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Seminars on Harmonic Analysis

Academic year 2025/26

Many lectures during the summer semester of the year 2024/25 were devoted to presentation of Chapters 6 - 10 of the book E. Meinrenken: Clifford algebras and Lie Theory, Springer, Series of modern surveys in Mathematics, vol 58, see below. Chapter 11 of this book with the title 'Clifford algebra of a reductive Lie algebra' will be presented in further lectures during this semester.

Oct 3 - Andrey Krutov: Group valued moment maps for even and odd simple G-modules; video
Oct 10 - Andrey Krutov: Transgression theorem; video
Oct 17 - Andrey Krutov: Hopf-Koszul-Samelson and transgression theorems I.; video
Oct 24 - Andrey Krutov: Hopf-Koszul-Samelson and transgression theorems II.; video

Academic year 2024/25

Seminar program

Oct 4 - Andrey Krutov: Equivariant cohomology I; video
Oct 11 - Andrey Krutov: Equivariant cohomology II; video
Oct 18 - Andrey Krutov: Weil algebra(s); video
Nov 1 - Andrey Krutov: Weil algebra II; video
Nov 8 - Andrey Krutov: Transgression in Weil algebras; video
Nov 15 - Libor Křižka: Quantization of Poisson algebras; video
Nov 29 - Libor Křižka: Quantum Weil algebras; video
Dec 6 - Libor Křižka: Weil algebras and cubic Dirac operator; video
Dec 13 - Libor Křižka: Cubic Dirac operators; video
Jan 10 - Libor Křižka: Duflo's theorem; video
Feb 21 - Libor Křižka: Duflo's theorem and its applications; video
Feb 28 - Karmen Grizelj: Harish-Chandra maps I.; video
Mar 7 - Karmen Grizelj: Harish-Chandra maps II.; video
Mar 14 - Andrey Krutov: Applications of Dirac operators; video
Mar 28 - Andrey Krutov: Dirac induction I; video
Apr 4 - Andrey Krutov: Dirac induction II; video
Apr 11 - Andrey Krutov: D(g,k) as a geometric Dirac operator I.; video
Apr 25 - Andrey Krutov: D(g,k) as a geometric Dirac operator II.; video

Academic year 2023/24

In the winter term, we follow mostly the book Neil Chriss, Victor Ginzburg: Representation Theory and Complex Geometry, Birkhauser, 1997.

Oct 6 - R. Golovko: Symplectic manifolds and Poisson algebras; video
Oct 20 - R. Golovko: Poisson structures arising from noncommutative algebras and the moment map; video
Oct 27 - R. Golovko: The moment map, coisotropic subvarieties and Lagrangian families 1; video
Nov 3 - R. Golovko: The moment map, coisotropic subvarieties and Lagrangian families 2; video
Nov 10 - Vít Tuček: Algebraic geometry 1; video
Nov 24 - Vít Tuček: Algebraic geometry 2; video
Dec 8 - Daniel Beďatš: Scalar-valued separation of variables in the non-stable range; video
Jan 5 - Vít Tuček: The deformation construction; video
Jan 12 - Andrey Krutov, Vít Tuček: C^* actions on projective varieties and fixed point reductions; video
Feb 23 - Andrey Krutov: Borel-Moore homology I; video
Mar 1 - Andrey Krutov: Borel-Moore homology II; video
Mar 8 - Andrey Krutov: Borel-Moore homology III; video
Mar 22 - Andrey Krutov: Convolution in Borel-Moore homology; video
Apr 5 - Hans-Peter Schroecker: Factorization of polynomials over Clifford algebras; video
Apr 12 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group I; video
Apr 19 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group II; video
Apr 26 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group III; video
May 3 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group IV; video
May 10 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group V; video
May 17 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group VI; video
May 24 - Vladimir Souček: Complex simple Lie algebras , flag manifolds and representations of the Weyl group VII; video

Academic year 2022/23

Oct 5 - A. Merino: Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup; video
Oct 14 - S. Afentoulidis-Almpanis: Motivation from the BGG category O, Coxeter systems; video
Nov 4 - S. Afentoulidis-Almpanis: Coxeter systems - Examples and geometric representation; video
Nov 11 - S. Afentoulidis-Almpanis: Coxeter systems - Affine reflection Groups (Part 1); video
Nov 18 - S. Afentoulidis-Almpanis: Coxeter systems - Affine reflection Groups (Part 2); video
Nov 25 - R. Lávička: Coxeter systems - general theory (Part 1); video
Dec 2 - R. Lávička: Coxeter systems - general theory (Part 2); video
Dec 9 - R. Lávička: Coxeter systems - general theory (Part 3); video
Dec 16 - Asmus K. Bisbo: Spinor-valued polynomials in non-commuting variables; video
Jan 6 - S. Afentoulidis-Almpanis: Matsumoto's theorem - Hyperbolic disc and Coxeter systems; video
Feb 17 - V. Souček: Hecke algebra of a Coxeter system, part 1; video
Feb 24 - M. Zimmermann: Introduction to q-deformed Clifford Analysis; video
Mar 10 - V. Souček: Hecke algebra of a Coxeter system, part 2; video
Mar 24 - V. Souček: Hecke algebra of a Coxeter system, part 3; video
Mar 31 - V. Souček: Hecke algebra of a Coxeter system, part 4; video
Apr 14 - V. Souček: Hecke algebra of a Coxeter system, part 5; video
Apr 21 - Libor Křižka: Introduction to Soergel bimodules, part 1; video
Apr 28 - Libor Křižka: Introduction to Soergel bimodules, part 2; video
May 5 - Libor Křižka: Introduction to Soergel bimodules, part 3; video
May 12 - S. Afentoulidis-Almpanis: The classical theory of Soergel bimodules I; video (the beginning of the lecture is contained at the end of the previous video)
May 26 - S. Afentoulidis-Almpanis: The classical theory of Soergel bimodules II; video

Academic year 2021/22

Oct 8 - S. Afentoulidis-Almpanis: Introduction to category O, part 1; video
Oct 15 - S. Afentoulidis-Almpanis: Introduction to category O, part 2; video
Oct 22 - I. Penkov: Automorphism groups of ind-varieties of generalized flags; video
Nov 5 - S. Afentoulidis-Almpanis: Introduction to category O, part 3; video
Nov 12 - R. Lávička: Introduction to category O, part 4; video
Nov 19 - R. Lávička/L. Křižka: Introduction to category O, part 5; video
Nov 26 - L. Křižka: Introduction to category O, part 6; video
Dec 3 - L. Křižka: Introduction to category O, part 7; video
Dec 17 - V. Tuček: Introduction to category O, part 8; video
Mar 18 - S. Afentoulidis-Almpanis: Homological dimension and Extensions in the category O; video
Mar 25 - V. Souček: Duality between algebraic and geometric versions of BGG complexes I.; video
Apr 8 - V. Souček: Duality between algebraic and geometric versions of BGG complexes II.; video
Apr 22 - S. Afentoulidis-Almpanis: Translation functors in the category O; video
Apr 29 - S. Afentoulidis-Almpanis: Translation functors in the category O, part 2; video
May 6 - S. Afentoulidis-Almpanis: Translation functors in the category O, part 3; video
May 20 - S. Afentoulidis-Almpanis: Translation functors in the category O, part 4; video

Academic year 2020/21

Oct 30 - Vít Tuček: Holomorphic functions on non-compact hermitian symmetric spaces and unitarizable highest weight representations; video
Nov 6 - Vít Tuček: Representation on the space of holomorphic functions on the Siegel domain; video
Nov 13 - Vít Tuček: Pluriharmonic polynomials; video
Nov 20 - Vladimír Souček: The Nishiyama oscillator representation of the super Lie algebra osp(m,2n), I.; video
Nov 27 - Vladimír Souček: The Nishiyama oscillator representation of the super Lie algebra osp(m,2n), II.; video
Dec 4 - Vladimír Souček: The Nishiyama oscillator representation of the super Lie algebra osp(m,2n), III.; video
Dec 11 - Pavle Pandžič: Unitary representations of the Lie superalgebra osp(n,2k); video
Dec 18 - Vladimír Souček: On certain unitary representations of Lie superalgebra osp(1,2n); video
Jan 8 - Pavle Pandžič: Unitary representations of the Lie superalgebra osp(n,2k), part 2; video
Mar 19 - Libor Křižka: Chiral differential operators I.; video
Mar 26 - Libor Křižka: Chiral differential operators II.; video
Apr 9 - Libor Křižka: Chiral differential operators III.; video
May 28 - S. Afentoulidis-Almpanis: Noncubic Dirac operators for finite-dimensional modules; video