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

## Menger Lecture

##### “From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?”

by George Karniadakis, Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics at Brown University

6 p.m. on Monday, April 8, 2024

We will review physics-informed neural networks (PINNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new neural networks that learn functionals and nonlinear operators from functions and corresponding responses for system identification. Finally, we will present first results on the next generation of these architectures to biologically plausible designs based on spiking neural networks that are more efficient and closer to human intelligence. We will present applications of physics-informed machine learning in engineering, physics, and biomedicine.

### Schedule of Events

*All events will be held in The McCormick Tribune Campus Center (MTCC) Auditorium and Ballroom at Illinois Tech’s Mies Campus.*

**From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?**

**Monday, April 8, 2024**

12:45–1:45 p.m. — Undergraduate Talk (John T. Rettaliata Building, Room 258)

3:15–4:30 p.m. — AMAT Faculty Research Overviews (MTCC Auditorium)

4:30–5:45 p.m. — Student Poster Exhibit (MTCC Ballroom)

6–7 p.m. — 14th Annual Menger Lecture (MTCC Auditorium)

7–7:15 p.m. — Awards Presentation (MTCC Auditorium)

7:25–9 p.m. — Reception and Alumni Networking (MTCC Faculty Lounge)

**Tuesday, April 9, 2024**

10:00–11:15 a.m. — Research Seminar: The Mathematics of Neural PDEs and Neural Operators, Stuart Building Auditorium, Room 104

**Abstract: **Physics-informed neural networks (PINNs) and neural operators like DeepOnet have formed the foundations of Scientific Machine Learning (SciML) with applications across all domains in science, engineering and biomedicine. Here, will present a mathematical view of these neural networks, analyzing their convergence, and provide interpretations for their successes and failures in some prototype benchmark problems but also realistic applications. Specifically, we will discuss how PINNs can be used to tackle the curse-of-dimensionality, and how DeepOnet can be used to obtain in real-time 3D flow fields for a large distribution of parameters. We will also discuss the limitations of these methods for predicting long-term dynamics even for simple problems for which conventional methods succeed.

### About the Lecturer

George Karniadakis’s research interests include diverse topics in computational science both on algorithms and applications. A main current thrust is physics-informed neural networks (PINNs) for stochastic multiscale modeling of physical and biological systems. Particular aspects include stochastic differential equations, modeling uncertainty with polynomial chaos, multiscale modeling of biological systems, atomistic/mesoscopic modelling – dissipative particle dynamics, low dimensional modeling - gappy data - data assimilation, spectral/hp element and discontinuous Galerkin methods, turbulent drag reduction, DNS/LES of turbulence in complex geometries, flow-structure interactions, micro-transport and dynamic self-assembly, flow and heat control applications, parallel computing, and interactive/virtual reality computer graphics.

George Karniadakis received his S.M. (1984) and Ph.D. (1987) from Massachusetts Institute of Technology. He was appointed lecturer in the Department of Mechanical Engineering at MIT in 1987 and subsequently he joined the Center for Turbulence Research at Stanford / Nasa Ames. He joined Princeton University as an assistant professor in the Department of Mechanical and Aerospace Engineering and as associate faculty in the Program of Applied and Computational Mathematics. He was a visiting professor at CalTech (1993) in the Aeronautics Department. He joined Brown University as associate professor of applied mathematics in the Center for Fluid Mechanics on January 1, 1994. He became a full professor on July 1, 1996. He has been a visiting professor and senior lecturer of ocean/mechanical engineering at MIT since September 1, 2000. He was visiting professor at Peking University (Fall 2007 & 2013). He is a fellow of AAAS (2019), the Society for Industrial and Applied Mathematics (SIAM, 2010-), fellow of the American Physical Society (APS, 2004-), fellow of the American Society of Mechanical Engineers (ASME, 2003-) and associate fellow of the American Institute of Aeronautics and Astronautics (AIAA, 2006-). He received the SIAM/ACM Prize in Computational Science & Engineering (2021), the SIAM Ralf Kleinman Award (2015), CFD award (2007) and the inaugural J Tinsley Oden Medal (2013) by the US Association in Computational Mechanics.

## Menger Awards

**Menger Graduate Award Citation**

The *2024 Karl Menger Graduate Awardee for Exceptional Scholarship* is** Gunjan Sharma.**

**Citation:**

Gunjan has just successfully defended her Ph.D. on “Extremal and Enumerative Problems on DP-coloring of graphs this past Friday! She is receiving this award on the strength of her research, which impressed the awards committee. Gunjan will be graduating with 4 completed research papers, including one published in the Journal of Graph Theory, one of the top journals in her field. Her papers include a collaboration with 3 graduate students from other universities, and she has delivered lectures at several seminars and conferences.

Gunjan came to our Ph.D. program with industry experience, and with community involvement, having invested some of her free time teaching STEM classes in orphanages in India. At Illinois Tech, she has been active on campus, and has served as the Vice-president and Secretary of the SIAM student chapter.

Finally, Gunjan is also an excellent teacher, who is no stranger to our department awards, having been a recipient of the Graduate Student Teaching Assistant award in 2020, and having consistently impressed the instructors who have worked with her.

**Undergraduate Award Citation**

The *2024 Karl Menger Undergraduate Awardee for Exceptional Scholarship* is **KAYLEE J. ROSENDAHL.**

**Citation: **

Kaylee is an exceptional undergraduate student who was nominated for this exact award every year for the past three years, by at least three distinct faculty members. Talented and hardworking, Kaylee is completing her Bachelor of Science in Applied Mathematics, and a Master of Science in Computer Science. Her academic excellence is unmistakable with a 4.0 math GPA and a 3.95 overall GPA. In addition, she has participated in several research and engineering projects on data filtering, satellite simulations, and Chicago lead poisoning, through our own SURE program, Professor Rob Ellis’ i-course, the Institute for Pure and Applied Mathematics, as well as a Chicago-based AI company.

Kaylee is also a leader on campus, having served as the President and Secretary of SIAM and has been instrumental in leading WiSTEM as well, and was instrumental in helping shape this year’s Undergraduate Panel event with Professor Petrovic.

**Graduate Teaching Assistant Award Citation**

But in a year with many strong recommendations, this year’s awardee, Aleksei Sorokin, still stands out. He is among the most frequently requested TA by our faculty for assisting with their advanced courses. He is knowledgeable, independent, professional, focused, very-strong theoretically, fair and a clear-communicator. It is not a mistake that he is the teaching assistant trusted to run our own preliminary examination preparation sessions for our graduate students. The instructors he has worked with rave about his good work ethic, his dedication, his accuracy, his meticulous grading and his clear concise feedback to the students.

The 2023 Menger Lecture was not held due to the COVID-19 pandemic.

### AWARDS

**Menger Award Graduate**

Guillermo Alonso Alvarez

Guillermo was not a stranger to the Awards committee as he was a very close contender for this exact award last year as well. In addition to his research, he has been an organizer of the Financial Math Seminar, and an exceptional teaching assistant.

He received this award for his excellence in mathematical scholarship. Guillermo completed impressive work on optimal contract design in the presence of multiple agents and with partial observations. This was applied to the problem of designing optimal brokerage fees. His scientific maturity and ability to think outside the box were qualities his Ph.D. advisor emphasized in his recommendation to the committee.

Guillermo successfully defended his Thesis in the past month, and is heading to a postdoctoral position at the University of Michigan.

**Menger Award Undergraduate**

Stanley Nicholson

Stanley graduated Summa Cum Laude this spring with a Bachelor in Applied Mathematics, minors in Computer Science and Bioinformatics, and Masters of Science in Applied Mathematics. Stanley excelled in his courses, passing the math graduate exams at the Ph.D. level. He pursued research projects within the department as well as interdisciplinary projects at the intersection of math, computation and biology. He was the recipient of the prestigious NSF Graduate Fellowship in Applied Mathematics. Stanley will be heading off to Brown University with that NSF fellowship to pursue doctoral studies in applied mathematics.

**Teaching Assistant Award**

Xiaoxia Tang

Xiaoxia was nominated this year independently by both the faculty members she worked with this year!

Professor Maslanka emphasizes her clear, concise, and thoughtful introductions to lab assignments in the classroom in his recommendation. Her students praised her approachability and helpfulness during her office hours.

Professor Jeong-Hyun Kang emphasizes what exceptional care she took when grading homework, leaving careful and thoughtful feedback; she emphasizes that while this may sound trivial, one takes grading that seriously and leaves such careful feedback only when they understand the purpose of it.

Her excellent work as a Teaching Assistant over her tenure in that role has been consistently highly praised by her faculty supervisors over the duration of her Ph.D. studies. Among the accolades that are consistently repeated: high reliability in her teaching tasks, obvious care for the students, careful exposition of mathematical concepts, and excellent communication with both the students and the supervisors.

With such a consistently excellent record, it seemed a surprising omission to the committee that Xiaoxia had not received this award in the past already.

**SIAM Recognition**

Jacob Thomas

The 2022 Menger Lecture was not held due to the COVID-19 pandemic

### AWARDS

**Menger Award Graduate**

Qi Zhang

**Menger Award Undergraduate**

Kylie Hance

**Teaching Assistant Award**

Min-Jhe Lu

The 2021 Menger Lecture was not held due to the COVID-19 pandemic.

### AWARDS

**Menger Award Graduate**

Jan-Eric Sulzbach

**Menger Award Undergraduate**

Victoria Belotti

**Teaching Assistant Award**

Ziteng Cheng

**SIAM Recognition**

Victoria Belotti

The Department of Applied Mathematics at Illinois Tech will host Russel Caflisch, Director and Professor of Mathematics, Courant Institute of Mathematical Sciences, as the 2020 Karl Menger Lecturer. He will speak on Friday, March 6, at 6 p.m. The event is part of the 13th annual Karl Menger Lecture and Awards, March 5–6, Illinois Institute of Technology Mies Campus.

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

## Menger Lecture

**Friday, March 6, 2020, 6 p.m. – Rettalliata Engineering Center (RE), Room 104 (Auditorium)**

“From Differential Equations to Data Science and Back,” delivered by Professor Russel Caflisch, Director and Professor of Mathematics, Courant Institute of Mathematical Sciences.

## Schedule of Events

**THURSDAY, MARCH 5, 2020**

*Professor Caflisch will meet with students and faculty.*

**10 a.m. – Research Seminar, Pritzker Science Center (PS), Room 111**

“Accelerated simulation methods for plasmas,” delivered by Professor Russel Caflisch.

**3:15 p.m. – Career Advice Seminar, Pritzker Science Center, Room 129**

**FRIDAY, MARCH 6, 2020**

*Pre-lecture events will begin at 12:50 p.m.*

**12:50 p.m. – AWM/SIAM/AmStats Clubs Meeting, Rettaliata Engineering Center, Room 104**

Professor Russel Caflisch will give the talk “Monte Carlo Methods,” hosted by the Association for Women in Mathematics, Society for Industrial and Applied Mathematics, and American Statistical Association clubs. All alumni are welcome. Light lunch provided.

**1:50 p.m. – Faculty Research Overviews, Rettaliata Engineering Center, Room 104**

**3:15 p.m. – Math Trivia Bowl, Rettaliata Engineering Center, Room 104**

This team trivia competition is for math enthusiasts of all experience levels. Prizes awarded. Having an advanced degree will not help you!

**4:45 p.m. – Poster Session, Rettaliata Engineering Center, Atrium**

**6 p.m. – Lecture, Rettaliata Engineering Center, Room 104**

“From Differential Equations to Data Science and Back,” delivered by Professor Russel Caflisch, Director and Professor of Mathematics, Courant Institute of Mathematical Sciences.

The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for data science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from differential equations, such as variational principles and nonlinear diffusion, to image and data analysis. Examples include denoising, segmentation and inpainting for images. The second focus is the development of new ideas in information science, such as compressed sensing and machine learning. The subsequent application of these ideas to differential equations and numerical computation is the third focus of this talk. Examples include solutions with compact support and “compressed modes” for differential equations that come from variational principles, and applications of machine learning to differential equations and physics.

**7 p.m. – Awards Presentation, Rettaliata Engineering Center, Room 104**

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, Rettaliata Engineering Center, Atrium**

## About the Menger Lecturer

Russ Caflisch is an applied mathematician whose research is on analysis and numerical methods for physical sciences. He is known for analysis of the fluid dynamic limit in kinetic theory and of vortex sheets in incompressible flow, for mathematical modeling of epitaxial growth, and for development of Monte Carlo methods for kinetic theory and finance. He is currently director of the Courant Institute of Mathematical Sciences at New York University and was director of the Institute for Pure and Applied Mathematics (IPAM) at UCLA 2008-2017. Caflisch graduated from Michigan State University with a BS in mathematics in 1975, and received his PhD in mathematics in 1978 at the Courant Institute, NYU. He held faculty positions at Stanford University, NYU and UCLA, before returning to NYU in 2017. He was a recipient of a Hertz Graduate Fellowship and a Sloan Research Fellowship. He is a fellow of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and the American Academy of Arts and Sciences, and is a member of the National Academy of Sciences.

### AWARDS

**Menger Award Graduate**

Min-Jhe Lu

**Menger Award Undergraduate**

Aleksei Sorokin

**Teaching Assistant Award**

Gunjan Sharma

### 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.

### AWARDS

**Menger Award Graduate**

Ziteng Cheng

**Menger Award Undergraduate**

Parker Joncus

**Teaching Assistant Award**

Quinn Stanton

**McMorris Award**

Min-Jhe Lu

**SIAM Recognition**

Yue Cao and Kan Zheng

### 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.

### AWARDS

**Menger Award Graduate**

Jeffrey Mudrock

**Menger Award Undergraduate**

Marissa Ashner

**Teaching Assistant Award**

Shini Feng

### 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

### AWARDS

**Menger Award Graduate**

Yicong Huang

**Menger Award Undergraduate**

Tianci Zhu

**Teaching Assistant Award**

Dane Wilburne

**McMorris Award**

Daniel Kosmas

**SIAM Recognition**

Adam Rumpf

### 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 canceled 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