraction | Canonical decomposition | MATHEMATICS | MATHEMATICS, APPLIED | SCHWARZ-LEMMA

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 6/2013, Volume 192, Issue 3, pp. 627 - 661

.... In combination with a general base-change lemma in harmonic analysis, we use this to prove a conjecture of Haines and Kottwitz for these Shimura varieties.

Mathematics, general | Mathematics | MATHEMATICS | REPRESENTATIONS | FUNDAMENTAL LEMMA | Fourier analysis

Mathematics, general | Mathematics | MATHEMATICS | REPRESENTATIONS | FUNDAMENTAL LEMMA | Fourier analysis

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 06/2012, Volume 62, Issue 6, pp. 720 - 735

A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary...

Domain integral | Poisson equation | Poincaré lemma | Fundamental theorem of calculus | Newton potential | Boundary element method | Poincare lemma | MATHEMATICS, APPLIED | SPACES | BEM | EQUATION | ONLY DISCRETIZATION | Theorems | Integrals | Mathematical analysis | Calculus | Boundaries | Three dimensional | SOURCE TERMS | BOUNDARY-VALUE PROBLEMS | INTEGRAL EQUATIONS | GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE | QUADRATURES | EUCLIDEAN SPACE | BOUNDARY ELEMENT METHOD | POISSON EQUATION | INTEGRAL TRANSFORMATIONS

Domain integral | Poisson equation | Poincaré lemma | Fundamental theorem of calculus | Newton potential | Boundary element method | Poincare lemma | MATHEMATICS, APPLIED | SPACES | BEM | EQUATION | ONLY DISCRETIZATION | Theorems | Integrals | Mathematical analysis | Calculus | Boundaries | Three dimensional | SOURCE TERMS | BOUNDARY-VALUE PROBLEMS | INTEGRAL EQUATIONS | GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE | QUADRATURES | EUCLIDEAN SPACE | BOUNDARY ELEMENT METHOD | POISSON EQUATION | INTEGRAL TRANSFORMATIONS

Journal Article

Inventiones Mathematicae, ISSN 0020-9910, 05/2017, Volume 208, Issue 2, pp. 501 - 552

We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that...

MATHEMATICS | ARITHMETIC QUOTIENTS | K-3 SURFACES | REPRESENTATIONS | PRODUCTS | K3 SURFACES | PICARD-GROUPS | VARIETIES | MODULI SPACE | AUTOMORPHIC-FORMS | FUNDAMENTAL LEMMA | Manifolds | Homology | Arithmetic | Theorems

MATHEMATICS | ARITHMETIC QUOTIENTS | K-3 SURFACES | REPRESENTATIONS | PRODUCTS | K3 SURFACES | PICARD-GROUPS | VARIETIES | MODULI SPACE | AUTOMORPHIC-FORMS | FUNDAMENTAL LEMMA | Manifolds | Homology | Arithmetic | Theorems

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2016, Volume 85, Issue 298, pp. 907 - 929

In the 1980s Bocherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin L-function attached to a Siegel modular...

MATHEMATICS, APPLIED | NOVODVORSKY SUBGROUPS | FOURIER COEFFICIENTS | SIEGEL MODULAR-FORMS | BESSEL | FUNDAMENTAL LEMMA | CONJECTURE

MATHEMATICS, APPLIED | NOVODVORSKY SUBGROUPS | FOURIER COEFFICIENTS | SIEGEL MODULAR-FORMS | BESSEL | FUNDAMENTAL LEMMA | CONJECTURE

Journal Article

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