Undergraduate Research News ISSUE#1 VOL#2 June 2015 Department News FACULTY Virginia Math NEWS Bulletin View from the Chair Kerchof Hall has been undergoing improvements over the last few years, with office and hallway renovations. The Mathematics Department had an This summer, the entire front entrance is undergoing a exciting 2014-15. Our new Institute major facelift and improvement. You may not recognize the of Mathematical Sciences began with building when it is done. This work will close our front en- series of talks by distinguished mathema- trance for most of the summer. ticians Alex Lubotzky in the Fall and Vaughan Jones in the Spring. We welc- In this newsletter, you will find articles about some omed Yen Do and Leonid Petrov to the of the research our undergraduates are doing, about the suc- the department this year as new Assistant Professors. We had an cesses of our faculty, and other news of the department. Tai active season of hiring. Jennifer Morse will be joining us begin- Melcher was promoted to Associate Professor since our last ning in Fall 2016 as a Full Professor. Thomas Koberda was hired newsletter; Andrei Rapinchuk became the new McConnell- last year, and joins us in Fall 2015. We were fortunate to hire Paul Bernard Professor of Mathematics and was elected a Fel- Bourdon, who will become our new Director of Lower Division low of the American Mathematical Society; and Andrew courses. He brings great experience, super teaching, new ideas and Obus won an All-University Teaching Award. Congratula- energy to our program. We also hired two postdocs: Aseel Farhat tions to all of them! will be a new Whyburn Instructor, and Lloyd West joins us as a Postdoctoral Research Fellow in Fall 2015. Mathematics and the sciences in general are threat- ened by large cuts of National Science Foundation funding Not only was 2014-15 a time of transitions in the Mathe- in both number and size for individual principal investiga- matics Department, but across Grounds as well. Over last summer, tors. These cuts affect the department, and we are all the the College of Arts and Sciences welcomed its new Dean, Ian Bau- more grateful for the gifts of people who contribute to our com. We are currently searching for a new Provost who will re- general gift fund and endowment to allow us to sustain and place John Simon. John Hawley continues to be our Associate improve our many activities. Thank you for your generosity. Dean overseeing science departments, including Mathematics. We also had losses. Last summer Tom Kriete retired, and Mike Hill is leaving to take a professorship at UCLA. We will miss both of them greatly. Luckily, Tom is finishing a book and is Craig Huneke in the department often. Sadly last Fall we had a devastating and Marvin Rosenblum Professor of Mathematics unexpected loss of our friend and long-time staff administrator, Julie Riddleberger. Many of us from the department were able to attend her memorial service. Although her expertise and institu- Supporting Us tional memory was unmatched, we are very glad we hired Kimber- ly Lamal to replace her. We are also excited to welcome Damar The Mathematics Department is grateful for the Watts, who is in Connie Abell's old position. generous support of its alumni and friends. The Department welcomes gifts annually to address The next few years will be a busy time for the department its most urgent needs, as well as to the endow- with many new hires and a restructuring of our undergraduate pro- ment which provides funding in perpetuity. To gram. Christian Gromoll spearheaded a year-long review of our undergraduate programs, culminating in a long report which de- learn about how you can make a difference by tails many improvements we will be implementing over the next supporting the Mathematics Department, please few years. contact Liz Blaine at [email protected] or (434) 924-6156. To make a gift online, please visit http://giving.virginia.edu/mathematics 1 Department Transitions New Faculty Joining the Department of Mathematics Yen Do Leonid Petrov Assistant Professor Assistant Professor Yen Do arrives at the University of Vir- A Mathematician whose work brings together ginia following a three–year appointment probability theory, representation theory and alge- at Yale University as a Gibbs Assistant braic combinatorics, Leonid Petrov seeks applications for his research Professor. At U.Va., Do will be focusing his research on to mathematical physics. harmonic analysis and its applications. Specifically, he is seeking to apply techniques from harmonic analysis to in- Part of his work revolves around the mathematical side of the vestigate research problems in mathematical physics and so-called Kardar-Parisi-Zhang equation, which originated in mathe- probabilistic analysis. matical physics in the 1980s. The equation represents the effort to describe random “nonlinear” growth phenomena, such as random pol- Do Received his PhD from UCLA (2010) and held ymers, polynuclear growth models, bacteria colonies and metastable an NSF Mathematical Sciences Institute postdoctoral ap- phases. Petrov and other mathematicians are investigating rigorous pointment at the Georgia Institute of Technology (2010- theories describing these phenomena employing specific tools based 2011). He completed a bachelors of engineering at the Uni- on exact combinatorial or algebraic identities. versity of technology, Sydney in Australia (2005). He re- ceived an NSF grant (2012-2015) to support his work on Petrov arrived at UVa following a postdoctoral appointment Fourier analysis and its application to completely integrable at Northeastern University. Prior to that, he was a research associate at systems. the Dobrushon Mathematics Laboratory in Moscow. Petrov received his PhD from the Institute for Information Transmissions Problems in This year, Do taught a course in calculus and a Moscow (2010) and completed his undergraduate studies in probabil- course in partial differential equations, while further devel- ity at Moscow State University (2007). oping his research program in analysis and probability. Petrov will be collaborating with our research groups in prob- ability, mathematical physics, and representation theory. This year he taught undergraduate courses on probability. Zezhou Zhang Whyburn Instructor Zezhou Zhang’s research interests include combinatorial and asymptotic aspects of group theory, nonassociative al- gebra and their interactions. Zhang is currently applying Lie and Jordan methods to enhance the understanding of certain groups. He received his PhD in Mathematics from the University of California, San Diego last year and completed his B.A. in Mathematics at Peking University (2009). Most recently, his article, “Nonassocaiative Algebra and Group with Property (t)” was published in the Inter- national Journal of Algebra and Computation. Zhang served as a teaching assistant for five years at UCSD and has delivered presentations on his work at USCD and at the Edwin Schrodinger International Institute for Mathematical Physics in Vienna, Austria. He looks forward to collaborating with an active research group at U.Va. 2 Department Transitions Professor Tai Melcher has been promoted from She directed the doctoral thesis of Daniel Dobbs Assistant to Associate Professor of Math- (PhD 2013, currently an assistant professor at ematics. Tai completed her PhD at UC San Die- Huntington University) and is presently super- go in 2004 under the guidance of Bruce Driver. vising Joshua Campbell in PhD research. She then held a postdoctoral posi- Tai has been involved in a variety of tion at UC Berkeley, before joining projects with UVa undergraduates, the faculty at UVa. including running REUs and organ- izing a “math and art” seminar as Tai’s research is in heat kernel anal- one of the 2013-14 UVa Mead Hon- ysis, which studies the behavior of ored Faculty. She is also active in diffusions in various geometric re- mathematics outreach at the local gimes. The interplay between parti- and international levels. Last cle or heat diffusion and the geome- year, she was one of two recipients try of the ambient space is well of the AWM Service Award, which studied and largely well understood recognizes individuals for helping in the context of “nice" geometries. to promote and support women in However, in certain (sometimes infinite- mathematics through exceptional volunteer ser- dimensional) physical models, the natural ge- vice to AWM. She also recently started the UVa ometry is degenerate in some sense, and much Math Ambassadors program, which involves less is known, particularly about graduate students in community mathematics the “smoothness” of diffusion in these spac- outreach, like visits to middle school class- es. Tai's work intersects parts of probability, rooms, hosting booth activities at local school analysis, and geometry, with a primary goal of science days, and coaching math competitions using probabilistic tools to understand the criti- like MATHCOUNTS. Tai also organized cal geometric quantities that allow smooth dif- Women in Probability, which provides net- fusion. working and mentoring opportunities for early career women researchers in probability. New Graduate Students Christopher Leonard Mark A. Schrecengost Mark Lewers Huy Dang Johnathon Upperman Matthew Feller Bogdan Krstic Liaosha Xu 3 New Institute of Mathematics The Institute of Mathematical Sciences is a new structure in Alex Lubotzky is the Maurice and Clara Weil the Department of Mathematics. Its mission is to promote professor of mathematics at the Hebrew Universi- mathematical research and education. One of the goals is to ty of Jerusalem and a professor at Yale Universi- provide additional opportunities for research collaboration ty. between our faculty and mathematicians from other universi- ties and thereby increase the visibility of our department as an Lubotzky has authored 4 books and more than institution of mathematical research. Another goal is to en- 130 research papers, many of which appeared in hance the role of the department as a center of mathematical such leading mathematical journals as the Annals education in the university and the community.