The Menger Lecture Series has hosted many prominent academics in mathematics. Learn more about our featured Menger Day speakers.

### MONDAY, APRIL 1, 2019

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

**12:50 p.m. – AWM/SIAM Clubs Meeting, Hermann Hall Ballroom**

Professor Xiao-Li Meng will give the talk “Bias-Variance Tradeoff: A Fundamental Statistical Principle That Can Render You Love or Pain,” 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. – Faculty Research Overviews, Hermann Hall Ballroom**

Several Illinois Tech Department of Applied Mathematics faculty summarize recent research in short-format talks.

**3:15 p.m. – Speed-Chatting/Speed-Mentoring, Hermann Hall Ballroom **

Faculty, alumni, and students pair up for short conversations to share insights.

**4:45 p.m. – Poster Session, Hermann Hall Ballroom **

Viewing of student research posters. Light refreshments will be served.

**6 p.m. – Lecture, Hermann Hall Ballroom**

“How Small Are Our Big Data: Turning the 2016 Surprise into a 2020 Vision,” delivered by Professor Xiao-Li Meng, Whipple V. N. Jones Professor of Statistics, Harvard University Faculty of Arts and Sciences.

The term “Big Data” emphasizes data quantity, not quality. However, many of the current measures of statistical uncertainties and errors are adequate only when the data are of the desired quality, that is, when they can be viewed as probabilistic samples. We show that once we take into account the data quality, the effective sample size of a “Big Data” set can be vanishingly small. Without understanding this phenomenon, “Big Data” can do more harm than good because of the drastically inflated precision assessment, hence a gross overconfidence, setting us up to be caught by surprise when the reality unfolds, as we all experienced during the 2016 U.S. presidential election. Data from the Cooperative Congressional Election Study (CCES, conducted by Stephen Ansolabehere, Douglas River, and others, and analyzed by Shiro Kuriwaki), are used to assess the data quality in 2016 U.S. election polls, with the aim to gain a clearer vision for the 2020 election and beyond.

**7 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, APRIL 2, 2019

*Professor Meng will meet with students and faculty.*

**10 a.m. – Research Seminar, Robert A. Pritzker Science Center, Room 240 **

“Is It a Computing Algorithm or a Statistical Procedure – Can You Tell or Should You Care?” delivered by Professor Xiao-Li Meng.

**3:15 p.m. – Career Advice Seminar, John T. Rettaliata Engineering Center, Room 104 **

“Conducting Highly Principled Data Science: A Statistician’s Job and Joy,” delivered by Professor Xiao-Li Meng.

### 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 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 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 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.

### MONDAY, APRIL 24, 2017

*Pre-lecture events will begin at 5 p.m. and will take place in the lobby, located in the Robert A. Pritzker Science Center building.*

**5 p.m. – Poster Session, North Hall, Robert A. Pritzker Science Center **

Viewing of student research posters. Light refreshments will be served.

**6 p.m. – Lecture, Auditorium, Robert A. Pritzker Science Center **

“The Search for Randomness” delivered by Professor Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University.

Diaconis will take a careful look at some of our most primitive images of random phenomena: tossing a coin, shuffling cards, and throwing a dart at the wall. Experiments and a bit of math show that while randomness is possible, usually things are not so random.

Applications of the use (and misuse) of stochastic models in all walks of life (health, finance, business) will be illustrated.

**7 p.m. – Awards Presentation, Auditorium, Robert A. Pritzker Science Center**

Presentation of Illinois Tech Karl Menger Student Awards for exceptional scholarship by a student and the applied mathematics poster competition winners.

**7:15 p.m. – Reception, Lobby, Robert A. Pritzker Science Center**

### TUESDAY, APRIL 25, 2017

*Professor Diaconis will meet with students and faculty.*

**10:10 a.m. – Research Seminar, Siegel Hall Auditorium, Room 118***“Adding Numbers and Shuffling Cards”* delivered by Professor Diaconis

When numbers are added in the usual way, “carries” occur. These carries form a Markov chain with an “amazing” transition matrix. Strangely, this same matrix occurs in analyzing the usual method of shuffling cards and in the mathematical analysis of fractals. Diaconis will explain all of this in “mathematical English” for a non-scientist audience.

**12:30 p.m. – Discussion, Siegel Hall Auditorium, Room 118 ***“How to Be a Successful Applied Mathematician”* with Professor Diaconis

### MONDAY, MARCH 28, 2016

*Pre-lecture events will begin at 12:45 p.m. and will take place in the McCloska Ballroom, located in **The McCormick Tribune Campus Center**.*

**12:45–1:40 p.m. – Math Club Meeting**

Professor Thomas Yizhao Hou will give the talk “How Mathematics Improves the Quality of Our Life.” All alumni are welcome. Light lunch provided.

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT and Professor Karl Menger.

**2:50 p.m. – Poster Session**

Viewing of student research posters. Light refreshments available.

**3:15–4:15 p.m. – Lecture, McCloska Auditorium, MTCC***“Recent Progress in the Clay Millennium Problem on Navier-Stokes Equations and Related Models”* delivered by Professor Thomas Yizhao Hou, Charles Lee Powell Professor of Applied and Computational Mathematics, California Institute of Technology.

Fluid flows are ubiquitous in scientific and engineering applications as well as in our daily life. It is well known that the motion of fluid flows is governed by the Navier-Stokes equations. Despite the widespread applications of these equations, the global existence and regularity of the three-dimensional incompressible Navier-Stokes equations remains one of the most challenging open questions in fluid dynamics and mathematics. This challenging question has been posted as one of seven Millennium Prize Problems by the Clay Mathematics Institute. In this lecture, Hou will review some of the classical results for the Navier-Stokes equations and explain why this problem is so challenging. The earliest work due to Leray led to the notion of weak solutions for partial differential equations. In recent years, there has been a growing interest in the study of the Navier-Stokes equations. This includes the celebrated partial regularity result due to Caffarelli-Kohn-Nirenberg, the work of Sverak and Tsai on the non-existence of self-similar solutions under certain conditions, the role of geometric regularity of vorticity vectors in depleting potential singularity due to Constantin-Fefferman-Majda, and the very recent work due to Terence Tao on the finite time blowup of a model of the Navier-Stokes equations. Hou also will review some of his recent work in Navier-Stokes equations and related models, which demonstrates the stabilizing effect of convection. Very recently, he obtained strong numerical evidence on the finite time blowup of the incompressible 3-D Euler equations.

**4:15–4:25 p.m. – Presentation of Awards**

Presentation of the IIT Karl Menger Student Award for exceptional scholarship by a student and the Applied Mathematics poster competition winners.

**4:25 p.m. – Reception, McCloska Ballroom, MTCC**

### TUESDAY, MARCH 29, 2016

*Professor Hou will meet with students and faculty.*

**11:25 a.m. – Research Seminar, Life Sciences Building, Room 240***“Blowup or no blowup? The interplay between theory and computation in the study of 3-D Euler equations” *delivered by Professor Hou

Whether the 3-D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3-D Navier-Stokes Equations. Hou will first review some recent theoretical and computational studies of the 3-D Euler equations. His study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. He will then present strong numerical evidence that the 3-D Euler equations develop finite time singularities. To resolve the nearly singular solution, he developed specially designed adaptive (moving) meshes with a maximum effective resolution of order 1012in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1-D model is proposed to study the mechanism of the finite time singularity. Very recently, he proved rigorously that the 1-D model develops finite time singularity. This is a joint work with Professor Guo Luo.

**4:40–5:30 p.m. – Discussion, Life Sciences Building, Room 152***“How to Be a Successful Applied Mathematician”* with Professor You

### MONDAY, MARCH 30, 2015

*Events will take place in the McCormick Tribune Campus Center (MTCC)*

**12:45–1:40 p.m.**

Math Club Meeting

Andrea Bertozzi will give a talk, “Mathematics in the Real World“ *All alumni are welcome. Light lunch provided.*

**2 p.m.**

Memories of IIT

Join in as alumni and friends tell their stories of IIT & Menger.

**2:50 p.m.**

Poster Session

Viewing of Student Research Posters.*Light refreshments available.*

**3:15–4:15 p.m.**

Menger Lecture, McCloska Auditorium, MTCC

“Mathematics of Crime” delivered by Andrea Bertozzi of the University of California Los Angeles.

**4:15–4:25 p.m.**

Presentation of Awards

Presentation of the IIT Karl Menger Student Award for exceptional scholarship by a student and the applied math poster competition winners.

**4:25 p.m.**

Reception, McCloska Ballroom, MTCC

Andrea Bertozzi is an applied mathematician with expertise in nonlinear partial differential equations and fluid dynamics. She also works in the areas of geometric methods for image processing, crime modeling and analysis, and swarming/cooperative dynamics. Bertozzi completed all her degrees in mathematics at Princeton. She was an L. E. Dickson Instructor and NSF Postdoctoral Fellow at the University of Chicago from 1991–1995. She was the Maria Geoppert-Mayer Distinguished Scholar at Argonne National Laboratory from 1995–6. She was on the faculty at Duke University from 1995–2004 first as associate professor of mathematics and then as professor of mathematics and physics. She has served as the director of the Center for Nonlinear and Complex Systems while at Duke. Bertozzi moved to UCLA in 2003 as a professor of mathematics. Since 2005 she has served as director of applied mathematics, overseeing the graduate and undergraduate research training programs at UCLA. In 2012 she was appointed the Betsy Wood Knapp Chair for Innovation and Creativity.

Bertozzi's honors include the Sloan Research Fellowship in 1995, the Presidential Early Career Award for Scientists and Engineers in 1996, and the Society of Industrial and Applied Mathematics's (SIAM) Kovalevsky Prize in 2009. She was elected to the American Academy of Arts and Sciences in 2010 and to the Fellows of the SIAM in 2010. She became a Fellow of the American Mathematical Society in 2013. Bertozzi serves on the editorial boards of 12 journals: *SIAM J. Math. Anal.*, *SIAM's Multiscale Modeling and Simulation*, *Interfaces and Free Boundaries*, *Applied Mathematics Research Express* (Oxford Press), *Applied Mathematics Letters*, *Mathematical Models and Methods in the Applied Sciences *(M3AS), *Communications in Mathematical Sciences*, *Nonlinearity, and Advances in Differential Equations*, *Journal of Nonlinear Science, Journal of Statistical Physics*, and *Nonlinear Analysis Real World Applications*.

She currently serves as chair of the Science Board of the NSF Institute for Computational and Experimental Research in Mathematics at Brown University and serves on the Science Boards for the Banff International Research Station and the Mathematical Sciences Research Institute at Berkeley.

To date she has graduated 23 Ph.D. students and has mentored 35 postdoctoral scholars.

### TUESDAY, MARCH 31, 2015

Bertozzi will meet with students and faculty.

**11:25 a.m.**

Research Seminar: “*The Ginzburg—Landau Functional and Threshold Dynamics on Graphs for Large Data Analysis.”*

Location: Engineering 1, Room 258.

**4:40–5:30 p.m.**

Discussion: “*How to Be a Successful Applied Mathematician”* with the SIAM student chapter.

Location: Engineering 1, Room 102.

The Menger Lecture was cancelled due to illness. The poster contest and presentation of the various awards (Menger student, Outstanding TA, and Buck McMorris summer stipend) still took place.

**Applied Mathematics Department Annual Poster Contest and Presentation of Student Awards
Monday, March 31, 2014, in the MTCC Ballroom**

4:15 p.m. – Reception and Viewing of posters

4:40 p.m. – Presentation of Awards

- IIT Karl Menger Award for Exceptional Scholarship by a student
- Department Teaching Assistant Award
- “Buck” McMorris Summer Stipend Award
- Applied Mathematics Poster Contest Awards
- Math Contest Awards

### MONDAY, APRIL 22, 2013

*Events will take place in The McCormick Tribune Campus Center (MTCC)*

**12:45–1:40 p.m. – Math Club Meeting**

Professor Philip Protter will give a talk: “What Actually Happened in 2008, and Who Is to Blame?”

All alumni are welcome. Light lunch provided.

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT & Professor Karl Menger.

**2:50 p.m. – Poster Session**

Viewing of student research posters. Light refreshments available.

**3:15–4:15 p.m. – Lecture, McCloska Auditorium, MTCC***“Financial Bubbles Through History Viewed Through Mathematics” *delivered by Professor Philip Protter of Columbia University

The history of the western industrialized world is one rich with the stories of financial bubbles. The ones we remember are the more spectacular ones, often leading to stock market crashes and subsequent economic depressions, ranging over history from Tulipmania in the 1630s to the South Sea Bubble in England in the eighteenth century and, in the United States, from the market crashes of 1837 and 1873 to the panic of 1907, and more recently from the market crash of 1987 and the dot-com crash of 2000 to the housing bubble collapse of 2008. Mathematics does not give us (yet) many insights into what causes bubbles, although economists have many good ideas on that score, but it does help us to detect, before the crash, whether or not a bubble might be occurring. This is something that is often surprisingly difficult to ascertain with the naked eye. We will discuss, in broad terms, how this process works, and how mathematics could—in principle—be used to reduce to some extent the wild swings of the markets.

Philip Protter works in probability theory, with specialties in stochastic calculus, weak convergence and limit theorems, stochastic differential equations and Markov processes, stochastic numerics, and mathematical finance. He is the author of one book and the co-author of three more, and he has published more than 100 research papers. He was a visiting member of the Institute for Advanced Study in 1978, a National Science Foundation/Centre National de la Recherche Scientifique (NSF/CNRS) Exchange Scientist (to France) in 1980, and a Fulbright – Tocqueville Distinguished Chaired Professor in Paris in 2007. He gave the inaugural R. Von Mises Lecture at Humboldt Universität, Berlin, in 2007 and the Bullitt Lecture at the University of Louisville in 2009. He is a fellow of the Institute of Mathematical Studies. Currently he is a professor of statistics at Columbia University. Before Columbia, he held positions at Cornell University, Purdue University, and Duke University.

**4:15–4:25 p.m. – Presentation of Awards**

Presentation of the IIT Karl Menger Student Award for Exceptional Scholarship by a Student and the Applied Math poster competition winners.

**4:25 p.m. – Reception, McCloska Ballroom, MTCC**

### TUESDAY, APRIL 23, 2013

Philip Protter will meet with students and faculty.

**11:25 a.m. – Research Talk Presentation: “Can One Detect a Financial Bubble in Real Time”** Location: Wishnick Hall, Auditorium

**12:30 p.m. – Lunch Provided**

**4:40–5:30 p.m. – Lecture: “The Balance Between Theory and Data: A Case Study with Liquidity”**

with the SIAM student chapter. Location: Wishnick Hall, Auditorium

### MONDAY, APRIL 23, 2012

*Events from 12:45–3:15 p.m. will take place in the McCloska Ballroom, The McCormick Tribune Campus Center.*

**12:45–1:40 p.m. – Math Club Meeting**

Professor Philip Holmes, Princeton University, will give a talk: “Chaos and Classical Mechanics: How a Double Pendulum is Like Throwing Dice.” All alumni are welcome. Light lunch provided.

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT and Professor Karl Menger.

**2:50 p.m. – Poster Session**

Viewing of student research posters. Light refreshments available.

**3:15–4:15 p.m. – Lecture, McCloska Auditorium, MTCC**

“One and a Quarter Centuries of Nonlinear Dynamics: More Is Different and Less Is More.”

Delivered by Professor Philip Holmes, Princeton University.

In 1889, for his paper on Hamiltonian dynamics and the three-body problem of celestial mechanics, Henri Poincare was awarded a prize established to honor the 60th birthday of King Oscar II of Sweden and Norway. As the paper was being edited for publication in *Acta Mathematica*, a serious error came to light. In correcting the error, Poincare discovered the phenomenon that we now call deterministic chaos. The resulting 270-page paper is essentially the first textbook in the modern geometrical theory of dynamical systems. I shall tell the story of this paper, some of the key contributions to which it led (Smale's horseshoe, Kolmogorov-Arnold-Moser theory, center manifolds and bifurcations), and end by describing some applications of dynamical systems theory in fluid, solid and celestial mechanics.

Philip Holmes is Eugene Higgins Professor of Mechanical and Aerospace Engineer, professor of applied computational mathematics, and a member of Princeton’s Neuroscience Institute. He currently works on the neuromechanics of animal locomotion and on the neurodynamics of decision making. He has co-authored over 200 scientific papers; three books on dynamical systems; and with Florin Diacu, ‘Celestial Encounters,’ an historical account of the origins of chaos theory.

**4:15 p.m. – Presentation of Awards**

Presentation of the IIT Karl Menger Student Award for Exceptional Scholarship by a Student and the Applied Math poster competition winners.

**4:25–4:45 p.m. – Break**

Light refreshments available.

**4:45–5:45 p.m. – Panel Discussion, McCloska Auditorium, MTCC**

The title of the discussion is “Future Challenges and Opportunities for Applied Mathematics.”

The panelists are: Steven Cunningham, Treasurer, Discover; Philip Holmes, Professor, Princeton University; and Rob Meyer, CEO, The Numerical Algorithms Group.

**6 p.m. – Reception, Ballroom, MTCC**

### TUESDAY, APRIL 24, 2012

Professor Holmes will meet with students and faculty.

**11:25 a.m. – Research Talk Presentation: “How Cockroaches Run Fast and Stably Without Much Thought.” **Location: SB 113.

**12:30 p.m. – Lunch with Faculty**

**4:40–5:30 p.m. – Lecture: “Adventures Inside and Outside the Math Department: How I Got Involved with Engineers, Biologists, Neuroscientists, Psychologists, and ...Mathematicians.”**

With the SIAM student chapter. Location: SB Auditorium.

### MONDAY, APRIL 4, 2011

*Events from 12:45–4:30 p.m. will take place in the McCloska Ballroom, The McCormick Tribune Campus Center.*

**12:45–1:40 p.m. – Math Club Meeting**

Professor Peter Winkler will give a talk: “Puzzles You Think You Must Not Have Heard Correctly.” All alumni are welcome. Light lunch provided.

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT and Professor Karl Menger.

**2:50 p.m. – Poster Session**

Viewing of student research posters. Light refreshments available.

**3:15 p.m. – Faculty/Student Research Presentation**

“Numerical Computations with Positive Definite Kernels” Professor Gregory E. Fasshauer and Michael Mongillo

**4:30 p.m. – Lecture, McCloska Auditorium, MTCC**

“Statistical Combinatorics” delivered by Professor Peter Winkle of Dartmouth University

Statistical physics is the study of global behavior resulting from interaction of many small particles. Combinatorics and graph theory have played a role in this subject from its very beginnings. In recent years, however, these areas have enjoyed a closer bond both in method and objectives, with some spectacular results. We will explain some of these results and how they came, then indicate some of the many intriguing questions that remain.

Peter Winkler is professor of mathematics and computer science, and Albert Bradley Third Century Professor in the Sciences, at Dartmouth College. His mathematical research is primarily in combinatorics, probability, statistical physics, and the theory of computing, optical networking, marine navigation. He is the author of two collections of mathematical puzzles, a portfolio of compositions for ragtime piano, and (just published) a book on cryptologic methods in the game of bridge. Winkler is a past winner of the Lester R. Ford award for mathematical exposition, and just won the MAA's 2011 Robbins Prize for his part in a paper that solved the problem of how far a stack of bricks can be made to hang over the edge of a table.

**5:40 p.m. – Presentation of Awards**

Presentation of the IIT Karl Menger Student Award for Exceptional Scholarship by a Student and the Applied Math poster competition winners.

**6 p.m. – Reception, McCloska Ballroom, MTCC**

### TUESDAY, APRIL 5, 2011

Peter Winkler will meet with students and faculty.

**11:25 a.m. – Research Talk Presentation: “Coordinate Percolation”**

Location: Faculty Dining Room, Hermann Hall, Lower Level

**12:30 p.m. – Lunch with Faculty**

**4:40–5:30 p.m. – Lecture: “How to Be a Successful Applied Mathematician” **with the SIAM student chapter. Location: E1 121

### MONDAY, APRIL 19, 2010

**11:30 a.m.–12:30 p.m. ****Recent Alumni Reception****, LaSalle Bank Executive Conference Room, MTCC**

Alumni from the classes of 1999–2008 will share their experiences since graduating.

*Events from 12:45–4:30 p.m. will take place in the McCloska Ballroom, MTCC*

**12:45–1:40 p.m. – Math Club Meeting**

Professor Donald Saari, University of California, Irvine, will talk informally with members of the Math Club; all alumni are welcome. Light lunch provided.

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT and Professor Karl Menger.

**2:50 p.m. – Poster Session**

Viewing of Student Research Posters

**3:15 p.m. – Faculty Research Presentation***“How Does Noise Affect Dynamics?”*

Presentation by Professor Jinqiao Duan, together with his student, Xingye Kan.

**4:30 p.m. – Lecture, McCloska Auditorium, MTCC***“Arrow's Theorem: What Does It Really Mean and How Does It Affect All Academic Disciplines?” *delivered by Professor Donald Saari of the University of California

“Arrow's Theorem” is a beautiful mathematical result; it is among the mathematical theorems that have had the greatest impact over the last half century. Yet, most mathematicians have, at best, only a passing acquaintance with it. After introducing the theorem in this expository lecture, I will then explain why the result does not mean what almost everyone has accepted for 50 years. After a reinterpretation and extension, it will then be shown how this result has serious implications for all disciplines, in particular, engineering, astronomy, decision analysis, and so forth.

Donald Saari is a Distinguished Professor in the Departments of Economics and Mathematics at the University of California, Irvine, where he also serves as the director of the Institute for Mathematical Behavioral Sciences. His research crosses several mathematical disciplines, and he is a fellow of both SIAM and the American Academy of Arts and Sciences. Professor Saari is also a member of the National Academy of Sciences.

**5:40 p.m. – Presentation of Awards**

Presentation of the IIT Karl Menger Student Award for Exceptional Scholarship by a Student and the Applied Math poster competition winners.

**6 p.m. – Reception, McCloska Ballroom, MTCC**

### TUESDAY, APRIL 20, 2010

Donald Saari will meet with students and faculty.

**11:25 a.m. – Research Talk Presentation: ****Dark Matter: A Mathematician's Perspective**** **Location: E1 244

**12:30 p.m. – Lunch with Faculty**

**4:40–5:30 p.m. – Lecture: “How to Be a Successful Applied Mathematician”**

with the SIAM student chapter. Location: E1 244

### MONDAY, APRIL 20, 2009

**11:30 a.m.–12:30 p.m. Recent Alumni Reception, LaSalle Bank Executive Conference Room, MTCC**

Alumni from the classes of 1999–2008 will share their experiences since graduating.

**12:50–1:40 p.m. – Math Club Meeting, Engineering-1 123**

This year's Menger lecturer, Professor Richard Durrett, Cornell University, will talk informally with members of the Math Club; all alumni welcome.*Events from 1:45–5:40 p.m. will take place in the McCloska Ballroom, MTCC*

**2 p.m. – Memories of IIT**

Join in as alumni and friends tell their stories of IIT & Professor

Karl Menger

**2:50 p.m. – Poster Session**

Viewing of 2009 Student Research Posters

**3:15 p.m. – Research Presentation**

Recent Applied Mathematics Department Research Advances—“How to Model Credit Markets if You Must.” Presentation by Professor Tomasz Bielecki, together with his students, Andera and Luca Vidozzi.

**4:30 p.m. – Lecture**

“Truth Is Stranger Than Fiction: A Look at Some Improbabilities” delivered by Professor Richard Durrett of Cornell University.

Professor Durrett will discuss several situations in which probabilities are misunderstood in the mathematical world, using examples to explain and clarify the issues.

Durrett is a distinguished mathematician working in probability and stochastic analysis with applications in ecology and genetics. Author of popular books in stochastic analysis and probability, including *Stochastic Calculus: A Practical Introduction* and *Probability Models for DNA Sequence Evolution*, he also has published more than 160 refereed research papers and supervised 38 Ph.D. students. He is a member of the National Academy of Sciences and of the American Academy of Arts and Sciences.

**5:40 p.m. – Presentation**

Presentation of the IIT Karl Menger Student Award for exceptional scholarship by a student**6 p.m. – Dinner**

Pritzker Club, MTCC

### TUESDAY, APRIL 21, 2009

Richard Durrett will meet with students and faculty

10 a.m. – Stochastic and Multiscale Modeling Seminar: “Probability Problems Arising from the Study of Cancer” WH 117

Noon – Lunch with Faculty

4:40–5:30 p.m. – Lecture: “How to Be a Successful Applied Mathematician” with the SIAM student chapter. Location: E1 027

### MONDAY, APRIL 14, 2008

The McCormick Tribune Campus Center (MTCC), Main Campus**12:45 p.m.—Campus Tour**

A Mies Society Campus Tour will leave MTCC at 12:45 p.m.

**12:50–1:40 p.m.—Math Club with Professor Trefethen**

Talk title: “Eigenmodes of Drums (and Physics Nobel Prizes)”

Life Sciences Building, Room 111

*Events from 1:45 - 5:40 p.m. will take place in the McCloska Ballroom, MTCC***1:45 p.m.—Reception and Memories of Karl Menger**

Join in as alumni and friends tell their stories of Professor Karl Menger

**2:35 p.m.—Poster Session**

Viewing of 2008 Student Research Posters

**3:15 p.m.—Research Presentation**

Recent Applied Mathematics Department Research Advances—Presentation by Assistant Professor Robert Ellis and Jon Beagley, fourth year undergraduate

**4:30 p.m.—Lecture**

“Computing numerically with functions instead of numbers”

Delivered by Professor Lloyd N. Trefethen, professor of numerical analysis and fellow of Balliol College at Oxford University. Trefethen is the professor of numerical analysis and head of the Numerical Analysis Group at Oxford University. He was educated at Harvard and Stanford and held professorial positions at New York University, Massachusetts Institute of Technology, and Cornell before 1997. He is a fellow of the Royal Society and a member of the United States National Academy of Engineering.

As an author he is known for his books *Numerical Linear Algebra* (1997), *Spectral Methods in MATLAB* (2000), *Schwarz-Christoffel Mapping* (2002), and *Spectra and Pseudospectr*a (2005). He is an ISI Highly Cited Researcher, with about 90 journal publications in numerical analysis and applied mathematics, and has served as editor for many of the leading numerical analysis journals. He has lectured in about 15 countries and 25 American states, including invited lectures at both ICM and ICIAM congresses.

Some of Trefethen’s recent activities include the SIAM 100-Dollar, 100-Digit Challenge, the notion of 10 Digit Algorithms (“10 digits, five seconds, and just one page”), the Chebfun system for numerical computation with functions instead of numbers, and a book in preparation called *Neoclassical Numerics*.

**5:40 p.m.—Presentation**

Presentation of the IIT Karl Menger Student Award for exceptional scholarship by a student

**6:00 p.m.—Dinner**

Pritzker Club, MTCC

### TUESDAY, APRIL 15, 2008

Nick Trefethen will meet with students and faculty

**12:30 p.m.—Lunch with Faculty**

**3:30 p.m.—Meshfree Methods Seminar: Informal Discussion, Location TBA**

**4:40 p.m.—Lecture: “How to Be a Successful Applied Mathematician”**

A talk for graduate students, location TBA

### MONDAY, APRIL 9, 2007

**Mies Campus****Noon**

Welcome reception and light lunch**Hermann Union Building**, lower level, Armour Dining Room

**1:30 p.m.**

Campus Tour*Leaves from IITRI Tower*

**2:45 p.m.**

Department update*Will include a tribute to **Professor Maurice (Jerry) Frank,** retiring this spring after 30 years of service to IIT.***Engineering 1**, 10 West 32nd Street, Room 242

**4 p.m.**

Pre-lecture reception: “Memories of Menger”**Wishnick Hall**, 3255 South Dearborn, Room 119

**4:30 p.m.**

Lecture: “Menger, Games, and Morals” delivered by Karl Sigmund, University of Vienna*A member of the Austrian Academy of Science, Sigmund is an internationally known mathematician and a pioneer of evolutionary game dynamics. In recent years, he has been interested in the history of mathematics, especially the Vienna Circle. Sigmund has co-edited the works of Karl Menger.***Wishnick Hall Auditorium**, 3255 South Dearborn, Room 113

**5:30 p.m.**

Presentation of the IIT Karl Menger Award for exceptional scholarship by a student

### WEDNESDAY, APRIL 11, 2007

Karl Sigmund will meet students at IIT.

**12:50 p.m.–1:40 p.m.**

Lunch with the Math Club

Lecture: “The Rock Paper Scissors Game for Adult Players”

E1 Room 121

**4:30 p.m.**

Lecture: “How to Have a Successful Career as a Mathematician”*A talk for graduate students*

E1 Room 244