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We consider the set C of pairs of real numbers (x, y), or equivalently of points on the plane R2. Two vectors z1 = (x1, x2) and z2 = (x2, y2) are equal if and only if x1 = x2 and y1 = y2. Two vectors ...
Trace formulas for Schroinger operators from the view point of complex analysis
Schrodinger operators trace formula eigenvalues resonances Spectral Theory
2011/9/6
Abstract: We consider the Schr{\"o}dinger operator $-\Delta +V(x)$ in $L^2({\bf R}^3)$ with a real short-range (integrable) potential $V$. Using the associated Fredholm determinant, we present new tra...
Applications of Differential Chains to Complex Analysis and Dynamics
Differential Chains Complex Analysis Dynamics
2011/2/28
First and foremost, I would like to thank my advisor Sarah Koch for being so generous with her time and energy.
Discrete Complex Analysis and Probability
Discrete complex analysis discrete analytic function Ising model
2010/12/15
We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl...