Now showing items 21-27 of 27

• #### Positivity of the T-system cluster algebra ﻿

[OWP-2009-21] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-14)
We give the path model solution for the cluster algebra variables of the $A_r$ T-system with generic boundary conditions. The solutions are partition functions of (strongly) non-intersecting paths on weighted graphs. The ...
• #### On the distribution of a second class particle in the asymmetric simple exclusion process ﻿

[OWP-2009-22] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-15)
We give an exact expression for the distribution of the position $X(t)$ of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin ...
• #### On Siegel modular forms of level p and their properties mod p ﻿

[OWP-2009-23] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-16)
Using theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 ...
• #### Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich ﻿

[OWP-2009-24] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-17)
We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture ...
• #### A new counting function for the zeros of holomorphic curves ﻿

[OWP-2009-25] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-18)
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the ...
• #### Weighted Fourier inequalities for radial functions ﻿

[OWP-2009-26] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-19)
Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function.
• #### Optimal bounds for the colored Tverberg Problem ﻿

[OWP-2009-27] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-20)
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color ...