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Minicourses
 2017

Past minicourses
 2016

2015
 The Quantum ManyBody Problem and BoseEinstein Condensation
 PreAlpbach Minicourse  Special cycles on Shimura curves
 Aspects of nonlocal regularity theory
 Recent progress in nonasymptotic random matrix theory
 Risk aggregation and Fréchet problems
 On irregular singularities of algebraic connections
 Multiplicatively defined sets with additive structure
 2014

2013
 Optimal transport and hedging
 The Boltzmann Equation and Harmonic Analysis
 SNF ProDoc Minicourse on "Numerik"
 Quantitative stochastic homogenization of HamiltonJacobi equations
 Current Subcategory: Holomorphic maps between bounded domains which preserve invariant forms
 Propagation of chaos and irreversibility for systems of particles in the low density limit

2012
 Stochastic Variational Analysis
 Hall algebras, Cherednik algebras and Walgebras
 Causal Graphical Models and Counterfactuals
 Topics in Noncommutative Geometry
 Polygonal Billiards and Teichmüller Dynamics
 SNF Prodoc Minicourses on Numerics
 Gluing methods for geometric PDE
 A quantitative isoperimetric inequality in higher codimension
 2011
 2010
 Nachdiplom lectures
Holomorphic maps between bounded domains which preserve invariant forms
Main content
Prof. Ngaiming Mok (The University of Hong Kong)
May 30, 2013, 15:15  17:00, HG G 19.2
Holomorphic isometries on bounded domains
(ProDoc Seminar, see here www.arithgeo.ethz.ch/prodocseminar/index)
May 31, 2013, 14:15  15:15, HG G 43
Germs of measurepreserving holomorphic maps from bounded symmetric domains to their Cartesian products
(Number Theory Seminar, see here: www.math.ethz.ch/arithmetikgeometrie/seminars)
Abstract
Consider a germ of holomorphic isometry \(f: (X,ds_X^2;x_0)\to (Y,ds_Y^2;y_0)\) between Kähler manifolds \((X,ds_X^2)\) and \((Y,ds_Y^2)\) equipped with realanalytic Kähler metrics. When \(X\) is simplyconnected and \((Y,ds_Y^2)\) is a complete Kähler manifold, Calabi proved in his seminal work on holomorphic isometries that \(f\) extends to a global holomorphic isometric immersion. He also proved rigidity results when \(Y\) is a space form, including the case of \(\Bbb P^N, 1 \le N \le \infty,\) equipped with the FubiniStudy metric. Motivated by differentialgeometric questions raised by ClozelUllmo in connection to a problem in arithmetic dynamics concerning commutants of certain Hecke correspondences, we consider the analytic continuation of germs of holomorphic isometries between bounded domains equipped with multiples of the Bergman metric, and also of holomorphic measurepreserving maps from a bounded symmetric domain into its Cartesian products. Building upon the works of Calabi and results in CRgeometry by WebsterHuang, we have developed techniques of analytic continuation using Kähler geometry and several complex variables which in particular answer the aforementioned questions. This serves to illustrate that there is fertile soil in the interaction between complex geometry and problems of arithmetic and algebrogeometric origin, especially those concerning bounded symmetric domains and their finitevolume quotients including various modular varieties.