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!
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-goergen-s25-join@mis.mpg.deThis course discusses the concepts and maths-specific services you often only learn about during thesis writing 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 got 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 infoFriday, 09:15-10:45KeywordsInfrastructur for mathematics, data management
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-rvl-s25-join@mis.mpg.dePart I: Jonas Hirsch - Harmonic maps
Part II: Dani Kaufman - Introduction to Mapping Class Groups
Abstract: The mapping class group is a symmetry group of a surface and appears naturally through out many topics in algebra, geometry and topology. Through this lecture series I will give an introduction to the study of these groups including their action on the curve complex and Teichmüller space, generation by Dehn Twists, their appearance as outer automorphism groups and the Nielson-Thurston classification.
I will generally follow "A Primer on Mapping Class Groups" by Farb and Margalit.
Part III: Bernd Rosenow - Statistical Physics of Learning
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-mascarin-s25-join@mis.mpg.deThe date and time for the reading group are as follows:
April 22, 10:00 - 12:00 CET
April 25, 10:00 - 12:00 CET
April 29, 16:00 - 18:00 CET
May 2, 16:00 - 18:00 CET
May 6, 16:00 - 18:00 CET
May 9, 16:00 - 18:00 CET
May 13, 16:00 - 18:00 CET
May 16, 16:00 - 18:00 CET
May 20, 16:00 - 18:00 CET
May 23, 16:00 - 18:00 CET
May 27, 16:00 - 18:00 CET
May 30, 16:00 - 18:00 CET
June 3, 16:00 - 18:00 CET
June 6, 16:00 - 18:00 CET
June 10, 16:00 - 18:00 CET
June 13, 16:00 -18:00 CET
To get more information and receive the Zoom link please subscribe to the mailing list.Date and time infodifferent dates
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-portakal-s25-join@mis.mpg.deWe begin the lecture with an introduction to normal-form games and Nash's classical result on the existence of equilibrium, along with examples. Next, we analyze the set of Nash equilibria by studying a system of multilinear equations. In general, the set of Nash equilibria is finite, and we explore lower- and upper-bound results for the number of Nash equilibria using tools from convex and algebraic geometry. We also examine cases where the set is infinite and possesses a rich algebro-geometric structure.
To generalize Nash equilibria, various concepts have been introduced in game theory. One such concept is correlated equilibria, which form a convex polytope within the probability simplex. We investigate some combinatorial properties of this polytope and examine where the Nash equilibria lie on it. Another generalization is dependency equilibria, which have an algebro-geometric model known as the Spohn variety. This framework allows us to explore connections to Nash equilibria and provides insights into Pareto-optimal equilibria, such as in the Prisoner's Dilemma.
Lastly, after examining existing equilibrium concepts, we introduce a new one: conditional independence equilibria. This concept marks the first intersection between game theory and algebraic statistics. Here, we model a game using discrete undirected graphical models, where the vertices represent players as discrete random variables, and the edges capture dependencies in their choices.
Throughout the lecture, we aim to utilize mathematical software, including the upcoming GameTheory package in Macaulay2.
Further Information about the lecture is provided on the course webpage https://www.irem-portakal.de/algebraic-game-theory.htmlDate and time infoTuesdays from 11:00 AM to 12:30 PM and Wednesdays from 1:30 PM to 3 PM. First lecture: Tuesday April 29, 2025. Last lecture: Wednesday June 18, 2025Keywordsequilibrium, Nash, semialgebraic set, correlated, polytope, dependency, variety, conditional independence, graphical modelPrerequisitesKnowledge of basic algebraic geometry is helpful but not required.Remarks and notesEveryone, including non-algebraists, is welcome! We will work through examples using mathematical software as well.
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-stecker-s25-join@mis.mpg.deWe investigate connections on principal fiber bundles. To this end we discuss basics of Lie groups and their representations. Then we dive into the theory of smooth fiber bundles, with emphasis on principal fiber bundles and associated vector bundles. The third section will be about defining and investigating connections on such bundles and their curvature. As a final note we introduce the Yang-Mills equations.Date and time infoThu, 15.15-16.45KeywordsLie groups, fiber bundles, principal fiber bundles, connections, curvaturePrerequisitesDifferential Geometry
SubscriptionSubscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-taha2-s25-join@mis.mpg.deDate and time infoMondays at 2 PM