Friedrich Hirzebruch Lecture
The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.
MPI-Oberseminar
The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.
This often leads to further mathematical interaction, and in any case it is very interesting to know what one's colleagues are working on.
This implies two things:
- When you speak at the Oberseminar you should try to make sure that your talk is understandable and interesting to everyone, not just to the people in the same field. (We have many specialized seminars where you can present your work at a more technical level.)
- Please always attend the Oberseminar, even if the title of the talk seems technical, because you know that the speaker is going to do a good job. The only reason for absence is that the talk is in your field and thus will be too easy for you.
We hope to see you at the Oberseminar!
Christian Kaiser (organizer)
The directors:
Prof. Ballmann (em.)
Prof. Faltings
Prof. Gaitsgory
Prof. Harder (em.)
Prof. Hirzebruch †
Prof. Manin (em.)
Prof. Scholze
Prof. Teichner
Prof. Zagier (em.)
Upcoming talks
Thu, 28 Mar 2024
Past talks
For the abstracts click on the titles or see the list of abstracts.
Thu, 21 Mar 2024
Thu, 14 Mar 2024
Thu, 07 Mar 2024
Thu, 29 Feb 2024
Thu, 22 Feb 2024
Thu, 15 Feb 2024
Thu, 01 Feb 2024
Thu, 25 Jan 2024
Thu, 18 Jan 2024
Thu, 11 Jan 2024
Thu, 14 Dec 2023
Thu, 07 Dec 2023
Thu, 30 Nov 2023
Thu, 23 Nov 2023
Thu, 16 Nov 2023
Thu, 09 Nov 2023
Thu, 02 Nov 2023
Thu, 26 Oct 2023
Thu, 19 Oct 2023
Thu, 12 Oct 2023
Thu, 28 Sep 2023
Thu, 21 Sep 2023
Thu, 07 Sep 2023
Thu, 31 Aug 2023
Thu, 24 Aug 2023
Thu, 17 Aug 2023
Thu, 10 Aug 2023
Thu, 03 Aug 2023
Thu, 27 Jul 2023
Thu, 20 Jul 2023
Thu, 13 Jul 2023
Thu, 06 Jul 2023
Thu, 29 Jun 2023
Thu, 15 Jun 2023
Thu, 01 Jun 2023
Thu, 25 May 2023
Thu, 11 May 2023
Thu, 04 May 2023
Thu, 27 Apr 2023
Thu, 20 Apr 2023
Thu, 13 Apr 2023
Thu, 06 Apr 2023
Thu, 23 Mar 2023
Thu, 16 Mar 2023
Thu, 02 Mar 2023
Thu, 23 Feb 2023
Thu, 09 Feb 2023
Thu, 02 Feb 2023
Thu, 26 Jan 2023
Thu, 19 Jan 2023
Seminar Circle method for Diophantine equations
We are organizing a seminar that aims to offer an introduction to the circle method. Initially developed by Hardy, Littlewood, and Ramanujan, the circle method has been successfully applied to many problems in number theory, including Waring’s problem, Goldbach’s weak conjecture, and estimating the number of partitions. We will follow Davenport's lecture notes* that explains the Hardy-Littlewood circle method with a minimum of fuss by looking at its applications to Waring's problem.
We plan to cover the first ten sections of * and we will meet on Mondays starting from February 19 at 2:00-4:00 pm in the seminar room. All who are interested in this topic are welcome to join!
(*Analytic methods for Diophantine equations and Diophantine inequalities. The University of Michigan, Fall Semester, 1962)
Abstract Homotopy Theory Seminar
MPIM Math-Phys Seminar
A seminar about different topics in Mathematical Physics, broadly around Quantum Field Theory, Algebraic Topology and Differential Geometry. Our meetings are hosted by an assigned speaker, who gives an informal introduction to his topic. Alongside, we will have questions from the audience, which typically lead to a lively discussion.
Seminar-Webseite: https://davidprinz.org/seminar/
IMPRS seminar on various topics: Mostow rigidity
IMPRS seminar on various topics: Single talk
IMPRS seminar on various topics: Schur–Weyl duality
Infinty: Introducing New Faces in Number TheorY
Short presentations of new arrivals at MPIM working in number theory.
Seminar "Arithmetic Geometry and Representation Theory"
Bonn symplectic geometry seminar
Exponential Sum Reading Seminar
We are excited to announce a semester-long reading seminar on the exponential sum over finite fields. Throughout the seminar, participants will delve into the interaction of analytic number theory and arithmetic geometry. Specifically, we will learn Stepanov's “elementary” method to prove Weil’s Conjecture for curves over finite fields. We kindly invite all Ph.D students and postdocs who are interested in this topic.
The main reference is “Equations over Finite Fields: An Elementary Approach” by Schmidt. We will try to cover Chapter I, II, IV of the book. More details will be discussed during the organization meeting.
Seminar on Abstract Homotopy Theory
IMPRS seminar on various topics: Farrel–Jones-Conjecture
IMPRS seminar on various topics: Cerf theory
Student Seminar on Derived Geometry
IMPRS seminar on various topics: Graded geometry
Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)
Course on slice knots and knot concordance
Low-dimensional topology seminar
Organizers: Roberto Ladu, Arunima Ray, Isaac Sundberg, Paula Truoel, Laura Wakelin, Hugo Zhou
Reading seminar on six functors for equivariant cohomology
Time/Venue
Time/venue: Thursday 10:15-12:00, Max Planck Institute for Mathematics, seminar room
Seminar description
Sheaves and cohomology are ubiquitous in geometry and topology. The derived category of sheaves on a space, together with the so-called "six functors" (and the various relations between them), form an "enhancement" of the cohomology groups of spaces that provides more insight into the structure behind these cohomology groups (see e.g. [A1]).
Equivariant cohomology is a cohomology theory for G-spaces (spaces equipped with a group action), that remembers much more about the G-space than just the singular cohomology of its orbit space (rather, it should be thought of as cohomology of the "quotient stack"). In the book Equivariant sheaves and functors [1], Bernstein and Lunts construct a generalization of the aforementioned derived category and six functors for G-spaces, that forms an "enhancement" of equivariant cohomology.
The aim of this reading seminar will be to get to understand parts I and II of this book, with as our end-goal Theorem 12.7.2. Before turning to this book, we will spend some time to first learn about the more classical story for sheaves on spaces (without a group action).
Prerequisites
Some knowledge about abelian categories will probably be assumed. A basic knowledge of Lie groups is also useful.
Seminar organization
The seminar will have weekly talks of 1:00-1:30 hours.
Seminar plan
- Introduction to sheaf theory (23 March 2023)
Sheaves as pre-sheaves and as étalé spaces, local systems, Serre-Swan, push-forward, pull-back, lower shriek. - Introduction to triangulated categories (30 March 2023)
Definition of triangulated categories, the category K(A). (Weibel 10.1 and 10.2) - The derived category of an abelian category (6 April 2023)
Localization, construction of the derived category, derived functors (Weibel 10.3-10.5) - Verdier duality for sheaves on nice topological spaces I: preparation (13 April 2023)
Composition formulas (including base change), soft sheaves, cohomological dimension. - Verdier duality for sheaves on nice topological spaces II: proof (27 April 2023)
Proof of Verdier duality, examples. - Further properties of six functors for topological spaces (4 May 2023)
Properties of upper-shriek, smooth base change, acyclic maps and remainder. (Bernstein-Lunts Chapter 1) - Definition of the bounded equivariant derived category (11 May 2023)
(Bernstein-Lunts 2.1-2.3, parallel part of 2.9) - Further properties of the bounded equivariant derived category (18 May 2023)
Description in terms of fibered categories, structure of triangulated category (Bernstein-Lunts 2.4, 2.5, 2.7, parallel part of 2.9) - Introduction to t-structures on triangulated categories (25 May 2023)
To be decided... - T-structure on the bounded equivariant derived category (1 June 2023)
Simplicial description of the equivariant derived category, the t-structure and its heart (Berstein-Lunts Appendix B to Chapter 2) - To be decided... (... June 2023)
The dates of the session are subject to changes and not strict since some topics may take more time than an entire meeting and some less.
Literature
Textbooks
[1] J. Bernstein and V. Lunts, Equivariant sheaves and functors, Springer-Verlag 1994.
[2] A. Borel et al. , Intersection cohomology, Birkhauser 1984.
[3] B. Iversen, Cohomology of sheaves, Springer-Verlag 1986.
[4] C.A. Weibel, An introduction to homological algebra, Cambridge University Press 1994.
Additional literature
[A1] Martin Gallauer, https://homepages.warwick.ac.uk/staff/Martin.Gallauer/docs/m6ff.pdf
More to be added along the way.
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