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Views from the Chairs in Phi Beta Kappa and Sebastian Haney these additions comes a feeling of was awarded a Goldwater Scholarship. On anticipation and activity with the new term Zoran Grujić the graduate side, Mariano Echeverria and just around the corner. I know that we are Professor of Veronica Shalotenko were the recipients of all dedicated to making the department the All-University Graduate Teaching Awards best it can possibly be, by working as hard Interim Chair and Mike Reeks received Class of 1985 as we can to find excellence in new hires 2017-2018 Fellowship for Creative Teaching. and new admissions, and by fostering a nurturing environment for newcomers and The Institute of Mathematical Sciences Greetings friends, veterans alike. old and new. I am (IMS) experienced a flurry of activity, writing this after including two series of Virginia The upcoming year will be a busy one, with completing my Mathematics Lectures,by Yair Minsky a faculty search in the works, several one year-term as the Interim Chair, happy (Yale) in the Fall and Irene Fonseca promotions to attend to (a welcome and to report that the Department is alive and (Carnegie Mellon) in the Spring, two IMS natural consequence of the hiring we have well! Special Lectures by Barry Simon (Caltech), been doing), and continued expansion of an IMS Public Lecture (co-sponsored with calculus reform (with new faculty member The stage set by Craig Huneke's four-year Physics) by Jacob Sherson (Aarhus) on James Rolf joining Paul Bourdon in that term as the Chair was the one of a citizen science, as well as two workshops. effort). department in which the faculty and the In addition, the public lectures sponsored Readers of this newsletter series will see students (graduate and undergraduate by theA&S Diversity and Inclusion Grant, over the last few issues all the momentous alike) were pursuing a variety of exciting awarded to Sara Maloni, sparked the avenues of the mathematical inquiry, a interest of the broader University changes and accomplishments over these years. My heartfelt thanks goes to Zoran department committed to exploring new community; the lectures were given by for accepting the chair position during the ways of how we teach mathematics Moon Duchin (Tufts), Abby Stewart last year. During this time, I was able to (particularly Calculus) by adopting/ (Michigan) and Henry Segerman pursue a year of research leave in redesigning a variety of student-centered, (Oklahoma State), addressing the topics of Princeton, developing exciting ideas and active learning methodologies, as well as a mathematics of , changing new collaborations that will keep me busy department fully engaged in outreach departmental culture to be more inclusive, during lulls in department business -- across the University, the Commonwealth and artistic mathematics, respectively. and beyond; hence, it should come as no assuming there are any! His dedication to surprise that the academic year 2017-2018 On a personal note, I am quite ready to go the department's well-being has been was a productive one. A glimpse of what back to research and teaching as my evident from the beginning. I realize that transpired can be gained from the rest of favorite pastimes. The good news is that every challenge he faced and surmounted the newsletter, in what follows, I will just John Imbrie is here ready to take our during the last year makes my work that touch on several highlights. department to the exciting new much easier. I only hope I can serve the adventures. department as well as Craig and Zoran Our Calculus transformation efforts have. With the efforts of our dedicated initiated by Craig and spearheaded by Paul faculty, staff, and students, and with the Bourdon received a boost this year by support of the Dean's office and alumni, I hiring James Rolf who previously served as John Imbrie Professor of have every expectation for another banner Director of Quantitative Learning at Yale. year in Kerchof Hall. Mathematics A number of our faculty members received Chair national honors and awards; in particular, Karen Parshall received The Albert Leon I write this note as Supporting Us Whiteman Memorial Prize of the AMS, Julie I begin a three- Bergner received The Ruth I. Michler year term as chair. The Mathematics Department is grateful for the Memorial Prize of the AWM, Nicholas Kuhn I am humbled by generous support of its alumni and friends. The and Weiqiang Wang were inducted in the all that has been Department welcomes gifts annually to address its most urgent needs, as well as to the endow- 2018 Class of the Fellows of AMS, and John accomplished in the department during the ment which provides funding in perpetuity. To five years since my interim chairmanship Imbrie and Andrei Rapinchuk held their learn about how you can make a difference by Simons Fellowships in Mathematics. in 2012-3: four years under Craig Huneke's supporting the Mathematics Department, please guidance, and last year with Zoran Grujic at contact Liz Blaine at [email protected] or On the undergraduate side, Grace Dwyer, the helm. There have been quite a few new Kevin Lee and Luca Scerbo were inducted (434) 924-6156. To make a gift online, please faculty added over this timespan, and with visit http://giving.virginia.edu/mathematics New Faculty Profiles

Benjamin graduate student who does the best job (Mathematical Association of America, Hayes explaining their research to someone 2012). His work has been supported by Assistant outside of their . numerous grants funded by the Association Professor of American Universities, the National (2017- ) Hayes received his B.S. in mathematics from Science Foundation; Microsoft Corporation, the University of Washington (2009) and Working with Yale's Center for Teaching and Learning, and earned his Ph.D. in mathematics from UCLA colleagues in the others. (2014). Department of Rolf received a Ph.D. from Duke Mathematics’ Hayes will be teaching an Introductory Real University in 1997, a Master of Divinity from operator theory Analysis course in the fall and Calculus on Southwestern Theological Seminary, and a group, Benjamin Hayes Manifolds in the spring. Excited to work with bachelor's of science from Baylor University. researches topics involving the the department’s operator theory group, Before coming to the , measurement of how many finitary Hayes also plans to explore possible he served as the Shizuo Kakutani Lecturer at approximations there are of a given collaborations and connections with the , as an associate professor of infinitary object, including: entropy for department’s algebra and probability mathematics at the United States Air Force actions of nonamenable groups, free groups. Academy and as an assistant professor at the probability with connections to von Jim Rolf United States Military Academy at West Neumann algebras and random matrices, Point. and sofic groups. Associate Professor Joining the Department of Mathematics, Rolf Hayes arrives at the University of Virginia (2018- ) will teach Math 1320 (Integral Calculus) this with a grant from the National Science next year and will help design metrics to Foundation’s Division of Mathematical Trained as a assess changes in student learning and Sciences for his continuing research. He has numerical analyst, attitudes in this course when changes to published nine papers, including articles in James (Jim) Rolf course design are implemented. Geometric and Functional Analysis, currently focuses International Mathematics Research Notices on the scholarship He also will continue to work with other and Journal of the Institute of Mathematics of teaching and institutions as they seek to implement and Jussieu. As a graduate student at UCLA, learning assess innovative ways to help incoming Hayes earned a Dissertation Year mathematics. He has published a number of students prepare for quantitative reasoning Fellowship and the Heaviside Wealth articles and is a co-author of the book requirements at their institution. Management Award, which recognizes the Explorations in Complex Analysis

Vivek ideals, multiplicity theory, koszul algebras National Board for Higher Mathematics Mukundan and other topics. postdoctoral fellowship from India’s Postdoctoral Department of Atomic Energy, an Vivek received his master’s degree in Fellow INSPIRE Faculty Award from India’s (2017- ) mathematics from the Indian Institute of Ministry of Science & Technology, a Technology in Madras, India, and a Ph.D. Working in the Jawaharlal Nehru Centre for Advanced in mathematics from . areas of Scientific Research Fellowship, and travel Before coming to the University of commutative grants from the American Mathematical Virginia, he was a visiting fellow at the algebra and Society and the Mathematical Research Tata Institute of Fundamental Research in algebraic geometry, Communities program. Mumbai, India. Vivek Mukundan’s research spans At UVA, he plans on furthering his methods for computing the defining ideal Mukundan’s research grants and research in the fields of commutative of the Rees algebra, studying the fellowships include multiple summer algebra and algebraic geometry while invariants of powers of edge research grants from Purdue University, a expanding his teaching repertoire. New Faculty Profiles

Prasit professor (2015-2017). introduced in the last decade, which have brought about a surge of interest in the area. Bhattacharya Bhattacharya has taught mathematics Whyburn courses at all college levels, including Liron will be joining the University of Instructor pre-calculus, calculus (at various levels), Virginia directly from Osaka University, (2017- ) linear algebra and finite mathematics. He Japan, where he held a postdoctoral Working in the area of enjoys mentoring undergraduate students fellowship funded by the Japan Society for algebraic topology, as well as high-school students. the Promotion of Science. After receiving his Prasit Bhattacharya Bhattacharya hopes to continue mentoring Ph.D. in mathematical sciences from Queen researches computational aspects of stable students at UVA and to teach courses at Mary University of London, and his master’s homotopy theory. Specifically, he explores various levels while degree in mathematics from the University stable homotopy groups of spheres, using organizing of Warwick, he held a visiting postdoctoral chromatic homotopy theory. He studies vn graduate-level position at the University of East Anglia, self-maps that result in infinite families of seminars, as he has at funded by the London Mathematical Society. previous institutions. elements in stable homotopy groups of Liron’s work has been published in spheres, and his current research involves C Liron Speyer Transactions of The American Mathematical 2- equivariant computations, with a focus on Whyburn Society, Proceedings of The American the telescope conjecture. Instructor Mathematical Society, International Bhattacharya completed his bachelor’s (2017- ) Mathematics Research Notices, as well as degree (2007) and his master’s degree in three top algebra journals. A postdoctoral mathematics (2009) at the Indian Statistical researcher specializing in representation This academic year, Liron will teach algebra Institute in Bangalore, India. He completed theory, Liron Speyer focuses his work on the courses for science majors, while his his Ph.D. at Indiana University (2015). study of a fundamental object known as the research will largely focus on constructing a Bhattacharya comes to the University of symmetric group, as well as several families vast generalization of the famous Littlewood Virginia from the University of Notre Dame, of related mathematical objects. These –Richardson Rule in the context of quiver where he served as a visiting assistant include the quiver Hecke algebras Hecke algebras.

Jinbo Ren Besides the pursuit of excellent Equations and Mathematical Physics. Postdoctoral mathematical research, Jinbo has a great Recently, his work centers on his interest in Research Associate passion for teaching. For him, each day with the description of longtime behavior of some (2018- ) lectures is a holiday. He radiates an models that arise from fluid dynamics and infectious enthusiasm in making everyone in relativistic quantum mechanics via the Working in the areas of his class enjoy the beauty of theory of invariant measures. This method number theory and mathematics, instead of only coping with employs statistical equilibria of systems to algebraic geometry, Jinbo exams. Jinbo also takes classical literature as predict the individual behavior of their Ren’s research mainly a pastime. constitutive particles. concerns subjects on the arithmetic and geometric properties of Mouhamadou Sy He also likes working with students in order abelian varieties and Shimura varieties, for Postdoctoral to introduce them to different mathematical example the André-Oort and Zilber-Pink Research concepts and scientific thought. During his conjectures. He also works in related topics Associate graduate studies at UCP, he supervised in symmetric spaces, transcendental number and Whyburn undergraduate students working on their final dissertations. In 2015, he received an theory, model theory, and group theory. Lecturer award in recognition of this work from the (2017- ) Jinbo received his master’s degree in FSPM (Mathematical Sciences Foundation of mathematics from both Universiteit Leiden, Mouhamadou Sy attended high school in Paris), in collaboration with the Casden the Netherlands and Université Paris-Sud, Mauritania, then joined the University of Bank. France. He completed his Ph.D. in Cergy-Pontoise in France for his At UVa, he plans to develop probabilistic mathematics from Université Paris-Sud, undergraduate and graduate studies. France. Before coming to the University of methods to approach the Cauchy problem of Virginia, he spent three years at Institut des In 2017, he received his PhD from the supercritical equations - an outstanding Hautes Études Scientifiques (IHES), France. University of Cergy-Pontoise. His current open problem in the theory of Partial research interests include Partial Differential Differential Equations. Faculty Awards and Honors KAREN PARSHALL access, and computing facilities will be General Faculty this year. He came to UVa in RECEIVES 2018 provided by Cornell. The award is to be used 2013 as a Visiting Professor of Mathematics, AMS WHITEMAN during the 2018-2019 academic year. having held appointments at Michigan State University, the University of Tennessee at PRIZE She was selected for her “proposed project Knoxville, and Washington & Lee University to connect some of her recent work with the Commonwealth Professor where he was Cincinnati Professor of research of Cornell faculty member Inna of Mathematics and History Karen Hunger Mathematics. Bourdon’s research interests Zakharevich, including simultaneous Parshall received the 2018 Albert Leon are operator theory (especially composition developments by both women (and their Whiteman Memorial Prize of the AMS for her operators acting on spaces of analytic respective coauthors) on algebraic K-theory outstanding work in the history of functions), function theory (analytic & constructions.” Bergner’s research has been mathematics, and in particular, for her work harmonic), and quantum-information theory in the areas of homotopy theory. Her on the evolution of mathematics in the USA (superdense coding with partially entangled proposed research will bring together and on the history of algebra, as well as for quantum particles). His research has been several facets of her work: the theoretical her substantial contribution to the supported through four grants and two framework of homotopical categories and international life of her discipline through research-opportunity awards from the generalizations, the realization of 2-Segal students, editorial work, and conferences. National Science Foundation. Bourdon spaces as a form of algebraic K-theory, and received, April 2000, the John Smith Award The Albert Leon Whiteman Memorial Prize looking at derived Hall algebras as algebraic for Distinguished Teaching of Mathematics, recognizes notable exposition and homotopical categories. exceptional scholarship in the history of conferred by the MD-VA-DC Section of the mathematics. It was established in 1998 NICHOLAS KUHN Mathematical Association of America. He is using funds donated by Mrs. Sally AND WEIQIANG currently Director of Lower Division Courses Whiteman in memory of her husband, WANG NAMED 2018 for the Mathematics Department. Albert Leon Whiteman. The 2018 prize was AMS FELLOWS BEN HAYES AWARDED awarded Thursday, January 11, 2018, at the Joint Mathematics Meetings in San Diego. Professors Nicholas J. Kuhn EXCELLENCE IN and Weiqiang Wang have been named 2018 POSTDOCTORAL JULIE BERGNER Fellows of the American Mathematical RESEARCH PRIZE RECEIVES MICHLER Society: MEMORIAL PRIZE Assistant Professor of Nicholas Kuhn “For contributions to Mathematics Ben Hayes Associate Professor Julie homotopy theory, group cohomology and was awarded the Amir Bergner has been selected as representation theory.” Aldroubi and Amira Azhari Prize for the winner of the 2018-2019 Excellence in Postdoctoral Research from Weiqiang Wang “For Ruth I. Michler Memorial Prize Vanderbilt University on Wednesday, April contributions to Lie theory competition. 18, 2018. and representation theory The Ruth I. Michler Memorial Prize of the and service to the The Samir Aldroubi and Amira Azhari Prize AWM is awarded annually to a woman mathematical community.” for Excellence in Postdoctoral Research is recently promoted to Associate Professor or awarded every two years to recognize the Sixty-three mathematical scientists have an equivalent position in the mathematical research achievements of current and recent been named 2018 Fellows of the AMS. AMS sciences. The Ruth I. Michler Memorial Prize postdoctoral fellows in the department. It President Kenneth A. Ribet says, “This year’s honors outstanding women at this stage of was established by Mathematics Professor class of AMS Fellows has been selected from their careers and enable them to focus on Akram Aldroubi in honor of his parents, a large and deep pool of superb candidates. their research in the stimulating Samir Aldroubi and Amira Azhari. It is my pleasure and honor as AMS environment of the Cornell University Candidates for the Aldroubi-Azhari Award President to congratulate the new Fellows Mathematics Department. are nominated by the faculty of the for their diverse contributions to the department, and the recipient is selected by A USD 47,000 prize will be awarded to a mathematical sciences and to the a departmental committee. The chosen woman, recently promoted to associate mathematics profession.” mathematician receives $1,000 and is professor or the equivalent, for a semester of PAUL BOURDON invited to Vanderbilt to deliver a mathematical research without teaching mathematics colloquium reflecting his or her obligations in the Mathematics Department PROMOTED TO FULL research interests. of Cornell University. A supplement PROFESSOR housing/subsistence stipend award of USD Paul Bourdon was promoted 3,000 will be provided. Office space, library to Professor of Mathematics, Transforming Calculus

The course was challenging, but I learned a lot of new material in ways that were easier to understand and implement. I liked the “flipped” aspect of the class because I find that doing problems is the best way to learn mathematics. Overall, the course went well and I learned a lot. - Comment from a student’s course evaluation of “transformed” Calculus I (Math 1310)

By Paul Bourdon Students learn best when they take an active role In October of 2016, Mathematics- Department faculty approved a proposal  When they discuss what they are reading to transform calculus instruction at UVa  When they practice what they are by reducing class sizes, increasing the learning amount of time students spend in class engaged in problem-solving activities—  When they apply practices and ideas.1 especially group-based ones, and The first sections of Math 1310 having the augmenting learning objectives for the structure described above were offered course to include improvement of Instructor Jon Simone responds to a student’s question during Spring ’17. Four of eight sections offered Fall technical reading and writing skills as Calculus-I groupwork.

’17 were taught in the transformed, flipped well as development of confidence and Implementation -classroom style, and, starting this fall, all competence in communicating technical The “Transforming Calculus” proposal calls sections offered will be flipped. Spring information orally. for modifying courses gradually over a five- 2019, Calculus II (Math 1320) classes will be year period, with the “science track” The “Transforming Calculus” proposal, transformed, with implementation directed Calculus-I course (Math 1310) the first to be authored by Craig Huneke (Chair of the by Jim Rolf, a newly hired general-faculty transformed. During the Fall term of the Department, 2013-2017), also calls for member, formerly the director of 2016–2017 academic year, Paul Bourdon primary instructors to conduct all class quantitative learning at Yale University. (Math Department), Gail Hunger (Learning meetings (those labeled “discussion” as well Transformation of Math 1220, A Survey of De- sign and Technology), Peter Bonventre as those labeled “lecture”), adding a fourth Calculus II, is scheduled for implementation (Math GTA), and Katelynn Kochalski (Math hour of instruction in 1200- level calculus fall of 2020; and of Math 1210, A Survey of GTA) met weekly to design a transformed courses, creating new general-faculty and Calculus I, fall of 2021. Calculus-I course, based on a flipped- postdoctoral positions to provide additional classroom, groupwork-intensive model of Assessment. instructors needed to support smaller class instruction used successfully at the Our assessments of the effectiveness of the sizes and more hours of instruction per . The structure of format of the transformed Math 1310 course week, and expanding the Math Tutoring “Transformed Calculus I” is described as are consistent with research indicating that Center to increase support for calculus follows on the current syllabus for the students learn more when they engage in students outside of the classroom. course: collaborative problem solving with their

Some Background All sections of Math 1310 are based on active- and peers during class. For example, Fall ’17, The Department offers a two-tier system of cooperative-learning strategies designed to students in flipped sections of Math 1310, on calculus instruction: a one-year sequence further develop your problem-solving skills average, achieved normalized gains on the (1210–1220, A Survey of Calculus I–II) for applicable in any situation. “Calculus Concept Inventory” 11% higher students interested primarily in the life, During our Tuesday and Thursday class meetings, than those of students in traditionally taught managerial, and social sciences, and a one- at least 70% of the time you will be engaged in sections and scored between 5.9% and year sequence (1310–1320, Calculus I for groupwork with your classmates; the rest of the 38.2% higher on multiple-choice assessment students interested primarily in the natural time will be devoted to mini-lectures (by me), -problems on the common Math 1310 final sciences (including mathematics). In the problem-solution discussions (led by students), exam. Moreover, in their course evaluations, Spring and Fall of 2015, 1742 students took and whole-class discussions of concepts, students in flipped sections indicated greater techniques, and problem-solving principles. 1210 or 1220 in 44 sections. During the agreement with statements such as “I During our final class meetings on Fridays, we will same period, 514 students took 1310 or learned a great deal in this course,” and review topics from the first two class meetings of 1320 in 17 sections. A significant portion of the week and typically have a quiz on those topics. many praised the structure of the course. all students in the College pass through these For our Tuesday and Thursday class meetings, courses. Each course in the 1300-level you’ll be expected to familiarize yourself— 1 From Tools of Teaching by B.G. Davis, Jossey-Brass, San Francisco 1993. sequence carries four credits, providing 200 through on-line class-prep assignments minutes of class time per week, while (accompanied by a video)—with the basic notions currently each course in the 1200-level and ideas that will play a role in class. sequence carries three credits, providing 150 The design of this course is based on research minutes of instruction per week. showing: Department Activities

CIRMATH-AMERICAS Science, the Centro internazionale per la from the Americas working on related CONFERENCE ricerca matematica in Trento, Italy, the historical questions. Fourth International Conference on the A conference on the To provide researchers the opportunity History of Mathematics Education in role of journals in to explore the significant archival and Turin, Italy, and the Mittag-Leffler mathematics was library holdings at both the University of Institute in Stockholm. The CIRMATH- hosted by Professor Virginia and the nearby Library of Americas meeting at the University of Karen Parshall and Congress. Virginia was the group’s first meeting in sponsored by IMS. the United States, a country which - To provide opportunities for American CIRMATH includes researchers from especially in the period from 1850 to and European researchers at earlier Europe, the United States, Canada, and 1950 - played an increasingly large role stages in their careers to develop Latin America. Since 2014, it has in international mathematical significant and enduring research sponsored a series of colloquia at the developments. collaborations with established scholars Institut Henri Poincaré in Paris and at the in the history of mathematics. The CIRMATH-Americas meeting has the University of Lorraine., while various of following goals: To trace the impact of journals on the its members have participated in circulation of mathematics within the conferences at the Royal Society of To provide a venue in which European Americas and between the Americas and London, the Lisbon meeting of the CIRMATH members can intensively Europe from 1850 to 1950. European Society for the History of interact with historians of mathematics IMS Special Lectures

Barry Simon: Tales of our Jacob Sherson on Citizen from understood the human ability to reach Forefathers Science: Benchmarking fast, intuitive and correct decisions based on often seemingly too little data. In the Human and Artificial The UVa www.scienceathome.org project, we have Department of Intelligence developed games allowing so far 250,000 Mathematics & On April 19th, Jacob players to contribute to research in The Institute of Sherson (Department quantum and classical physics, Mathematical of Physics and mathematics, chemistry, behavioral Sciences presented Astronomy, Aarhus economics, corporate management, two Special University, Denmark psychology and cognitive science. We Lectures by Barry and ScienceAtHome) believe that this wealth of data from human Simon (California delivered a public individual and collective problem solving Institute of lecture entitled can be used to generate novel insights Technology). The first of these, entitled “Citizen Science: about human intuition and innovation that “Tales of our Forefathers,” took place on Benchmarking Human and Artificial could potentially form the basis of novel February 26th, with “More Tales of our Intelligence,” co-sponsored by the IMS and forms of human-inspired AI. Forefathers” occurring on the 28th, Departments of Mathematics and Physics. Sherson concluded the talk with a discussing Riemann, Newton, Krein, and description of how the work is situated Noether, among other mathematicians. To use Sherson’s own words: “Artificial intelligence (AI) is a field is in rapid “within the new global educational Simon described the lecture as “not a development and there are almost-daily movement, Think Like a Scientist, in which mathematics talk, but...a talk for news reports about how AI has we introduce citizen science games to the mathematicians.” He argued that “too often, revolutionized yet another industrial formal school setting at all levels as a we think of historical mathematicians as domain. Some researchers claim that means to make the world of research and only names assigned to theorems. With within a few decades we will reach a so- knowledge generation available to the vignettes and anecdotes,” he continued, “I’ll called singularity in which computer students from an early age.“ convince you they were also human beings intelligence will surpass human capabilities and that, as the Chinese say, ‘May you live in all domains. Other AI-researchers, in interesting times’ really is a curse.” however, maintain that we have still far Virginia Mathematics Lecture Series The Virginia Mathematics Lectures are a Distinguished Lecture Series that IMS established in 2014 Spotlight: ways in which hyperbolic geometry interacts varying geometry on the interior to 2- Yair Minsky with topology in three dimensions also dimensional combinatorial and geometric informs our understanding of many related structures.” The lecture explored these ideas Yair Minsky of Yale fields, such as and before moving on to a brief explanation of University was our complex dynamics.” The lecture served to “how they provide a complete set of guest in mid- provide “a brief introduction to this subject,” invariants for deformation spaces of 3- November and with a focus on “examples, geometric manifolds.” delivered three intuition and overall structure. The final lecture, “Quantitative models, lectures as part of The second lecture took place the following Thurston's skinning map, and beyond,” the Virginia day, and was entitled “Between 2 and 3 occurred on November 15th. “While the Mathematics dimensions: Teichmuller theory, pleated theory has had many successes,” Minsky Lectures series. surfaces, and the complex of curves.” concludes, “we are still far from The first lecture, “Hyperbolic 3-manifolds, having a complete ‘effective’ recipe for pre- “One can probe the geometry of a 3- their structure and deformations,” took dicting the geometry of a hyperbolic 3- manifold,” he continues, “by mapping in place on November 13th, 2017. Minsky manifold from its topological description.” surfaces in different ways: conformal describes hyperbolic geometry as the Minsky then highlighted some current work boundaries at infinity give us a “richest and most interesting of Thurston’s being done in the area, as well as the parametrization of families of 3-manifolds eight geometries for 3-manifolds,” unanswered questions that future work will using classical Teichmuller space, and explaining that “a good understanding of the need to address. Thurston’s pleated surfaces relate the

Spotlight: Irene Fonseca Undergraduate Experiences: talked about her experience as the only AWM Lunch with Irene female professor in the CMU math On March department, and how that has been true for Fonseca 15th and almost the entirety of her 30 years teaching. By Mia Shaker 16th, the It opened up a larger conversation about On March 15, the AWM chapter of the UVA Department what the admitted graduate students had Math Department hosted a lunch with the was pleased seen in regards to representation in their Professor Irene Fonseca from Carnegie to host Ire- own schools. ne Fonseca Mellon University. Professor Fonseca is a of Carnegie renowned mathematician, the director of Another interesting dimension to the issue Mellon Carnegie Mellon’s Center for Nonlinear of women in mathematics that Irene University, Analysis. She came to UVA to give a series of Fonseca raised is the “two-body problem,” who gave lectures on “Variational Methods for which refers to how spouses in academia two talks on “Variational Methods for Materials and Imaging Sciences” in our often struggle to obtain jobs at the same Materials and Imaging Sciences” as part of ``Virginia Mathematics Lecture Series" university, or within commuting distance of the Virginia Mathematics Lectures series. sponsored by the Institute for Mathematical each other. Fonseca, while having seen the Sciences. She also kindly agreed to meet two-body problem stop several women she Fonseca explains that “recently developed with a group of the AWM members as well knows from getting the best job available to methods and a deep articulation of ideas as the visiting admitted mathematics them, felt that CMU originally hired her in from the Calculus of Variations, Geometric graduate students. large part because they were hiring her then Measure Theory, and nonlinear Partial -husband. Differential Equations (PDEs), have been At the beginning of the event, Irene Fonseca instrumental in the mathematical rigorous shared a little bit about her research As an undergraduate in the AWM, I often understanding of nonlinear phenomena in a interests, and she heard from everyone in focus on the representation of women plethora of physical and technological attendance about what their areas of among students, but this lunch really applications, ranging from analyzing interest in mathematics are. broadened my perspective and had me instabilities in novel advanced materials to looking towards the future. I found myself But the real focus of the lunch and the denoising of medical images.” inspired by the way Irene Fonseca and other discussion was on the representation of like her have been striving to succeed in women in mathematics. Irene Fonseca such a male-dominated field. Undergraduate Accomplishments

Arun Kannan Becomes First Graduate of the algebras and superalgebras at the level of second year PhD Distinguished Major Program in Mathematics students. Arun successfully defended his thesis on April 4, By Andrei Rapinchuk 2018 and was presented with the DMP Completion Certificate at the Math majors dinner. In his 4th year, Arun will pursue a The 2017-18 academic year saw the Master’s Degree in mathematics. department roll out the revamped Distinguished Major Program (DMP). Sebastian Haney Awarded Goldwater The program provides an opportunity for Scholarship math majors, typically during their 4th Mathematics major Sebastian Haney, year, to work on a research project under currently in his third year, was the one of the supervision of a faculty member. The about 20 students in the nation selected to findings are then organized in the receive the 2018 Goldwater Scholarship. Distinguished Major Thesis and presented at a public defense. The Goldwater Foundation awards the The first graduate of the program was Arun Kannan who scholarships, which Congress established wrote his thesis, entitled Characters of Projective Modules in in 1986 to perennially honor the lifetime the BGG category O for General Linear Lie Superalgebras, work of Senator Barry Goldwater, to under the supervision of Professor Weiqiang Wang during his college sophomores and juniors who 3rd year. While working on the thesis, Arun had developed the “intend to pursue research careers in the understanding of representation theory of semisimple Lie natural sciences, mathematics, and engineering.”

Gordon E. Keller Mathematics Majors Dinner E. J. McShane Prize in Mathematics Speaker: Angus Mitchell April 2018 The 2018 Gordon E. Keller Mathematics Majors The 2018 E. J. McShane Prize in Mathematics Dinner, supported by a generous gift by Doug was given to Stephen Davis and Arun Kannan and Laurel Costa, took place last Spring. This for their achievements in mathematics. year featured Angus Mitchell as our guest speaker, who lectured about data analytics. Angus graduated from UVA in 2013 with a 2018 E.J. McShane Prize winners degree in Financial Mathematics, as well as an Edwin E. Floyd Prize in Mathematics interdisciplinary degree in Computer Science. April 2018 He has had a dynamic career in the intervening years, including work with the NBA . The 2018 Edwin E. Floyd Prize in Mathematics was awarded to Sebastian Haney, Benjamin Keigwin, Yichen Ma, and Ethan Zell. The prize is 2018 Floyd Prize Winners awarded to second- or third-year students who show exceptional promise in mathematics. William Lowell Three Majors elected into Phi Beta Kappa Putnam Mathematical Congratulations to Grace Dwyer, Kevin Lee, and Luca Scerbo! As the Competition oldest and most distinguished honor society in the country, Phi Beta Award Ira Herbst with 2018 Putnam Award Kappa offers membership to less than one percent of all undergraduates. winners April 2018 Many of the leading figures in American history and culture have begun their careers with election to the society, including seventeen presidents The 2018 William Lowell Putnam Mathematical of the United States. As a result, membership is a remarkable Competition Award was given to Emmett Dorlester, accomplishment, both for the student who achieves it and the faculty Zachary Baugher, and Luca Scerbo for their outstanding scores on the exam. and staff whose support and guidance has led to this milestone. SUMMER RESEARCH Bhattacharya and Axel Saenz Rodriguez. PROGRAM FOR The program began with a one-week series of lectures and exercises led by the graduate UNDERGRADUATES students and postdocs. At the end of the first

By AXEL SAENZ week, the students chose and were

selected to create This summer, the Math department was excited and pleased as it hosted, for the first two research groups focusing on time, a two-month summer Research topics in group Program for Undergraduates beginning in Program Participants and Organizers theory and the middle of May and ending in the middle The summer program was intended to bridge probability theory, of July. The program was organized by the the gap between textbook mathematics and respectively. From strong efforts and admirable vision of research-level mathematics showing the then on out, the Associate Professor Julie Bergner and students that the subject is still evolving groups would convene on a Cedric Harper Presents to Group Associate Professor Thomas Mark. The through an immersive first-hand research daily basis in the common areas of Kerchof participants included a total of seven experience. Moreover, there was a strong undergraduate students: Hall to carry out their research projects. This emphasis in developing the communication included independent readings, meetings Cedric Harper, skills of the students as it is often the case with graduate and postdoc advisors, frequent Trent Lucas, that the seemingly obtuse and technical presentations on the students’ progress, and Fernanda language of research-level mathematics weekly talks related to the research projects Yepez-Lopez, prevents beginners to express their ideas presented by faculty, postdocs, and graduate and Ethan Zell clearly. To this effect, the students were students. Throughout the summer, both the from the introduced to selected research problems in students and advisors were delighted by the experience as advisor Prasit Bhattacharya University of mathematics apt to their diverse academic would comment that he was “... impressed by Virginia; Eric backgrounds and were asked to tackle these Keener from the level of depth and understanding the problems through attentive advising of UVa students were able to attain in one James Mad- Fernanda Yepez=Lopez Presents to Group math graduate students - Rostislav summer ...” and participant Ethan Zell would ison University; and Connor Mallin from the Akhmechet, Zachary Gates, Andrew Kobin, also remark that he “... enjoyed the University of Alabama. Mark Schrecengost, and Richard camaraderie of the [summer program] and

Vrandenburgh- and postdocs - Prasit felt very productive.”

Reaching Out: Math Circles UVA Mathematics Professor, Graduate Students Introduce New Program to Inspire Talented, Young Mathematicians This article is reprinted with permission from pairs at their tables, dueling over graph Lorenzo Perez, the Senior Writer for the Dean’s It was only when Professor Slava Krushkal paper as they played extra rounds of the Office of the College and Graduate School of Arts & Sciences. The photos are the work of called for a short break that the 14 Shannon switching game of strategy Molly Angevine, A&S Communications assembled students reverted back to introduced earlier by Krushkal, a Coordinator, and have been reprinted here with elementary-school form. A few remained in mathematics professor in UVA’s College and her permission. Graduate School of Arts & Sciences. The talented mathematicians sat hunched over their calculations as they The rest gravitated to the worked through a series of problems wheelchair ramp at the far corner on an unseasonably warm Sunday of the room, giggling as they took afternoon last December. Sunlight turns hanging over the railings now streamed through the windows of the serving as their own personal University of Virginia’s Charles L. jungle gym. “Graduate students will Brown Science & Engineering Library, just sit down and work for hours but no one, not even the small number on a problem, but I’ve learned that cruncher wearing yellow soccer socks, with kids, you have to entertain shin guards and cleats, directed a them and take breaks,” Krushkal wistful gaze outdoors as they wrestled says. with a triangular array of binomial

coefficients known as Pascal’s Math professor Slava Krushkal with 4th- and 5th-grade

Triangle. Continued on Page 10 — Math Circle, continued applications of math to real things. Some of with us after we told them what the solution A different approach them are fun mathematical games that was,” Reeks said. “Even if they were wrong, Math-enrichment programs for interested feature deep mathematical principles what really matters is that they had really young students are no longer uncommon in underneath.” taken ownership of the solution and the the United States. For the new Math Circle problem. One of the great things this Earlier in the fall, Krushkal, Islambouli and program that Krushkal launched last fall for program does is it exposes kids to different Reeks introduced the students to “Hex,” a 15 local 4th- and 5th-graders nominated by perspectives on what math is and how they strategic game devised independently in the their schools, he looked for inspiration in his can use quantitative reasoning in their lives. 1940s by two mathematicians, Piet Hein and own educational experience growing up in And I think that’s helpful in heading off this John Nash. On another Sunday, Krushkal Russia. As students achieved fluency in symptom where people say, ‘Oh I’m bad at dipped the frame of a triangular pyramid, different mathematical concepts, the math,’ or ‘I just don’t like math’ and close built with sticks, into a soap solution. After mathematics curriculum there stressed the themselves off to that forever.” he pulled the tetrahedron-shaped frame out importance of students honing their of the solution, the bubble created within the The UVA Math Circle took a break during the creativity as they think their way through frame came together at a single point smack spring semester and was revived for the fall. increasingly difficult logic problems. The in the middle of the open frame. That led to a Parents of the program’s initial class of first Math Circles in the United States were discussion explaining how bubbles seek students said their children are eager to organized by the Mathematical Sciences stability by minimizing their surface area. continue in the Math Circle next school year. Research Institute in Berkeley, California. Soon, students were crafting other Today, there are more than 200 Math Circles Michael Garcia said that the Math Circle polyhedra out of sticks to make different around the country. program provided his son, a 5th-grade bubbles. With the assistance of Gabriel Islambouli and student at Walker Elementary, an “The bubbles are beautiful, and the students Michael Reeks, two Ph.D. students in the opportunity to meet other students his age are saying, ‘Wow!’, and then we discuss the Department of Mathematics, Krushkal who share his interest in learning math. mathematical principles underlying the organized a semester-long schedule of “He was always eager to go and to share experiment as we explain how the soap Sunday afternoon Math Circle sessions. what he had learned,” Garcia said. “I bubbles try to minimize area as they achieve Setting up the program, he received some appreciated that he was given the ultimate shape,” Krushkal said. guidance from the Curry School of exposure to university faculty and Education, as well as from his students, introducing the idea that faculty colleague and former learning math is a long-term Department of Mathematics endeavor. The hands-on nature of chair, Craig Huneke. the class really captured my son’s

“We have many first-rate attention.” mathematicians at UVA, and the Michele Paige Claibourn’s daughter establishment of Math Circles Fred (short for Winifred) came allows us to use this talent to home from Math Circle eager to help K-12 students in our area,” challenge her parents to play the Huneke said. “It is enormously strategic math games she learned empowering for children to in the Brown Science & think actively about the solution of Islambouli said it was important for them to Engineering Library. mathematical problems, and to develop the present the Math Circle students with “Maybe it’s not the primary intent of the solution themselves. No matter what the interesting problems that not only challenge program, but one of the ways it’s really future holds for the children who go through them, but also reward them for pursuing helped Fred is the discovery of how fun it Math Circles, the lessons they learn in prob- creative solutions. was to be in a room full of other students lem-solving and self-reliance will be invalua- “At first, of course, they were a little shy, he who also were really excited about math,” ble for them.” said. There’s a lot of ego type stuff tied to Claibourn said. “That shared enthusiasm was The goal of the program, Krushkal said, is to math in school, so maybe they were afraid to new for her in some ways, and I think that as stoke the curiosity of young students who be seen as dumb. But pretty soon, they much as anything helped really reinforce to have displayed an early aptitude for realized, ‘Oh, we’re just playing games.’ Once her that, ‘This is cool, and here are some mathematics, while steering away from the you rephrase it, and they realized they other people my age who also think this is rote memorization that may accompany weren’t being graded on their performance, cool.’” their traditional instruction. it’s no longer ‘You versus your grade.’ It’s all The Math Circle program continued in Fall 2018. of us trying to understand a problem “We are exposing them to logical problems, This year the program, taught by Slava Krushkal topology and other concepts that they may together.” with the help of graduate students Peter Johnson and Rostislav Akhmechet, is geared towards 5-th never see in school,” Krushkal said. “Some of “It’s really great to see some of the students and 6-th grade students from Charlottesville the things we show them are practical really get into a problem and start arguing area schools. Recent PhDs

Mariano Veronica Michael Zachary Echeverria Shalotenko Reeks Gates Moon Duchin Speaks about Mathematics and Gerrymandering

By Sara Maloni event was very well attended. I think for all the courts step in? Recently, some the participants from the Math Department interventions from mathematics and On March 21-22-23, 2018, Moon it was exciting to see such interesting and computing have sprung on the redistricting Duchin visited us, as the last speaker of the important applications to problems we scene, and they seem to hold a lot of series "Math &...". Moon Duchin is an study in our research. On Friday, Moon promise. For example, at the beginning of associate professor of Mathematics, a senior joined Quantitative Collaborative and gave a the year the Pennsylvania Governor Tom fellow in the Jonathan M. Tisch College of talk titled "Data-Driven Approaches to Wolf asked Moon to aid him in coming up Civic Life, and the director of the Program in Identifying a Gerrymander." with nonpartisan Congressional district Science, Technology, and Society at Tufts maps. Moon surveyed some geometric, University. Her pure math work is in statistical, and algorithmic approaches geometry, topology, groups, and to identifying and addressing dynamics, and she is currently gerrymandering that have gotten collaborating with civil rights traction in Wisconsin, North Carolina, organizers, coders, political scientists, and Pennsylvania. In particular, she lawyers, geographers, and explained how she used algorithmic philosophers on a large-scale project to sampling methods to explore the space detect and address gerrymandering. of possible districting plans. On Thursday she gave a public talk This visit was made possible by the titled "Mathematics of generous help from the Arts & Science Gerrymandering: Geometry, Diversity and Inclusion Grant, Algorithms, and (Crimes Against) the Department of Mathematics, Democracy". After the talk, Moon was joined Department of Politics, Frank Batten School on stage by Brian Cannon In her talk Moon pointed out that the power of Leadership and Public Policy, (from OneVirginia2021) and Sally Hudson to draw boundary lines is often the power to OneVirginia2021, and Quantitative (from Frank Batten School of Leadership control election outcomes, and hence the Collaborative. and Public Policy) who moderated the key question she wants to study is: how discussion between Moon and Brian. The much skew is too much, and when should

The Problem Corner

1. Find all differentiable functions f(x) on the real line such that [f ' (x)]2 = 4f(x) and f(-2) = f(2) = 1.

2. A microbe either splits into two perfect copies of itself or else disintegrates. If the probability of splitting is p, what is the probability that one microbe will produce an everlasting colony?

3. A game of solitaire is played as follows. After each play, according to the outcome, the player receives either a or b points, where a and b are positive integers and a > b. Their score What are you Doing? accumulates from play to play. It is noticed that there are exactly 35 non-attainable scores and that one of those is 58. Find a and b. We’d like to hear from you! Email: [email protected] 4. You are given 13 integers, all of them at least 1. They have the property that if we remove any one of them, you can divide the remaining 12 into News & Events: http://math.virginia.edu/allnews/ two groups of 6 each such that the sum of those 6 are equal. Prove all thirteen numbers are the same. Department of Mathematics University of Virginia P. O. Box 400137 Charlottesville, VA 22904-4137