The 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.
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
"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.
Complimentary parking is available in all visitor parking lots. Contact Gladys Collins at 312.567.8980 or collinsg(at)iit(dot)edu for details.
Out-of-state travelers: for questions or hotel suggestions, please call 312.567.3132
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.
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.
- Biography of Karl Menger, compiled by Professor Greg Fasshauer at IIT.
- Calculus: A Modern Approach, Menger's Calculus textbook.
- Selecta Mathematica, Vol 1 & 2, a compilation of Menger's major mathematical papers.
- Unexplored Dimensions: Karl Menger on Economics and Philosophy, a collection of Menger's papers while at the University of Vienna.
Previous Menger Lecturers
- Remembering Menger 2017: Persi Diaconis
- Remembering Menger 2016: Thomas Yizhao Hou
- Remembering Menger 2015: Andrea Bertozzi
- Remembering Menger 2014
- Remembering Menger 2013: Philip Protter
- Remembering Menger 2012: Philip Holmes
- Remembering Menger 2011: Peter Winkler
- Remembering Menger 2010: Donald Saari
- Remembering Menger 2009: Richard Durrett [slideshow]
- Remembering Menger 2008: Lloyd N. Trefethen FRS [slideshow]
- Remembering Menger 2007: Karl Sigmund