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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Deligne-Beilinson cohomology of the universal K3 surface
泛K3曲面 Deligne-Beilinson 同调
2023/5/15
O'Grady's generalized Franchetta conjecture is concerned with algebraic cycles of codimension 2 on the universal polarized K3 surface of genus g. This conjecture has been confirmed only for certain sm...
We discuss a method for curve estimation based on n noisy
data; one translates the empirical wavelet coecients towards the origin by
an amount p
2 log(n) =p
n. The method is nearly minimax for...
Brauer's generalized decomposition numbers and universal deformation rings
Universal deformation rings Brauer’s generalized decomposition numbers tame blocks dihedral defect groups semidihedral defect groups
2012/4/17
We study the problem of lifting to local rings certain mod 2 representations V of finite groups G which belong to 2-modular tame blocks B of G having at least two isomorphism classes of simple modules...
The universal Askey-Wilson algebra and the equitable presentation of $U_q(\mathfrak{sl}_2)$
Askey-Wilson relations Leonard pair Casimir element
2011/9/14
Abstract: Let $F$ denote a field, and fix a nonzero $q \in F$ such that $q^4\not=1$. The universal Askey-Wilson algebra is the associative $F$-algebra $\Delta=\Delta_q$ defined by generators and relat...
Integral Bases for the Universal Enveloping Algebras of Map Algebras
the Universal Enveloping Algebras Map Algebras Integral Bases Representation Theory
2011/8/26
Abstract: Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral f...
Universal equivalence of partially commutative metabelian Lie algebras
Lie algebras Universal equivalence Rings and Algebras
2011/8/23
Abstract: In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabel...
Universal deformation rings and dihedral blocks with two simple modules
Universal deformation rings dihedral defect groups special biserial algebras
2011/1/19
Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG with a dihedral
defect group D su...
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compre...
Universal Polynomials for Severi Degrees of Toric Surfaces
Enumerative geometry toric surfaces Gromov-Witten theory
2011/2/25
The Severi variety parameterizes plane curves of degree d with nodes.Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of CP2....
Stable cohomology of the universal Picard varieties and the extended mapping class group
moduli spaces Picard variety stable cohomology
2011/1/18
We compute the stable cohomology of the universal Picard stack Pic g ! M g, and also its Picard group. The degree zero Picard stack Pic0 g has homotopy type the classifying space of Kawazumi’s extende...
A topological space TO(S) of total orderings on any given set S is introduced and it is shown that TO(S) is compact if S is countable. The set NO(N) of all normal orderings of the nth Weyl algebra W ...
Universal central extensions of twisted forms of split simple Lie algebras over rings
Universal central extensions Lie algebras
2010/11/23
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central exten...
Splice Diagram Singularities and The Universal Abelian Cover of Graph Orbifolds
Splice Diagram Singularities The Universal Abelian Cover of Graph Orbifolds
2010/11/9
Given a rational homology sphere M, whose splice diagram satisfy the semigroup condition, Neumann and Wahl were able to define a complete intersection surface singularity called splice diagram singul...
On universal oracle inequalities related to high-dimensional linear models
On universal oracle inequalities high-dimensional linear models
2010/11/17
This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed tha...
Co-universal C*-algebras associated to generalised graphs
Higher rank graph co-universal algebra graph algebra Cuntz- Krieger algebra
2010/11/30
We introduce P-graphs, which are generalisations of directed graphs in which paths have a degree in a semigroup P rather than a length in N. We focus on semigroups P arising as part of a quasi-lattice...