Every Brieskorn homology sphere (p; q; r) is a double cover of the 3{sphere ramiied over a Montesinos knot k(p; q; r). We relate Floer homology of (p; q; r) to certain invariants of the knot k(p; q; r), among which are the knot signature and the Jones polynomial. We also deene an integer valued invariant of integral homology 3{spheres which agrees with the {invariant of W. Neu-mann and L. Siebe...

In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a para...

We describe the emergence of a nephropathogenic avian infectious bronchitis virus (IBV) with a novel genotype in India. The Indian IBV isolate exhibited a relatively high degree of sequence divergence with reference strains. The highest homology was observed with strain 6/82 (68%) and the least homology with strain Mex/1765/99 (34.3%).

We introduce several geometric notions, including the width of a homology class, to theory persistent homology. These ideas provide interpretations persistence diagrams. Indeed, we give quantitative and descriptions “life span” or “persistence” class. As case study, analyze power filtration on unweighted graphs explicit bounds for life spans classes in diagrams all dimensions.

Speaker: Petter Andreas Bergh (NTNU) Title: Hochschild (co)homology of quantum complete intersections Abstract: This is joint work with Karin Erdmann. We construct a minimal projective bimodule resolution for finite dimensional quantum complete intersections of codimension 2. Then we use this resolution to compute the Hochschild homology and cohomology for such an algebra. In particular, we sho...

Contact homology for Legendrian submanifolds in standard contact (2n + 1)space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. The homology provides new invariants of Legendrian isotopy. These invariants show that the theory of Legendrian isotopy is very rich. For example, they detect infinite families of pairwise non-isotop...

Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of representatives. The mentioned representatives are geometric manifestations corresponding holes and often carry desirable information.We propose a new method using In summary, we first compute cohomology use obtained informat...

Dynamic programming [1] has full sensitivity, but too slow for large scale homology search. FASTA / BLAST type of heuristics [2] trade sensitivity for speed. Can we have both sensitivity and speed? We present the mathematical theory of optimized spaced seeds which allows modern homology search to achieve high sensitivity and high speed simultaneously. The spaced seed methodology is implemented ...