BIMSA

The algebraic approach to complex analysis, the D-module language, was pioneered by the Japanese school (Kashivara, Sato,...) and found applications in a wide variety of subjects. One of the analytic results in the theory is due to P. Schapira and J.-P. Schneiders, (Index theorem for elliptic pairs, Elliptic pairs II, Asterisque vol. 224, 1994.) As the title suggests, they gave conditions for ellipticity of holonomic modules, and formulated a conjecture giving the value of the index of such elliptic system. This should be understood as a very general reformation of the classical Riemann-Roch theorem which computes the Euler characteristic of a holomorphic vector bundle on a compact complex manifold. In this series of lectures we will review basic elements of the theory of D-modules and develop it sufficiently to end up with the proof of the Schapira-Schneider conjecture..
It is in some way a continuation of the previous lectures on non-commutative calculus, since the final formulas use the same type of arguments as those in the proofs of algebraic index theorem.
The course will be based on the lecture notes of Bernstein "Algebraic theory of D-modules", "Lectures on algebraic D-modules" by Alexander Braverman and Tatyana Chmutova" and two older papers on the Riemann-Roch theorem for D-modules, Bresler, Nest, Tsygan, "RiemannRoch Theorems via Deformation Quantization, I, II", Advances in Mathematics 167, Issue 1 (2002) pp. 1-25 and pp. 26-73.

2025年02月19日至 04月16日

Weekday	Time	Venue	Online	ID	Password
周三,周四	10:40 - 12:15	A3-2-301	Zoom 15	204 323 0165	BIMSA

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英文

I am interested in non-commutative geometry in the widest sense. Some topics that I have been involved in:
• The C*-algebraic picture of the standard model, approach to quantum gravity and structure of Quantum Groups;
• Non-commutative probability, von Neumann algebras and applications to the invariants of three manifolds, and TQFT;
• Equivariant K- and KK-theory including homological approach and applications to Baum-Connes conjecture and classification theory of nuclear C*-algebras;
• Index theory in both analytic and formal algebraic context theory with applications to analysis, to complex and differential geometry;
• Homological algebra, deformation theory, algebraic K-theory and cyclic homology;
• Quantum Field Theory, Solitons, Loop Quantum Gravity, eksperimental low temperature physics.

My publication list: https://publicationslist.org/Ryszard_Nest
For PhD-students, see https://genealogy.math.ndsu.nodak.edu/id.php?id=43937

A bit about my past:
1976 master degree - in between a high school teacher - 1987 phD-degree, both Copenhagen University. Since then tenured position at Copenhagen University
2005 - 2020 professor, Mathematics Institute, Copenhagen University, since 2020 professor emeritus position
2004 - Main organiser (with Max Karoubi) of the semester on Non-commutative geometry and K-theory, centre Emile Borel, Paris, France
2005-2008 - Director of the FNU Center of Non-commutative Geometry, at Mathematics Department, Copenhagen University
2007 - Member of the board of Center for noncommutative geometry and topology, Fredericton, Canada
2009 - Invited speaker at the International Congress of Mathematical Physics, Prague, 2009
2010 - Member of the advisory board of the Programme in Non-Commutative Geometry, RIMS, Kyoto
Since 2020 - Editor duties: The Journal of Non-Commutative Geometry, Georgian Journal of Mathematics
Since 2022 - Ulam professor, Boulder CO
Since 2023 - Gauss professor, Göttingen DE
2018-2024 - Member of the evaluation panel for the ERC advanced grants applications
Since 2024 - At present BIMSA visiting position