mathematical sciences news 2019 contents 2019 Editor-in-Chief Tom Bohman Contributing Writers Letter from Department 03 Tom Bohman Head, Tom Bohman Jocelyn Duffy Bruce Gerson Florian Frick 04 Ben Panko Emily Payne Faculty Notes Ann Lyon Ritchie Franziska Weber Graphic Design and Photography 10 Carnegie Mellon University Expanding the Boundaries on Marketing & Communications Summer Undergraduate Research Mellon College of Science Communications 14 Carnegie Mellon University Frick's Fellowship Department of Mathematical Sciences Wean Hall 6113 Pittsburgh, PA 15213 20 cmu.edu/math In Memorium Carnegie Mellon University does not discriminate in admission, employment, or administration of its programs or activities on the basis of race, color, national origin, sex, 24 handicap or disability, age, sexual orientation, gender identity, religion, creed, ancestry, belief, veteran status, or genetic information. Furthermore, Carnegie Mellon University does Alumni News not discriminate and is required not to discriminate in violation of federal, state, or local laws or executive orders. Inquiries concerning the application of and compliance with this statement should be directed to the university ombudsman, Carnegie Mellon University, 5000 Forbes 26 Avenue, Pittsburgh, PA 15213, telephone 412-268-1018. Obtain general information about Carnegie Mellon University Student News by calling 412-268-2000. Produced for the Department of Mathematical Sciences by Marketing & Communications, November, 2019, 20-137. ©2019 Carnegie Mellon University, All rights reserved. No 30 part of this publication may be reproduced in any form without written permission from Carnegie Mellon University's Department of Mathematical Sciences. Class of 2019 1 Letter from Mathematics Department Head, Tom Bohman Undergraduate research has become a hallmark of a Carnegie Mellon University education, with students citing that it has helped to prepare them for their futures in academia and the workforce. Mathematics hasn't traditionally been seen as a field where students do meaningful research; over the course of the last few years, the department has made a concerted effort to change that. In this issue of the Department of Mathematical Sciences Newsletter, we highlight undergraduate research in the department and the programs we have developed to provide research experiences for our students. Our main interest is in summer programs that allow students to focus on a project without the distractions of coursework. With the institution of these programs, the number of students engaged in summer research has grown over the last four years from a handful to more than 60 working on high-quality, open-ended mathematics projects. This is an extraordinary program that very few, if any, other mathematics departments can match. In addition to exposing students to research, the summer Cover Image programs, which include the Summer Undergraduate Research What Can You Draw? Fellowships (SURF) and the Mathematical Finance Summer Undergraduate Research Program (MFSURP), give students For his research project during the the opportunity to be mentored by our renowned faculty. The summer of 2019, Fei Peng raised the mathematical finance program, which has grown dramatically following deceptively simple question: in the last few years, is administered by Bill Hrusa. The SURF What can you draw? program involves a large fraction of the faculty, including Florian Frick, who recently joined us as an assistant professor and was Your canvas is the plane 2 — colored awarded a Sloan Research Fellowship this year (see the articles white to begin with — and you are given on pages 14 and 16 for more on Professor Frick and his research). a pencil, which produces a black unit disk wherever it meets the canvas, and The summer research programs have been made possible an eraser, which produces a white unit I hope that the through the support of our alumni, including David Simmons, disk. There are no further restrictions on many alumni of Larry Jennings, David and Jacqui Martin, and Elizabeth and your artistic freedom. You may raise the tool the Department Konstatin Andreev. To learn more about the research our off the canvas, that is, there is no continuity of Mathematical students engage in, see page 28 for details on the 2019 SURF requirement for the centers of disks you draw Sciences have projects and page 10 for an article on the evolution of the and you can switch tools as many times as a chance to summer programs. Additionally, the image on the cover of desired. Peng and his research mentor Florian reconnect with this issue is drawn from the SURF project of Fei Peng, a junior Frick showed the main result is that drawability the department mentored by Professor Frick. cannot be characterized by local obstructions. by visiting A bounded set can be locally drawable, while cmu.edu/math Of course, there have been many other developments in the not being drawable. The figure presented here department. In this issue you can also read about our new is an example of such a set; the boundary Let us know faculty, faculty awards (including Po-Shen Loh's receipt of the has curvature less than one, but the set is not what's new Presidential Early Career Award in Science in Engineering) drawable in the large. with you! and student awards. 2 3 faculty notes Ian Tice Wins Julius Ashkin Award Giovanni Leoni Wins Richard Moore Award Assistant Professor Ian Tice was awarded Additionally, Tice is a strong supporter of the Mellon College of Science's 2019 Julius undergraduate math research. His experience Professor Giovanni Leoni was honored Another focus of Leoni's has been to equip Ashkin Teaching Award for his devotion and as a research advisor inspired him to apply with the Mellon College of Science's postdoctoral students with the tools to effectiveness in teaching. for a National Science Foundation (NSF) 2019 Richard Moore Award. This award is effectively teach upper-level mathematics CAREER grant. NSF awarded him $38,500 presented every year to a faculty member in courses. In the summer of 2017, he Tice is an inspiring educator, both to fund summer research for 11 students the college who is making substantial and implemented an orientation program for challenging and guiding his students to over the next five years. One of Tice's favorite sustained contributions to the educational all incoming postdocs to instruct them become astute mathematicians equipped activities is organizing and supervising the mission of the college. on how to write syllabi in line with Faculty with inquisitive minds. Tice has crafted Department of Mathematical Sciences' Senate guidelines, how to conduct student hundreds of homework problems and written poster competition at Carnegie Mellon's Leoni created the department's assessments, how to work with teaching over 1,300 pages of notes for his courses. annual undergraduate research symposium, Undergraduate Curriculum Committee, assistants and how to use Canvas, the Meeting of the Minds. which has completely transformed and While his homework problems are known university's learning management system. strengthened the undergraduate program Leoni also provided constructive feedback for taking hours to complete, by the end, Beyond teaching, Tice has been a driving over the course of the last decade. Since for postdocs through "mock" classes. students understand step-by-step how to force in developing and modernizing parts its inception, Leoni has served as chair of assemble a proof for a full result; this, of the undergraduate and graduate the committee with the goal of providing In addition to his focus on the broader Tice says, helps students synthesize curriculum in the department. excellent mathematical education to all educational and administrative aspects mathematical arguments and trains them Carnegie Mellon University students, of the department, Leoni cares deeply to think like mathematicians. He completely revamped the undergraduate computational and applied mathematics regardless of major or college. The about his students and dedicates his time Tice knows he demands a lot of his students, concentration, helped reform the graduate committee's main achievements include a to making sure they succeed. He holds but his door is always open. Students will curriculum in analysis and partial differential complete redesign of the introductory course recitations for courses that do not have a spend hours in his office, be it to get help on equations (PDE) and revised courses in the sequence for math and computer science recitation and conducts research projects a problem, to revisit a concept from lecture math honors program. He has developed four students and a redesign of the honors with students over the summer. that they didn't understand or to talk more new courses, restructured the department's course sequence for mathematics majors. "Giovanni Leoni regularly steps in and about their interests in math. mathematical modeling and graduate PDE Leoni has worked with faculty across takes charge of administrative details that courses and took on teaching a number of "Professor Tice is someone who very clearly the university to tailor the mathematical have a very high impact on the education these courses, both new and old. loves teaching," wrote former student Jose sciences program to suit students from all of students in mathematics courses," Arrillaga. Arrillaga spoke with Tice about "Ian is an enthusiastic and devoted teacher majors. His efforts have also helped grow wrote Tom