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Remembering Karl Menger 2018

Karl MengerThe Department of Applied Mathematics at IIT will host René Carmona, Paul Wythes ’55 Professor of Engineering and Finance, Department of Operations Research and Financial Engineering, Princeton University, as the 2018 Karl Menger Lecturer. He will speak on "Mean Field Games: Mathematical Theory and Applications" on March 26 at 6:00 p.m., Hermann Hall Ballroom. The event is part of the eleventh annual Karl Menger Lecture and Awards, March 26-27, Illinois Institute of Technology Mies (Main) Campus.

Made possible with the generous support of the Menger family; Department of Applied Mathematics, Illinois Institute of Technology; and the Menger Fund.


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Illinois Tech encourages persons with disabilities to participate in its programs and activities. If you anticipate needing any type of accommodation or have questions about the physical access provided, please call Gladys Collins at 312.567.8980 in advance of your participation or visit.

Schedule of Events

Monday, MARCH 26, 2018

Pre-lecture events will begin at 12:50 p.m. and will take place in Hermann Hall Ballroom

12:50 p.m. – AWM/SIAM Clubs Meeting, Hermann Hall Ballroom
Professor René Carmona will give the talk "The New Financial Mathematics for the New Financial Markets," hosted by the Association for Women in Mathematics and Society for Industrial and Applied Mathematics clubs. All alumni are welcome. Light lunch provided.

1:50 p.m. – Mathematics Enrichment and Outreach, Hermann Hall Ballroom
Applied Mathematics faculty and students present mathematical research, applications, and amusements.

3:15 p.m. – Campus Tour, departing from Hermann Hall Ballroom

4:45 p.m. – Poster Session, Hermann Hall Ballroom 
Viewing of student research posters. Light refreshments will be served.

6:00 p.m. – Lecture, Hermann Hall Ballroom
Professor Rene Carmona"Mean Field Games: Mathematical Theory and Applications" delivered by Professor René Carmona, Paul Wythes ’55 Professor of Engineering and Finance, Department of Operations Research and Financial Engineering, Princeton University.

Motivated by a few concrete examples such as bird flocking, congestion for crowd motion, and bee swarming, we introduce the mean field game paradigm, and we present the underpinnings of the original analytic approach based on partial differential equations, and the probabilistic approach based on forward-backward stochastic differential equations. The theoretical results presented in the first part of the talk will be illustrated by the results of numerical implementations of a mean field game model for the synchronization of circadian rhythms and a mathematical model for jet lag recovery.

7:00 p.m. - Awards Presentation, Hermann Hall Ballroom
Presentation of IIT Karl Menger Student Awards for exceptional scholarship by a student and recognition of Applied Mathematics poster exhibition participants.

7:15 p.m. - Reception and Alumni Networking, Lobby, Hermann Hall Ballroom

Tuesday, MARCH 27, 2018

Professor Carmona will meet with students and faculty.

10:00 a.m. - Research Seminar, RE 124
"Control of McKean-Vlasov Dynamics (Mean Field Control) and the Price of Anarchy" delivered by Professor René Carmona.

We posit a new form of the optimal control of stochastic differential equations of McKean-Vlasov type (often called Mean Field Control), and we derive the corresponding Pontryagin maximum principle. This requires calculus over the Wasserstein space of probability measures. We contrast the resulting optima with the Nash equilibria of the associated Mean Field Games (MFGs), and we investigate the price of anarchy by comparing the results of centralized optimization to those of decentralized optimization of MFGs.


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About the Menger Lecturer

Professor René Carmona is a prolific scholar who has written seven monographs and over a hundred articles in probability, statistics, and financial mathematics. He has been elected Fellow of the Institute of Mathematical Statistics and of the Society for Industrial and Applied Mathematics, and is the founding chair of the SIAM Activity Group on Financial Mathematics and Engineering. He was the founding editor of sister journals Electronic Journal of Probability and Electronic Communications in Probability, and of the SIAM Journal on Financial Mathematics. He is recognized worldwide as leading researcher on commodity and energy markets, emissions regulations, and high-frequency trading, as well as for his groundbreaking work on mean-field games.

About Menger

Karl Menger was a faculty member in the Department of Mathematics at IIT from 1946 to 1971, and influenced many students, fellow faculty members, and friends during his lifetime. Regarded as one of the finest mathematicians of the 20th century, he made significant contributions to the fields of dimension theory, probability, economics, ethics, geometry, and calculus.

Each year we invite an outside speaker to be the Karl Menger Lecturer. It is the centerpiece of two days of events for students, faculty, and alumni.

Further Reading

Previous Menger Lecturers