**Mon Apr 08, 2019**

On Monday, April 1 and Tuesday, April 2, Illinois Tech’s Department of Applied Mathematics held its 12th annual “Remembering Karl Menger” lecture series and events, commonly known as Menger Day. This year, the Menger Lecturer was Professor Xiao-Li Meng, the Whipple V. N. Jones Professor of Statistics at Harvard University and the founding editor-in-chief of the Harvard Data Science Review.

The Menger Day events began during the lunch hour on April 1 when the Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) jointly hosted a lunch talk where Professor Meng gave his first lecture. It was entitled “Bias-Variance Tradeoff: A Fundamental Statistical Principle That Can Render You Love or Pain.” As this talk was geared towards an undergraduate level of understanding, Professor Meng began by explaining the statistical concepts of bias and variance, and he showed an example where they come into play in Simpson’s Paradox. He then went on to discuss some of their real-world applications of the study of those aforementioned concepts. One such application was of particular personal significance to Professor Meng himself; he spoke on the statistical thinking that went into his contemplation on how he should medically handle his own medical situation of kidney stones (the “rendering pain” part of the talk title). From there, he connected his talk to how statistics relates to the developing concept of personalized medicine. Professor Meng concluded this first talk by explaining the “rendering love” part of the title, by explaining how someone once told him that one of his research papers saved his marriage. The man and his wife shared a car and worked in the same building and regularly fought over where the car was parked. Professor Meng wrote about how, if you always park your car on the top level of the garage in the far corner (where no one else wants to park), you will always be able to remember your parking location. This stopped the couple’s arguments and thus saved their marriage.

After Professor Meng’s initial talk, several applied mathematics professors gave research overviews of both what research they are currently working on and what they have worked on in the past. Professor Maggie Cheng spoke on “Real-time Data Analytics for Power Grids.” Professor Matthew Dixon then talked on “Computational Frameworks for Dynamical Modeling” and spoke about how he uses neural networks, deep learning, and Voronoi diagrams in his work. Professor Shuwang Li talked on “Modeling and computation of tumor growth” and the factors that go into predict such growth. Professor Sergey Nadtochiy spoke on “Socially Responsible Investment,” which is about how to use optimal contract design to incentivize financial investors and managers to avoid investing in companies or organizations that you may morally oppose (such ones that commit genocide). Professor Despina Stasi’s talk was titled “Discrete Structures, Randomness, and Statistical Network Models.” Finally, Professor Sara Zelenberg talked on “Machine Learning for Math” and spoke about using algebraic concepts such as varieties and Gröbner bases in her work.

After the faculty research overviews was an event I personally helped create and plan: speed mentoring. Modelled after the concept of speed dating, students were able to meet one-on-one with applied math professors and alumni in a series of short meetings. Student mentees were able to ask questions about the field of mathematics, such as how to get a job, get into graduate school, what courses to take, or anything else they would want to ask. In fact, because of how many faculty and alumni were willing to volunteer as mentors, each mentee was able to meet with two faculty/alumni at once for each session. In addition to planning this event in collaboration with Professors Kiah Ong and Despina Stasi, I myself also participated as a mentee and found that I greatly benefited from hearing many different opinions on the career paths I am considering in mathematics.

Following the speed mentoring event was the poster session and exhibition where applied math undergraduates, graduates, and some faculty presented their research posters. For me, this also had particular personal significance: my friend Rena Haswah and I presented our poster, “Circularity of Hand-Drawn Circles” where we discussed our numerical methods for determining how close a hand-drawn circle is to being a perfect circle.

Then came the main event: Professor Fred Hickernell, vice provost of research and former chair of the applied mathematics department (re)introduced Professor Meng, who then delivered a Menger Lecture entitled “How Small Are Our Big Data: Turning the 2016 Surprise into a 2020 Vision.” This talk was highly fascinating; Professor Meng discussed some of the statistical reasons behind why so many predictive models failed to predict the United States 2016 presidential election and what statisticians are now learning and implementing to prevent such failure in the future. He discussed the importance of not only effective sample size choice, but also where that sample is drawn from. He also showed the drastic implications of seemingly small predictive errors. He concluded by discussing the statistical lessons from all of this, along with stating the big data paradox: “the bigger the data, the surer we fool ourselves.” This lecture was the highlight event and was very well attended, and from speaking to other people who came for it, everyone seemed to have learned and taken away some insight from Professor Meng’s lecture.

The main lecture was followed by Professor Robert Ellis, associate dean of the College of Science, presenting awards and recognizing poster exhibitors. This year, the undergraduate Karl Menger Student Award for Exceptional Scholarship went to Parker Joncus, a fourth year applied math undergraduate who will be graduating this spring with a co-terminal master’s degree in data science. The graduate Menger Student Award went to Ziteng Cheng, a fourth year Ph.D. applied mathematics student. The Graduate Teaching Assistant Award went to applied math Ph.D. student Quinn Stratton, who had a numerous amount of his students comment on his exceptional skills as a teaching aide (TA). The Fred F.R. “Buck” McMorris Summer Stipend went to Min-Jhe Lu who will be using it to do research with Professor Shuwang Li this summer. The first day of Menger events concluded after that with a reception and networking amongst students, alumni, and faculty.

The second day began with Professor Meng delivering a research seminar, “Is It a Computing Algorithm or a Statistical Procedure – Can You Tell or Should You Care?” This talk was much more high-level and faculty oriented. Later on that same day, Professor Meng delivered his final talk, “Conducting Highly Principled Data Science: A Statistician's Job and Joy.” As someone with an interest (and a double major) in statistics, I found this final talk to be extremely fascinating because of how Professor Meng discussed some key concepts that any principled statistician should keep in mind: to “develop and apply methodologies that are: scientifically justified, not merely motivated; statistically principled, not just verified; and computationally efficient, not simply reproducible.” This was followed by a question session where members of the audience could ask him questions about his career as a statistician. He was incredibly thoughtful and answered all of them deeply and with great relevance to an aspiring mathematician or statistician.

With this being my first Menger Day (sample size is n = 1), I have nothing to compare it against, but I can say I thoroughly enjoyed myself at all the talks and events I went to (and planned). Professor Meng not only had very relevant and interest things to say, but he also communicated them extremely well as a speaker. I look forward to what future Menger lecturers will contribute to the applied math department and community at future Menger Days.