Name of the Speakers with their affiliation.

No. of Lectures

Detailed Syllabus

Simon Marshall

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA

3 Hours

Periods and restrictions of eigenfunctions on locally symmetric spaces: A brief introduction to Hecke theory for SL(2,Z), and describe the method of arithmetic amplification, which uses Hecke operators to give improved bounds for periods and L^p restrictions.

Toshiyuki Kobayashi

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Tokyo 153-8914, Japan

6 Hours

Harish-Chandra’s tempered representations and geometry and Harish-Chandra’s admissibility theorem and beyond.

Amos Nevo

Technion-Israel Institute of Technology, Haifa, 32000 Israel

6 Hours

Representation theory, Harmonic analysis, and intrinsic Diophantine approximation on homogeneous varieties.  The spectral approach to Diophantine approximation averaging operators in dynamical systems, unitary representations, spectral estimates, and operator norm bounds. 

A brief introduction to some aspects of the representation theory of semisimple algebraic groups and the integrability of their matrix coefficients. The spectral transfer principle and effective ergodic theorems. The automorphic representation associated with a lattice subgroup, and effective counting of lattice points. Best possible spectral estimates for subgroup actions.  

Lattice actions on homogeneous spaces and fast equidistribution of dense lattice orbits. Intrinsic Diophantine approximation on homogeneous algebraic varieties, and best possible exponent for tempered subgroups. The effective duality principle on homogeneous spaces.  

Bernhard Krötz

Institute für Mathematik, Universität Paderborn, Germany

6 Hours

Plancherel theory for real spherical spaces: Harish-Chandra's Plancherel formula for real reductive groups G. Harish-Chandra's Plancherel formula up to the formal degrees of the discrete series as well as the theorem of Delorme and van den Ban-Schlichtkrull for symmetric spaces.

Jyoti Sengupta

Department of Mathematics, Indian Association for the Cultivation Of Science, Kolkata 700032, India

6 Hours

The Fourier transform on semisimple Lie Algebras and Lie groups. Ramifications and Applications.

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