Please find more information about the lectures at the detail pages.
For rooms at the MPI MiS please note: Use the entry doors Kreuzstr. 7a (rooms A3 01, A3 02) and Kreustr. 7c (room G3 10), both in the inner court yard, and go to the 3rd. floor. To reach the Leibniz-Saal (E1 05, 1st. floor) and the Leon-Lichtenstein Room (E2 10, 2nd. floor) use the main entry Inselstr. 22.
Please remember: The doors will be opened 15 minutes before the lecture starts and closed after beginning of the lecture!
We are reading the book "Analysis and Geometry of Markov Diffusion Operators" by Bakry, Gentil and Ledoux, which deals with the "interplay between analytic, probabilistic and geometric aspects of Markov diffusion operators" (Springer Link description). More specifically, we will treat Log- Sobolev Inequalities this term.
We started reading the book during the winter semester already, but it is possible to join. Some knowledge in semigroup theory and Markov Triples is necessary, but can be obtained by reading part of the book. It should definitely be possible to catch up.Date and time infoThursdays 15:15, starting April 13thKeywordsMarkov Triples, Poincare Inequalities, Log Sobolev Inequalities
About this lectureDue to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field.
Part 1 - Introduction to Random MatricesLecturer: Alexey BufetovBy now Random Matrices is the large research field with connections to most of mathematics. In this course we will prove a foundational result in the field — Wigner‘s theorem about eigenvalues of a random symmetric / Hermitian matrix — and briefly discuss several other results.Part 2 - Geometry of Feynman Integrals Lecturer: Simon TelenIn this lecture series, we study a class of integrals which appears under different names in the literature: generalized Euler integrals, hypergeometric integrals, or Euler-Mellin integrals. These have gained recent interest because of their application in particle physics, where they appear as Feynman integrals. We highlight geometric aspects and computational tools from nonlinear algebra. Along the way, we will encounter convex polytopes, critical points, very affine varieties and more.Date and time infoThursdays April 13, 20, 27; May 4, 11, 25; June 1, 8: always from 10.30-12.00
Algebraic Statistics studies and solves of problems in Statistical Data Analysis using tools from Algebraic Geometry, Commutative Algebra, Discrete Geometry and, numerical and symbolic computation. This is an active and exciting field of research that started almost three decades ago. The goal of this reading course is, in the first part, to establish a common language for statistics and algebra; in the second part we will focus on more advanced topics and current developments.
In the future months there will be many activities around Algebraic Statistics, these include the 3-Way-Interaction-Seminar, several Minisymposia at the SIAM AG23 Conference, and finally the semester long program Algebraic Statistics and Our Changing World at IMSI. Participants in this reading group will be set up for an enriched experience in attending any of the aforementioned events.Date and time infoThursdays at 1:30 pmKeywordsAlgebraic Statistics, toric varieties, exponential families, graphical models, conditional independenceAudienceMasters and Phd Students, PostdocsLanguageEnglishRemarks and notesLectures are given by participants in the course.
This lecture course features an introduction to tropical geometry, including the necessary parts of polyhedral and convex geometry. This course is meant to bridge the pure-mathematical view of tropical geometry towards a more computational and applied perspective. For this we will use mathematical software in exercises and examples, and, additionally, in the last few weeks, we will consider tropical geometry in the context of neural networks and/or extreme value statistics.
During this course exercises will be handed out, which will include computing examples using the software package OSCAR in Julia. It is recommended to install these before the course. Installation instructions can be found here.
The lecture course is also open for students from Leipzig University.Date and time infoMonday and Tuesday 9-11Keywordstropical geometry, polyhedral geometry, algebraic geometry, applicationsPrerequisitesLinear Algebra, knowledge about algebraic geometry (especially varieties) is helpful, but not necessary.
In this online course we aim to get acquainted with some of the recent progress in the mathematical understanding and theory of machine learning. Particular emphasis will be laid upon overparametrization, implicit bias and aspects of unsupervised learning. The aim of the course is to get an overview of a series of recent articles and the methods developed therein. The course is directed to non experts with a solid background in mathematics aiming to get an idea of recent progress in the mathematics of machine learning. Active contribution in form of a presentation of a research paper (to be chosen) is required for each participant.During the first five sessions of this course, an introduction to the field of (supervised and un-supervised) machine learning will be given.Date and time infoWednesdays 16:15-17:45
The first lecture will briefly cover prerequisites from Mattila's "Geometry of Sets and Measures" including: rectifiability and tangent measures. It will also give an overview of the types of results one could hope for relating the behavior of measures corresponding to a Dirichlet problem and the geometry of the boundary.
We will proceed to discuss the two phase harmonic measure free boundary problem, with an initial discussion of the special case of the complex plane. We will then study the blow-up analysis and techniques from Kenig-Toro 2003, Kenig-Toro 2006, and Kenig-Preiss-Toro 2009.Date and time infoTuesdays, 09.30-11.00Keywordsharmonic measure, geometric measure theory, blow-up analysis, free boundary problemsPrerequisitesReal analysis, a first course in PDE
This course discusses the concepts and maths-specific services you usually only learn about during thesis writing, during a doctorate or by word of mouth. We focus on how to do maths efficiently and sustainably. In particular:Do you know how to look for mathematical results, for formulae, for information about
algorithms? How do you find out what is the state of the art of a field? How can you
describe a mathematical object so that others know what it is? How can you make
sure you sensibly compare your new results to the best ones out there? How can you
make your own theoretical and computational results visible and usable for others?
How do you properly document all the steps in a research process, from a question you
are interested in to finding answers to that question up until sharing your results with
your peers? Why should you? What has this to do with applying for funding?
Have you ever wondered what arxiv is or how the publishing business works? What is
(technical) peer review? How are different types of maths, like papers or computations,
handled in such an evaluation process? Where and how should you store all the
analogue and digital files you handle when doing maths? What are good, sustainable
solutions? What is good scientific practice?Date and time infopossibly Fridays 9-11, not confirmed yetKeywordsgood scientific practice, research data, infrastructurePrerequisitesnoneAudiencemaths: undergraduate students nearing the end of their degree, PhD students, early postdocsLanguageEnglish, questions may be asked in German
April 14, 2-3pm: Preliminary lecture with background on semistable reduction, number theory, tropical geometry
April 17 - 20 2pm - 5pm, April 21 10am - 12pm: 1 hr lecture, break, then computational working session
Lecture topics TBADate and time infoApril 14, 2-3pm, April 17 - 20 2pm - 5pm, April 21 10am - 12pmKeywordsTropical Geometry, Number Theory, Semistable Models, Berkovich Spaces
This 2-days event is dedicate to real algebraic geometry, and related areas. We will learn what a real closed field and a real variety are, we will play with semialgebraic sets, and explore many applications, including convex geometry and optimization. There will be lectures and exercise sessions, as well as time for questions and discussions.Date and time infoJune 7 and 8
Combinatorics using some algebraic constructions. We use dimension arguments to get bounds on interesting combinatorial numbers. We study the eigenvalues of adjacency matrices on graphs to get information about graphs at hand. This has great applications in the so called extremal combinatorics.
In combinatorial geometry we will be studying combinatorial identities and inequalities that relate to point sets and polytopes. For instance, how many points in R^d can you find such that the distance between any two of them is one of two given real numbers? We will find bounds for these quantities using linear algebra.
Finally, we will be studying spectral theory on graphs. This has some interesting combinatorial consequences on graph properties.Date and time infoWednesday, 9am - 11amKeywordsgraph theory, convex geometry, extremal combinatorics, ham sandwich theoremPrerequisitesAbstract algebra, linear algebraLanguageEnglish
Date and time infoMontags von 11 bis 13 Uhr und Donnerstags von 15 bis 17 Uhr (tentative)Keywordsintersection theory: line bundles and divisors, Chow rings (in particular of Grassmannians), Chern classes, projective bundles, Segre classesPrerequisitesBasic notions in algebraic geometry (affine/projective variety, morphism, dimension, Grassmannian)LanguageEnglish
